Journal articles: 'Risk-neutral valuation'

1

Costantini, Cristina, Marco Papi, and Fernanda D’Ippoliti. "Singular risk-neutral valuation equations." Finance and Stochastics 16, no. 2 (December 9, 2011): 249–74. http://dx.doi.org/10.1007/s00780-011-0166-8.

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van Bragt, David, Marc K. Francke, Stefan N. Singor, and Antoon Pelsser. "Risk-Neutral Valuation of Real Estate Derivatives." Journal of Derivatives 23, no. 1 (August 31, 2015): 89–110. http://dx.doi.org/10.3905/jod.2015.23.1.089.

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Ibrahim, Siti Nur Iqmal, John G. O’Hara, and Nick Constantinou. "Risk-neutral valuation of power barrier options." Applied Mathematics Letters 26, no. 6 (June 2013): 595–600. http://dx.doi.org/10.1016/j.aml.2012.12.016.

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Balbás, Alejandro, Raquel Balbás, and Silvia Mayoral. "Risk-neutral valuation with infinitely many trading dates." Mathematical and Computer Modelling 45, no. 11-12 (June 2007): 1308–18. http://dx.doi.org/10.1016/j.mcm.2006.11.002.

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Clement, E., C. Gourieroux, and A. Monfort. "Econometric specification of the risk neutral valuation model." Journal of Econometrics 94, no. 1-2 (January 2000): 117–43. http://dx.doi.org/10.1016/s0304-4076(99)00019-6.

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Bauer, Daniel, Rüdiger Kiesel, Alexander Kling, and Jochen Ruß. "Risk-neutral valuation of participating life insurance contracts." Insurance: Mathematics and Economics 39, no. 2 (October 2006): 171–83. http://dx.doi.org/10.1016/j.insmatheco.2006.02.003.

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STEIN, HARVEY J. "FIXING RISK NEUTRAL RISK MEASURES." International Journal of Theoretical and Applied Finance 19, no. 03 (April 21, 2016): 1650021. http://dx.doi.org/10.1142/s0219024916500217.

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In line with regulations and common risk management practice, the credit risk of a portfolio is managed via its potential future exposures (PFEs), expected exposures (EEs), and related measures, the expected positive exposure (EPE), effective expected exposure (EEE), and the effective expected positive exposure (EEPE). Notably, firms use these exposures to set economic and regulatory capital levels. Their values have a big impact on the capital that firms need to hold to manage their risks. Due to the growth of credit valuation adjustment (CVA) computations, and the similarity of CVA computations to exposure computations, firms find it expedient to compute these exposures under the risk neutral measure. Here, we show that exposures computed under the risk neutral measure are essentially arbitrary. They depend on the choice of numéraire, and can be manipulated by choosing a different numéraire. The numéraire can even be chosen in such a way as to pass backtests. Even when restricting attention to commonly used numéraires, exposures can vary by a factor of two or more. As such, it is critical that these calculations be carried out under the real world measure, not the risk neutral measure. To help rectify the situation, we show how to exploit measure changes to efficiently compute real world exposures in a risk neutral framework, even when there is no change of measure from the risk neutral measure to the real world measure. We also develop a canonical risk neutral measure that can be used as an alternative approach to risk calculations.

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Bauer, Daniel, Daniela Bergmann, and Rüdiger Kiesel. "On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View." ASTIN Bulletin 40, no. 1 (May 2010): 65–95. http://dx.doi.org/10.2143/ast.40.1.2049219.

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AbstractIn recent years, market-consistent valuation approaches have gained an increasing importance for insurance companies. This has triggered an increasing interest among practitioners and academics, and a number of specific studies on such valuation approaches have been published.In this paper, we present a generic model for the valuation of life insurance contracts and embedded options. Furthermore, we describe various numerical valuation approaches within our generic setup. We particularly focus on contracts containing early exercise features since these present (numerically) challenging valuation problems.Based on an example of participating life insurance contracts, we illustrate the different approaches and compare their efficiency in a simple and a generalized Black-Scholes setup, respectively. Moreover, we study the impact of the considered early exercise feature on our example contract and analyze the influence of model risk by additionally introducing an exponential Lévy model.

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Carmona, René, and Juri Hinz. "Risk-Neutral Models for Emission Allowance Prices and Option Valuation." Management Science 57, no. 8 (August 2011): 1453–68. http://dx.doi.org/10.1287/mnsc.1110.1358.

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HAREL, ARIE, GIORA HARPAZ, and JACK CLARK FRANCIS. "PRICING SECURITIES WITH EXCHANGE-IMPOSED PRICE LIMITS VIA RISK NEUTRAL VALUATION." International Journal of Theoretical and Applied Finance 10, no. 03 (May 2007): 399–406. http://dx.doi.org/10.1142/s021902490700424x.

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Asian and European financial markets impose daily price fluctuation limits on individual securities. In the US several futures exchanges are regulated by price fluctuation limits as well. The price limits in most exchanges are set daily, and they are usually based on a percentage change from the previous day's closing price. We show that the future cash flows of a security subject to price limit regulation resemble that of a distinctive contingent claim. Assuming that the security price follows a lognormal distribution, we use the risk-neutral valuation relation (RNVR) developed by [4] to derive the security valuation, in the presence of price fluctuation limits. The characteristics of the pricing formula are examined analytically and numerically.

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Beissner, Patrick. "Coherent-Price Systems and Uncertainty-Neutral Valuation." Risks 7, no. 3 (September 17, 2019): 98. http://dx.doi.org/10.3390/risks7030098.

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This paper considers fundamental questions of arbitrage pricing that arises when the uncertainty model incorporates ambiguity about risk. This additional ambiguity motivates a new principle of risk- and ambiguity-neutral valuation as an extension of the paper by Ross (1976) (Ross, Stephen A. 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory 13: 341–60). In the spirit of Harrison and Kreps (1979) (Harrison, J. Michael, and David M. Kreps. 1979. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20: 381–408), the paper establishes a micro-economic foundation of viability in which ambiguity-neutrality imposes a fair-pricing principle via symmetric multiple prior martingales. The resulting equivalent symmetric martingale measure set exists if the uncertain volatility in asset prices is driven by an ambiguous Brownian motion.

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Câmara, Ana, António Câmara, Ivilina Popova, and Betty Jo Simkins. "FX risk-neutral valuation relationships for the SU jump-diffusion family." International Journal of Finance & Economics 16, no. 4 (October 21, 2010): 339–56. http://dx.doi.org/10.1002/ijfe.433.

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Franke, Guenter, James Huang, and Richard Stapleton. "Two-dimensional risk-neutral valuation relationships for the pricing of options." Review of Derivatives Research 9, no. 3 (November 2006): 213–37. http://dx.doi.org/10.1007/s11147-007-9009-3.

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Hürlimann, W. "On fair premium principles and pareto-optimal risk-neutral portfolio valuation." Insurance: Mathematics and Economics 17, no. 1 (August 1995): 66–67. http://dx.doi.org/10.1016/0167-6687(95)91063-r.

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15

Yu, Xisheng. "Risk-Neutrality of RND and Option Pricing within an Entropy Framework." Entropy 22, no. 8 (July 30, 2020): 836. http://dx.doi.org/10.3390/e22080836.

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This article constructs an entropy pricing framework by incorporating a set of informative risk-neutral moments (RNMs) extracted from the market-available options as constraints. Within the RNM-constrained entropic framework, a unique distribution close enough to the correct one is obtained, and its risk-neutrality is deeply verified based on simulations. Using this resultant risk-neutral distribution (RND), a sample of risk-neutral paths of the underlying price is generated and ultimately the European option’s prices are computed. The pricing performance and analysis in simulations demonstrate that this proposed valuation is comparable to the benchmarks and can produce fairly accurate prices for options.

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KOLBE, ANDREAS, and RUDI ZAGST. "A HYBRID-FORM MODEL FOR THE PREPAYMENT-RISK-NEUTRAL VALUATION OF MORTGAGE-BACKED SECURITIES." International Journal of Theoretical and Applied Finance 11, no. 06 (September 2008): 635–56. http://dx.doi.org/10.1142/s0219024908004968.

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In this paper we present a prepayment-risk-neutral valuation model for fixed-rate Mortgage-Backed Securities. Our model is based on intensity models as used in credit-risk modeling and extends existing models for individual mortgage contracts in a proportional hazard framework. The general economic environment is explicitly accounted for in the prepayment process by an additional factor which we fit to the quarterly GDP growth rate in the US. In our risk-neutral setting we account for both the fears of refinancing understatement and turnover overstatement which sometimes result in higher option-adjusted spreads (OAS) for premiums and discounts respectively. We apply our prepayment-risk-neutral pricing approach to a sample of generic 30yr GNMA MBS pass-throughs from 1996 to 2006. Our empirical results indicate that the GDP growth factor adds explanatory power to the model.

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WU, LIXIN, and DAWEI ZHANG. "xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT." International Journal of Theoretical and Applied Finance 23, no. 01 (February 2020): 2050006. http://dx.doi.org/10.1142/s0219024920500065.

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xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

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Zhang, Wenjun, and Jin E. Zhang. "GARCH Option Pricing Models and the Variance Risk Premium." Journal of Risk and Financial Management 13, no. 3 (March 9, 2020): 51. http://dx.doi.org/10.3390/jrfm13030051.

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In this paper, we modify Duan’s (1995) local risk-neutral valuation relationship (mLRNVR) for the GARCH option-pricing models. In our mLRNVR, the conditional variances under two measures are designed to be different and the variance process is more persistent in the risk-neutral measure than in the physical one, so that one is able to capture the variance risk premium. Empirical estimation exercises show that the GARCH option-pricing models under our mLRNVR are able to price the SPX one-month variance swap rate, i.e., the CBOE Volatility Index (VIX) accurately. Our research suggests that one should use our mLRNVR when pricing options with GARCH models.

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TENG, LONG, MATTHIAS EHRHARDT, and MICHAEL GÜNTHER. "BILATERAL COUNTERPARTY RISK VALUATION OF CDS CONTRACTS WITH SIMULTANEOUS DEFAULTS." International Journal of Theoretical and Applied Finance 16, no. 07 (November 2013): 1350040. http://dx.doi.org/10.1142/s0219024913500404.

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We analyze the general risk-neutral valuation for counterparty risk embedded in a Credit Default Swap (CDS) contract by adapting the recent findings of Brigo and Capponi (2009) to allow for simultaneous defaults among the two parties and the underlying reference credit, while the counterparty risk is considered bilaterally. For the default intensities, we employ a Markov copula model allowing for the possibility of a simultaneous default. The dependence between defaults of three names in a CDS contract and the wrong-way risk will thus be represented by the possibility of simultaneous defaults. We investigate numerically the effect of considering simultaneous defaults on the counterparty risk valuation of a CDS contract. Finally, we study a CDS contract between Royal Dutch Shell and British Airways based on Lehman Brothers applying this methodology, illustrating the bilateral adjustments with the possibility of simultaneous defaults in concrete crisis situations.

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Ruan, Xinfeng, Wenli Zhu, Shuang Li, and Jiexiang Huang. "Equilibrium Asset and Option Pricing under Jump-Diffusion Model with Stochastic Volatility." Abstract and Applied Analysis 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/780542.

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We study the equity premium and option pricing under jump-diffusion model with stochastic volatility based on the model in Zhang et al. 2012. We obtain the pricing kernel which acts like the physical and risk-neutral densities and the moments in the economy. Moreover, the exact expression of option valuation is derived by the Fourier transformation method. We also discuss the relationship of central moments between the physical measure and the risk-neutral measure. Our numerical results show that our model is more realistic than the previous model.

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Eom, Young Ho, and Woon Wook Jang. "On the Theoretical Valuation of V-KOSPI 200 Futures." Journal of Derivatives and Quantitative Studies 25, no. 3 (August 31, 2017): 405–24. http://dx.doi.org/10.1108/jdqs-03-2017-b0004.

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Although the V-KOSPI 200 Futures markets opened in November 2014, trading has not been active until recently. One of the reasons for the illiquidity is due to the lack of a market consensus on the stochastic process model for the underlying volatility index (V-KOSPI 200). Given this fact, there is no theoretical pricing model that can be used for the determination of the benchmark price for the V-KOSPI 200 Futures. In this paper, we use the generalized method of moments method to search for a model that fits well with the time series of V-KOSPI 200 under the historical measure. In addition, we compare the performance of each model for the pricing of the V-KOSPI 200 Futures under the risk neutral measure. In the empirical analysis, we find that the CEV (constant elasticity of variance) parameter with the value about 1.5 is needed to price both the underlying V-KOSPI 200 process (under the physical measure) and the V-KOSPI 200 Futures (under the risk neutral measure). We also find that the mean reversion property is necessary to explain the dynamics of V-KOSPI 200.

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Feltham, Gerald A., and James A. Ohlson. "Residual Earnings Valuation With Risk and Stochastic Interest Rates." Accounting Review 74, no. 2 (April 1, 1999): 165–83. http://dx.doi.org/10.2308/accr.1999.74.2.165.

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This paper provides a general version of the accounting-based valuation model that equates the market value of a firm's equity to book value plus the present value of expected abnormal earnings. Prior theoretical work (e.g., Ohlson 1995; Feltham and Ohlson 1995, 1996) assumes investors are risk neutral and interest rates are nonstochastic and flat. Our more general analysis rests on only two assumptions: no arbitrage in financial markets and clean surplus accounting. These assumptions imply a risk-adjusted formula for the present value of expected abnormal earnings. The risk adjustments consist of certainty-equivalent reductions of expected abnormal earnings. A key issue deals with the capital charge component of abnormal earnings. It is measured by applying the (uncertain) riskless spot interest rate to start-of-period book value. Risks do not affect the rate used in the capital charge, and accounting policies do not affect the formula's constructs. An application of the general formula shows how the classic risk-adjusted expected cash flows model derives as a special case.

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Tsai, Jeffrey T., and Larry Y. Tzeng. "THE PRICING OF MORTALITY-LINKED CONTINGENT CLAIMS: AN EQUILIBRIUM APPROACH." ASTIN Bulletin 43, no. 2 (May 2013): 97–121. http://dx.doi.org/10.1017/asb.2013.3.

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AbstractThis study introduces an equilibrium approach to price mortality-linked securities in a discrete time economy, assuming that the mortality rate has a transformed normal distribution. This pricing method complements current studies on the valuation of mortality-linked securities, which only have discrete trading opportunities and insufficient market trading data. Like the Wang transform, the valuation relationship is still risk-neutral (preference-free) and the mortality-linked security is priced as the expected value of its terminal payoff, discounted by the risk-free rate. This study provides an example of pricing the Swiss Re mortality bond issued in 2003 and obtains an approximated closed-form solution.

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Deelstra, Griselda, Pierre Devolder, Kossi Gnameho, and Peter Hieber. "VALUATION OF HYBRID FINANCIAL AND ACTUARIAL PRODUCTS IN LIFE INSURANCE BY A NOVEL THREE-STEP METHOD." ASTIN Bulletin 50, no. 3 (August 14, 2020): 709–42. http://dx.doi.org/10.1017/asb.2020.25.

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AbstractFinancial products are priced using risk-neutral expectations justified by hedging portfolios that (as accurate as possible) match the product’s payoff. In insurance, premium calculations are based on a real-world best-estimate value plus a risk premium. The insurance risk premium is typically reduced by pooling of (in the best case) independent contracts. As hybrid life insurance contracts depend on both financial and insurance risks, their valuation requires a hybrid valuation principle that combines the two concepts of financial and actuarial valuation. The aim of this paper is to present a novel three-step projection algorithm to valuate hybrid contracts by decomposing their payoff in three parts: a financial, hedgeable part, a diversifiable actuarial part, and a residual part that is neither hedgeable nor diversifiable. The first two parts of the resulting premium are directly linked to their corresponding hedging and diversification strategies, respectively. The method allows for a separate treatment of unsystematic, diversifiable mortality risk and systematic, aggregate mortality risk related to, for example, epidemics or population-wide improvements in life expectancy. We illustrate our method in the case of CAT bonds and a pure endowment insurance contract with profit and compare the three-step method to alternative valuation operators suggested in the literature.

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KAO, LIE-JANE. "LOCALLY RISK-NEUTRAL VALUATION OF OPTIONS IN GARCH MODELS BASED ON VARIANCE-GAMMA PROCESS." International Journal of Theoretical and Applied Finance 15, no. 02 (March 2012): 1250015. http://dx.doi.org/10.1142/s021902491250015x.

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This study develops a GARCH-type model, i.e., the variance-gamma GARCH (VG GARCH) model, based on the two major strands of option pricing literature. The first strand of the literature uses the variance-gamma process, a time-changed Brownian motion, to model the underlying asset price process such that the possible skewness and excess kurtosis on the distributions of asset returns are considered. The second strand of the literature considers the propagation of the previously arrived news by including the feedback and leverage effects on price movement volatility in a GARCH framework. The proposed VG GARCH model is shown to obey a locally risk-neutral valuation relationship (LRNVR) under the sufficient conditions postulated by Duan (1995). This new model provides a unified framework for estimating the historical and risk-neutral distributions, and thus facilitates option pricing calibration using historical underlying asset prices. An empirical study is performed comparing the proposed VG GARCH model with four competing pricing models: benchmark Black–Scholes, ad hoc Black–Scholes, normal NGARCH, and stochastic volatility VG. The performance of the VG GARCH model versus these four competing models is then demonstrated.

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Zaglauer, Katharina, and Daniel Bauer. "Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment." Insurance: Mathematics and Economics 43, no. 1 (August 2008): 29–40. http://dx.doi.org/10.1016/j.insmatheco.2007.09.003.

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Sureth, Caren. "Partially Irreversible Investment Decisions and Taxation under Uncertainty: A Real Option Approach." German Economic Review 3, no. 2 (May 1, 2002): 185–221. http://dx.doi.org/10.1111/1468-0475.00057.

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AbstractThe paper applies contingent claims analysis in a real option investment model in order to investigate taxation's influence on investor's decisions under uncertainty. The results show the distortion from realistic-type tax systems, allow to identify a tax-induced paradox in option valuation for specific settings and acknowledge the property of investment neutrality of well-known `ideal' tax systems in the context of different degrees of irreversibility. Furthermore, it is clarified that the idea of risk-neutral valuation cannot be adopted by the real option approach in general.

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Bielecki, Tomasz R., Stéphane Crépey, Monique Jeanblanc, and Marek Rutkowski. "Defaultable Game Options in a Hazard Process Model." Journal of Applied Mathematics and Stochastic Analysis 2009 (July 21, 2009): 1–33. http://dx.doi.org/10.1155/2009/695798.

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The valuation and hedging of defaultable game options is studied in a hazard process model of credit risk. A convenient pricing formula with respect to a reference filteration is derived. A connection of arbitrage prices with a suitable notion of hedging is obtained. The main result shows that the arbitrage prices are the minimal superhedging prices with sigma martingale cost under a risk neutral measure.

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Han, Miao, Xuefeng Song, Huawei Niu, and Shengwu Zhou. "Pricing Vulnerable Options with Market Prices of Common Jump Risks under Regime-Switching Models." Discrete Dynamics in Nature and Society 2018 (2018): 1–15. http://dx.doi.org/10.1155/2018/8545841.

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This paper investigates the valuation of vulnerable European options considering the market prices of common systematic jump risks under regime-switching jump-diffusion models. The way of regime-switching Esscher transform is adopted to identify an equivalent martingale measure for pricing vulnerable European options. Explicit analytical pricing formulae for vulnerable European options are derived by risk-neutral pricing theory. For comparison, the other two cases are also considered separately. The first case considers all jump risks as unsystematic risks while the second one assumes all jumps risks to be systematic risks. Numerical examples for the valuation of vulnerable European options are provided to illustrate our results and indicate the influence of the market prices of jump risks on the valuation of vulnerable European options.

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Rakic, Biljana, and Tamara Radjenovic. "Real options methodology in public-private partnership projects valuation." Ekonomski anali 59, no. 200 (2014): 91–113. http://dx.doi.org/10.2298/eka1400091r.

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PPP offers numerous benefits to both public and private partners in delivery of infrastructure projects. However this partnership also involves great risks which have to be adequately managed and mitigated. Private partners are especially sensitive to revenue risk, since they are mostly interested in the financial viability of the project. Thus they often expect public partners to provide some kind of risk-sharing mechanism in the form of Minimum Revenue Guarantees or abandonment options. The objective of this paper is to investigate whether the real option of abandoning the project increases its value. Therefore the binominal option pricing model and risk-neutral probability approach have been implemented to price the European and American abandonment options for the Build-Operate-Transfer (BOT) toll road investment. The obtained results suggest that the project value with the American abandonment option is greater than with the European abandonment option, hence implying that American options offer greater flexibility and are more valuable for private partners.

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LAU, KA WO, and YUE KUEN KWOK. "VALUATION OF EMPLOYEE RELOAD OPTIONS USING UTILITY MAXIMIZATION APPROACH." International Journal of Theoretical and Applied Finance 08, no. 05 (August 2005): 659–74. http://dx.doi.org/10.1142/s0219024905003189.

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The reload provision in an employee stock option is an option enhancement that allows the employee to pay the strike upon exercising the stock option using his owned stocks and to receive new "reload" stock options. The usual Black–Scholes risk neutral valuation approach may not be appropriate to be adopted as the pricing vehicle for employee stock options, due to the non-transferability of the ownership of the options and the restriction on short selling of the firm's stocks as hedging strategy. In this paper, we present a general utility maximization framework to price non-tradeable employee stock options with reload provision. The risk aversion of the employee enters into the pricing model through the choice of the utility function. We examine how the value of the reload option to the employee is affected by the number of reloads outstanding, the risk aversion level and personal wealth. In particular, we explore how the reload provision may lower the difference between the cost of granting the option and the private option value and improve the compensation incentive of the option award.

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LEUNG, TIM, and PENG LIU. "RISK PREMIA AND OPTIMAL LIQUIDATION OF CREDIT DERIVATIVES." International Journal of Theoretical and Applied Finance 15, no. 08 (December 2012): 1250059. http://dx.doi.org/10.1142/s0219024912500598.

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This paper studies the optimal timing to liquidate credit derivatives in a general intensity-based credit risk model under stochastic interest rate. We incorporate the potential price discrepancy between the market and investors, which is characterized by risk-neutral valuation under different default risk premia specifications. We quantify the value of optimally timing to sell through the concept of delayed liquidation premium, and analyze the associated probabilistic representation and variational inequality. We illustrate the optimal liquidation policy for both single-name and multi-name credit derivatives. Our model is extended to study the sequential buying and selling problem with and without short-sale constraint.

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Cairns, Andrew J. G., David Blake, and Kevin Dowd. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk." ASTIN Bulletin 36, no. 01 (May 2006): 79–120. http://dx.doi.org/10.2143/ast.36.1.2014145.

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It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

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Cairns, Andrew J. G., David Blake, and Kevin Dowd. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk." ASTIN Bulletin 36, no. 1 (May 2006): 79–120. http://dx.doi.org/10.1017/s0515036100014410.

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It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

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Kim, Joseph H. T., and Johnny S. H. Li. "Risk-neutral valuation of the non-recourse protection in reverse mortgages: A case study for Korea." Emerging Markets Review 30 (March 2017): 133–54. http://dx.doi.org/10.1016/j.ememar.2016.10.002.

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Wu, Lixin, and Chonhong Li. "FVA and CVA under margining." Studies in Economics and Finance 32, no. 3 (August 3, 2015): 298–321. http://dx.doi.org/10.1108/sef-08-2014-0162.

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Purpose – The purpose of this paper is to provide a framework of replication pricing of derivatives and identify funding valuation adjustment (FVA) and credit valuation adjustments (CVA) as price components. Design/methodology/approach – The authors propose the notion of bilateral replication pricing. In the absence of funding cost, it reduces to unilateral replication pricing. The absence of funding costs, it introduces bid–ask spreads. Findings – The valuation of CVA can be separated from that of FVA, so-called split up. There may be interdependence between FVA and the derivatives value, which then requires a recursive procedure for their numerical solution. Research limitations/implications – The authors have assume deterministic interest rates, constant CDS rates and loss rates for the CDS. The authors have also not dealt with re-hypothecation risks. Practical implications – The results of this paper allow user to identify CVA and FVA, and mark to market their derivatives trades according to the recent market standards. Originality/value – For the first time, a line between the risk-neutral pricing measure and the funding risk premiums is drawn. Also, the notion of bilateral replication pricing extends the unilateral replication pricing.

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RUTKOWSKI, MAREK, and ANTHONY ARMSTRONG. "VALUATION OF CREDIT DEFAULT SWAPTIONS AND CREDIT DEFAULT INDEX SWAPTIONS." International Journal of Theoretical and Applied Finance 12, no. 07 (November 2009): 1027–53. http://dx.doi.org/10.1142/s0219024909005579.

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The paper provides simple and rigorous, albeit fairly general, derivations of valuation formulae for credit default swaptions and credit default index swaptions. Results of this work cover as special cases the pricing formulae derived previously by Jamshidian [Finance and Stochastics8 (2004) 343–371], Pedersen [Quantitative Credit Research (2003)], Brigo and Morini (2005), and Morini and Brigo (2007). Most results presented in this work are completely independent of a particular convention regarding the specification of the fee and protection legs and thus they can also be used for valuation of other credit derivatives that exhibit similar features (for instance, options on CDO tranches). The main tools are a judicious choice of the reference filtration and a suitable specification of the risk-neutral dynamics for the pre-default (loss-adjusted) fair market spread.

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FRAHM, GABRIEL. "PRICING AND VALUATION UNDER THE REAL-WORLD MEASURE." International Journal of Theoretical and Applied Finance 19, no. 01 (February 2016): 1650006. http://dx.doi.org/10.1142/s0219024916500060.

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In general it is not clear which kind of information is supposed to be used for calculating the fair value of a contingent claim. Even if the information is specified, it is not guaranteed that the fair value is uniquely determined by the given information. A further problem is that asset prices are typically expressed in terms of a risk-neutral measure. This makes it difficult to transfer the fundamental results of financial mathematics to econometrics. I show that the aforementioned problems evaporate if the financial market is complete and sensitive. In this case, after an appropriate choice of the numéraire, the discounted price processes turn out to be uniformly integrable martingales under the real-world measure. This leads to a Law of One Price and a simple real-world valuation formula in a model-independent framework where the number of assets as well as the lifetime of the market can be finite or infinite.

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Lindström, Erik. "Implications of Parameter Uncertainty on Option Prices." Advances in Decision Sciences 2010 (May 5, 2010): 1–15. http://dx.doi.org/10.1155/2010/598103.

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Financial markets are complex processes where investors interact to set prices. We present a framework for option valuation under imperfect information, taking risk neutral parameter uncertainty into account. The framework is a direct generalization of the existing valuation methodology. Many investors base their decisions on mathematical models that have been calibrated to market prices. We argue that the calibration process introduces a source of uncertainty that needs to be taken into account. The models and parameters used may differ to such extent that one investor may find an option underpriced; whereas another investor may find the very same option overpriced. This problem is not taken into account by any of the standard models. The paper is concluded by presenting simulations and an empirical study on FX options, where we demonstrate improved predictive performance (in sample and out of sample) using this framework.

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Esparcia, Carlos, Elena Ibañez, and Francisco Jareño. "Volatility Timing: Pricing Barrier Options on DAX XETRA Index." Mathematics 8, no. 5 (May 4, 2020): 722. http://dx.doi.org/10.3390/math8050722.

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This paper analyses the impact of different volatility structures on a range of traditional option pricing models for the valuation of call down and out style barrier options. The construction of a Risk-Neutral Probability Term Structure (RNPTS) is one of the main contributions of this research, which changes in parallel with regard to the Volatility Term Structure (VTS) in the main and traditional methods of option pricing. As a complementary study, we propose the valuation of options by assuming a constant or historical volatility. The study implements the GARCH (1,1) model with regard to the continuously compound returns of the DAX XETRA Index traded at daily frequency. Current methodology allows for obtaining accuracy forecasts of the realized market barrier option premiums. The paper highlights not only the importance of selecting the right model for option pricing, but also fitting the most accurate volatility structure.

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JARROW, ROBERT. "THE THIRD FUNDAMENTAL THEOREM OF ASSET PRICING." Annals of Financial Economics 07, no. 02 (December 2012): 1250007. http://dx.doi.org/10.1142/s2010495212500078.

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The importance of market efficiency to derivative pricing is not well understood. The purpose of this paper is to explain this connection using the third fundamental theorem of asset pricing. The third fundamental theorem of asset pricing characterizes the conditions under which an equivalent martingale probability measure exists in an economy. Noting that the existence of an equivalent martingale probability measure is both necessary and sufficient for the market being informationally efficient, we prove that in a complete market, the market being efficient is both necessary and sufficient for the validity of the risk neutral valuation methodology.

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Dario, Alan De Genaro. "Apreçamento de Ativos Referenciados em Volatilidade." Brazilian Review of Finance 4, no. 2 (January 1, 2006): 203. http://dx.doi.org/10.12660/rbfin.v4n2.2006.1162.

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Volatility swaps are contingent claims on future realized volatility. Variance swaps are similar instruments on future realized variance, the square of future realized volatility. Unlike a plain vanilla option, whose volatility exposure is contaminated by its asset price dependence, volatility and variance swaps provide a pure exposure to volatility alone. This article discusses the risk-neutral valuation of volatility and variance swaps based on the framework outlined in the Heston (1993) stochastic volatility model. Additionally, the Heston (1993) model is calibrated for foreign currency options traded at BMF and its parameters are used to price swaps on volatility and variance of the BRL / USD exchange rate.

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HIKSPOORS, SAMUEL, and SEBASTIAN JAIMUNGAL. "ENERGY SPOT PRICE MODELS AND SPREAD OPTIONS PRICING." International Journal of Theoretical and Applied Finance 10, no. 07 (November 2007): 1111–35. http://dx.doi.org/10.1142/s0219024907004573.

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In this article, we construct forward price curves and value a class of two asset exchange options for energy commodities. We model the spot prices using an affine two-factor mean-reverting process with and without jumps. Within this modeling framework, we obtain closed form results for the forward prices in terms of elementary functions. Through measure changes induced by the forward price process, we further obtain closed form pricing equations for spread options on the forward prices. For completeness, we address both an Actuarial and a risk-neutral approach to the valuation problem. Finally, we provide a calibration procedure and calibrate our model to the NYMEX Light Sweet Crude Oil spot and futures data, allowing us to extract the implied market prices of risk for this commodity.

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van der Heide, Arjen. "Model migration and rough edges: British actuaries and the ontologies of modelling." Social Studies of Science 50, no. 1 (December 6, 2019): 121–44. http://dx.doi.org/10.1177/0306312719893465.

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The existing literature on modelling provides two main ways of viewing model migration: a modular view, which seeks to decompose models in their constitutive elements, and thus provides a view on what it is that migrates; and a practice-based view, which focuses on modelling as an activity, and understands a model as intricately entangled with its context of use. This article brings together these two sensitivities by focusing on ontologies of modelling. The paper presents a case study of the appropriation of modern finance theory’s ‘no-arbitrage’ models by British actuaries – a process that gradually unfolded at around the turn of the century and led to significant friction within the UK’s insurance industry. We can distinguish two main modelling ontologies: a ‘risk-neutral ontology’, which underpins no-arbitrage models and holds that the value of financial instruments is determined by ‘arbitrage’; and, a ‘real-world ontology’, which assumes that the economic world consists of real probabilities that may be approximated through a combination of archival-statistical methods and expert judgment. The appropriation of the risk-neutral modelling ontology was made possible by the declining legitimacy of actuarial expertise as ‘financial stewards’ of life insurance companies. The risk-neutral modelling ontology provided an ‘objective’ alternative to the traditional actuarial models, which explicitly required actuaries to make ‘prudent’ judgments. Despite the fact that the no-arbitrage modelling was considered an ‘objective’ affair, the valuation models that insurers use today are strongly shaped by political compromises, a result of the ‘rough edges’ of models.

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EKSTRÖM, ERIK, and JOHAN TYSK. "DUPIRE'S EQUATION FOR BUBBLES." International Journal of Theoretical and Applied Finance 15, no. 06 (September 2012): 1250041. http://dx.doi.org/10.1142/s0219024912500410.

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We study Dupire's equation for local volatility models with bubbles, i.e. for models in which the discounted underlying asset follows a strict local martingale. If option prices are given by risk-neutral valuation, then the discounted option price process is a true martingale, and we show that the Dupire equation for call options contains extra terms compared to the usual equation. However, the Dupire equation for put options takes the usual form. Moreover, uniqueness of solutions to the Dupire equation is lost in general, and we show how to single out the option price among all possible solutions. The Dupire equation for models in which the discounted derivative price process is merely a local martingale is also studied.

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Bondi, Alessandro, Dragana Radojičić, and Thorsten Rheinländer. "Comparing Two Different Option Pricing Methods." Risks 8, no. 4 (October 19, 2020): 108. http://dx.doi.org/10.3390/risks8040108.

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Motivated by new financial markets where there is no canonical choice of a risk-neutral measure, we compared two different methods for pricing options: calibration with an entropic penalty term and valuation by the Esscher measure. The main aim of this paper is to contrast the outcomes of those two methods with real-traded call option prices in a liquid market like NASDAQ stock exchange, using data referring to the period 2019–2020. Although the Esscher measure method slightly underperforms the calibration method in terms of absolute values of the percentage difference between real and model prices, it could be the only feasible choice if there are not many liquidly traded derivatives in the market.

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Posedel Šimović, Petra, and Azra Tafro. "Pricing the Volatility Risk Premium with a Discrete Stochastic Volatility Model." Mathematics 9, no. 17 (August 25, 2021): 2038. http://dx.doi.org/10.3390/math9172038.

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Investors’ decisions on capital markets depend on their anticipation and preferences about risk, and volatility is one of the most common measures of risk. This paper proposes a method of estimating the market price of volatility risk by incorporating both conditional heteroscedasticity and nonlinear effects in market returns, while accounting for asymmetric shocks. We develop a model that allows dynamic risk premiums for the underlying asset and for the volatility of the asset under the physical measure. Specifically, a nonlinear in mean time series model combining the asymmetric autoregressive conditional heteroscedastic model with leverage (NGARCH) is adapted for modeling return dynamics. The local risk-neutral valuation relationship is used to model investors’ preferences of volatility risk. The transition probabilities governing the evolution of the price of the underlying asset are adjusted for investors’ attitude towards risk, presenting the asset returns as a function of the risk premium. Numerical studies on asset return data show the significance of market shocks and levels of asymmetry in pricing the volatility risk. Estimated premiums could be used in option pricing models, turning options markets into volatility trading markets, and in measuring reactions to market shocks.

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Behera, Prashanta kumar, and Dr Ramraj T. Nadar. "Dynamic Approach for Index Option Pricing Using Different Models." Journal of Global Economy 13, no. 2 (June 26, 2017): 105–20. http://dx.doi.org/10.1956/jge.v13i2.460.

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Option pricing is one of the exigent and elementary problems of computational finance. Our aims to determine the nifty index option price through different valuation technique.Â In this paper, we illustrate the techniques for pricing of options and extracting information from option prices. We also describe various ways in which this information has been used in a number of applications. When dealing with options, we inevitably encounter the Black-Scholes-Merton option pricing formula, which has revolutionized the way in which options are priced in modern time. Black and Scholes (1973) and Merton (1973) on pricing European style options assumes that stock price follows a geometric Brownian motion, which implies that the terminal stock price has a lognormal distribution. Through hedging arguments, BSM shows that the terminal stock price distribution needed for pricing option can be stated without reference to the preference parameter and to the growth rate of the stock. This is now known as the risk-neutral approach to option pricing. The terminal stock price distribution, for the purpose of pricing options, is now known as the state-price density or the risk-neutral density in contrast to the actual stock price distribution, which is sometimes referred to as the physical, objective, or historical distribution.

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Antonacci, Flavia, Cristina Costantini, and Marco Papi. "Short-Term Interest Rate Estimation by Filtering in a Model Linking Inflation, the Central Bank and Short-Term Interest Rates." Mathematics 9, no. 10 (May 20, 2021): 1152. http://dx.doi.org/10.3390/math9101152.

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We consider the model of Antonacci, Costantini, D’Ippoliti, Papi (arXiv:2010.05462 [q-fin.MF], 2020), which describes the joint evolution of inflation, the central bank interest rate, and the short-term interest rate. In the case when the diffusion coefficient does not depend on the central bank interest rate, we derive a semi-closed valuation formula for contingent derivatives, in particular for Zero Coupon Bonds (ZCBs). By using ZCB yields as observations, we implement the Kalman filter and obtain a dynamical estimate of the short-term interest rate. In turn, by this estimate, at each time step, we calibrate the model parameters under the risk-neutral measure and the coefficient of the risk premium. We compare the market values of German interest rate yields for several maturities with the corresponding values predicted by our model, from 2007 to 2015. The numerical results validate both our model and our numerical procedure.

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SHAO, DAN. "A NUMERICAL METHOD FOR PRICING AMERICAN-STYLE ASIAN OPTIONS UNDER GARCH MODEL." International Journal of Theoretical and Applied Finance 09, no. 08 (December 2006): 1323–50. http://dx.doi.org/10.1142/s0219024906003986.

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This article develops a numerical method to price American-style Asian option in the context of the generalized autoregressive conditional heteroscedasticity (GARCH) asset return process. The development is based on dynamic programming coupled with the replacement of the normally distributed variable with a binomial one and the whole procedure is under the locally risk-neutral valuation relationship (LRNVR). We investigate the computational and implementation issues of this method and compare them with those of a candidate procedure which involves piecewise-polynomial approximation of the value function. Complexity analysis and computational results suggest that our method is superior to the candidate one and the generated GARCH option prices are capable of reflecting the changes in the conditional volatility of underlying asset.

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Journal articles on the topic 'Risk-neutral valuation'

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