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Journal articles on the topic 'Stochastic volatility Monte carlo simulation'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

VAN DER STOEP, ANTHONIE W., LECH A. GRZELAK, and CORNELIS W. OOSTERLEE. "THE HESTON STOCHASTIC-LOCAL VOLATILITY MODEL: EFFICIENT MONTE CARLO SIMULATION." International Journal of Theoretical and Applied Finance 17, no. 07 (2014): 1450045. http://dx.doi.org/10.1142/s0219024914500459.

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In this paper we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a nonparametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by Dupire (1994) and Derman & Kani (1998). In particular, the additional local volatility component acts as a "compensator" that bridges the mismatch between the nonperfectly calibrated Heston model and the market quotes for European-type options. By means of numerical experiments we show that our scheme enab

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?imandl, Miroslav, and Tom�? Soukup. "Simulation Monte Carlo methods in extended stochastic volatility models." International Journal of Intelligent Systems in Accounting, Finance & Management 11, no. 2 (2002): 109–17. http://dx.doi.org/10.1002/isaf.215.

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Chalimatusadiah, Chalimatusadiah, Donny Citra Lesmana, and Retno Budiarti. "Penentuan Harga Opsi Dengan Volatilitas Stokastik Menggunakan Metode Monte Carlo." Jambura Journal of Mathematics 3, no. 1 (2021): 80–92. http://dx.doi.org/10.34312/jjom.v3i1.10137.

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ABSTRAKHal yang utama dalam perdagangan opsi adalah penentuan harga jual opsi yang optimal. Namun pada kenyataan sebenarnya fluktuasi harga aset yang terjadi di pasar menandakan bahwa volatilitas dari harga aset tidaklah konstan, hal ini menyebabkan investor mengalami kesulitan dalam menentukan harga opsi yang optimal. Artikel ini membahas tentang penentuan harga opsi tipe Eropa yang optimal dengan volatilitas stokastik menggunakan metode Monte Carlo dan pengaruh harga saham awal, harga strike, dan waktu jatuh tempo terhadap harga opsi Eropa. Adapun model volatilitas stokastik yang digunakan d

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Alghalith, Moawia, Christos Floros, and Konstantinos Gkillas. "Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility." Risks 8, no. 2 (2020): 35. http://dx.doi.org/10.3390/risks8020035.

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We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far simpler than the existing ones. Using intraday prices for the Standard & Poor’s 500 equity index, the estimates revealed strong evidence that both volatility and the volatility of volatility are stochastic. We also proceeded in a Monte Carlo simulation analysis and found that the estimates were reasona

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Raggi, Davide, and Silvano Bordignon. "Comparing stochastic volatility models through Monte Carlo simulations." Computational Statistics & Data Analysis 50, no. 7 (2006): 1678–99. http://dx.doi.org/10.1016/j.csda.2005.02.004.

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Cathcart, Mark J., Hsiao Yen Lok, Alexander J. McNeil, and Steven Morrison. "CALCULATING VARIABLE ANNUITY LIABILITY “GREEKS” USING MONTE CARLO SIMULATION." ASTIN Bulletin 45, no. 2 (2015): 239–66. http://dx.doi.org/10.1017/asb.2014.31.

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AbstractThe implementation of hedging strategies for variable annuity products requires the calculation of market risk sensitivities (or “Greeks”). The complex, path-dependent nature of these products means that these sensitivities are typically estimated by Monte Carlo methods. Standard market practice is to use a “bump and revalue” method in which sensitivities are approximated by finite differences. As well as requiring multiple valuations of the product, this approach is often unreliable for higher-order Greeks, such as gamma, and alternative pathwise (PW) and likelihood-ratio estimators s

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7

Fouque, Jean-Pierre, and Tracey Andrew Tullie. "Variance reduction for Monte Carlo simulation in a stochastic volatility environment." Quantitative Finance 2, no. 1 (2002): 24–30. http://dx.doi.org/10.1088/1469-7688/2/1/302.

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8

Albuquerque, Pedro Henrique Melo, Yaohao Peng, and Igor Ferreira Do Nascimento. "Stochastic volatility modelling in portfolio selection via sequential Monte Carlo simulation." International Journal of Portfolio Analysis and Management 2, no. 3 (2021): 249. http://dx.doi.org/10.1504/ijpam.2021.10038382.

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Nascimento, Igor Ferreira Do, Pedro Henrique Melo Albuquerque, and Yaohao Peng. "Stochastic volatility modelling in portfolio selection via sequential Monte Carlo simulation." International Journal of Portfolio Analysis and Management 2, no. 3 (2021): 249. http://dx.doi.org/10.1504/ijpam.2021.115633.

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Laurini, Márcio Poletti. "A Hybrid Data Cloning Maximum Likelihood Estimator for Stochastic Volatility Models." Journal of Time Series Econometrics 5, no. 2 (2013): 193–229. http://dx.doi.org/10.1515/jtse-2012-0025.

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Abstract: In this article, we analyze a maximum likelihood estimator using Data Cloning for Stochastic Volatility models. This estimator is constructed using a hybrid methodology based on Integrated Nested Laplace Approximations to calculate analytically the auxiliary Bayesian estimators with great accuracy and computational efficiency, without requiring the use of simulation methods such as Markov Chain Monte Carlo. We analyze the performance of this estimator compared to methods based on Monte Carlo simulations (Simulated Maximum Likelihood, MCMC Maximum Likelihood) and approximate maximum l

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11

Liang, Yijuan, and Xiuchuan Xu. "Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities." Sustainability 11, no. 3 (2019): 815. http://dx.doi.org/10.3390/su11030815.

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Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with stochastic volatilities. First, a conditional Monte Carlo (CMC) pricing formula is constructed to reduce the dimension and variance of the MC simulation. Then, an efficient martingale control variate (CV), based on the martingale representation theorem, is designed by selecting volatility parameters in the a

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Bonetti, Daniel, Dorival Leão, Alberto Ohashi, and Vinícius Siqueira. "A General Multidimensional Monte Carlo Approach for Dynamic Hedging under Stochastic Volatility." International Journal of Stochastic Analysis 2015 (February 8, 2015): 1–21. http://dx.doi.org/10.1155/2015/863165.

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We propose a feasible and constructive methodology which allows us to compute pure hedging strategies with respect to arbitrary square-integrable claims in incomplete markets. In contrast to previous works based on PDE and BSDE methods, the main merit of our approach is the flexibility of quadratic hedging in full generality without a priori smoothness assumptions on the payoff. In particular, the methodology can be applied to multidimensional quadratic hedging-type strategies for fully path-dependent options with stochastic volatility and discontinuous payoffs. In order to demonstrate that ou

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Sumei, Zhang, and Zhao Jieqiong. "Efficient Simulation for Pricing Barrier Options with Two-Factor Stochastic Volatility and Stochastic Interest Rate." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/3912036.

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This paper presents an extension of the double Heston stochastic volatility model by combining Hull-White stochastic interest rates. By the change of numeraire and quadratic exponential scheme, this paper develops a new simulation scheme for the extended model. By combining control variates and antithetic variates, this paper provides an efficient Monte Carlo simulation algorithm for pricing barrier options. Based on the differential evolution algorithm the extended model is calibrated to S&P 500 index options to obtain the model parameter values. Numerical results show that the proposed s

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14

Benth, F. E., and L. Vos. "Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets." Advances in Applied Probability 45, no. 02 (2013): 545–71. http://dx.doi.org/10.1017/s0001867800006431.

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Spot prices in energy markets exhibit special features, such as price spikes, mean reversion, stochastic volatility, inverse leverage effect, and dependencies between the commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. The second-order structure and stationarity of the model are analyzed in detail. A simulation method for Monte Carlo generation of price paths is introduced and a numerical example is presented.

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Benth, F. E., and L. Vos. "Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets." Advances in Applied Probability 45, no. 2 (2013): 545–71. http://dx.doi.org/10.1239/aap/1370870129.

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Spot prices in energy markets exhibit special features, such as price spikes, mean reversion, stochastic volatility, inverse leverage effect, and dependencies between the commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. The second-order structure and stationarity of the model are analyzed in detail. A simulation method for Monte Carlo generation of price paths is introduced and a numerical example is presented.

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Lay, Harold A., Zane Colgin, Viktor Reshniak, and Abdul Q. M. Khaliq. "On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters." Monte Carlo Methods and Applications 24, no. 4 (2018): 309–21. http://dx.doi.org/10.1515/mcma-2018-2025.

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Abstract We explore different methods of solving systems of stochastic differential equations by first implementing the Euler–Maruyama and Milstein methods with a Monte Carlo simulation on a CPU. The performance of the methods is significantly improved through the recently developed antithetic multilevel Monte Carlo estimator, which yields a computation complexity of {\mathcal{O}(\epsilon^{-2})} root-mean-square error and does so without the approximation of Lévy areas. Further improvements in performance are gained by moving the algorithms to a GPU - first on a single device and then on a mul

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Gao, Xuemei, Dongya Deng, and Yue Shan. "Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models." Discrete Dynamics in Nature and Society 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/165259.

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The aim of this paper is to extend the lattice method proposed by Ritchken and Trevor (1999) for pricing American options with one-dimensional stochastic volatility models to the two-dimensional cases with strangle payoff. This proposed method is compared with the least square Monte-Carlo method via numerical examples.

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18

Ewald, Christian-Oliver. "Local volatility in the Heston model: a Malliavin calculus approach." Journal of Applied Mathematics and Stochastic Analysis 2005, no. 3 (2005): 307–22. http://dx.doi.org/10.1155/jamsa.2005.307.

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We implement the Heston stochastic volatility model by using multidimensional Ornstein-Uhlenbeck processes and a special Girsanov transformation, and consider the Malliavin calculus of this model. We derive explicit formulas for the Malliavin derivatives of the Heston volatility and the log-price, and give a formula for the local volatility which is approachable by Monte-Carlo methods.

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Ma, Jun Mei, and Gui Ding Gu. "Efficient Monte Carlo Simulation for Pricing Variance Derivatives under Multi-Factor Stochastic Volatility Models." Applied Mechanics and Materials 411-414 (September 2013): 1089–94. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.1089.

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This paper studied the pricing of variance swap derivatives under the multi-factor stochastic volatility models by Monte Carlo simulation. Control variate technique was well used to reduce the variance of the simulation effectively. How to choose the high efficient control variate was also contained. Then the numerical results show the high efficiency of the speed up method. The pricing structure in the paper is also applicable for the valuation of other types of variance swaps and other financial derivatives under multi-factor models.

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20

SCHOUTENS, WIM, and STIJN SYMENS. "THE PRICING OF EXOTIC OPTIONS BY MONTE–CARLO SIMULATIONS IN A LÉVY MARKET WITH STOCHASTIC VOLATILITY." International Journal of Theoretical and Applied Finance 06, no. 08 (2003): 839–64. http://dx.doi.org/10.1142/s0219024903002249.

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Recently, stock price models based on Lévy processes with stochastic volatility were introduced. The resulting vanilla option prices can be calibrated almost perfectly to empirical prices. Under this model, we will price exotic options, like barrier, lookback and cliquet options, by Monte–Carlo simulation. The sampling of paths is based on a compound Poisson approximation of the Lévy process involved. The precise choice of the terms in the approximation is crucial and investigated in detail. In order to reduce the standard error of the Monte–Carlo simulation, we make use of the technique of co

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KOURITZIN, MICHAEL A. "EXPLICIT HESTON SOLUTIONS AND STOCHASTIC APPROXIMATION FOR PATH-DEPENDENT OPTION PRICING." International Journal of Theoretical and Applied Finance 21, no. 01 (2018): 1850006. http://dx.doi.org/10.1142/s0219024918500061.

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New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: (1) stochastic approximation replaces regression in the LSM algorithm; (2) explicit weak solutions to stochastic differential equations are developed and applied to Heston model simulation; and (3) importance sampling expands these explicit solutions. The approach complements Heston [(1993) A closed-form solutions for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies 6, 327

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22

Li, Pengshi, Wei Li, and Haidong Chen. "Importance Sampling for Monte Carlo Simulation to Evaluate Collar Options under Stochastic Volatility Model." E+M Ekonomie a Management 23, no. 2 (2020): 144–55. http://dx.doi.org/10.15240/tul/001/2020-2-010.

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23

Rambharat, Bhojnarine R., and Anthony E. Brockwell. "Sequential Monte Carlo pricing of American-style options under stochastic volatility models." Annals of Applied Statistics 4, no. 1 (2010): 222–65. http://dx.doi.org/10.1214/09-aoas286.

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AVELLANEDA, MARCO, ROBERT BUFF, CRAIG FRIEDMAN, NICOLAS GRANDECHAMP, LUKASZ KRUK, and JOSHUA NEWMAN. "WEIGHTED MONTE CARLO: A NEW TECHNIQUE FOR CALIBRATING ASSET-PRICING MODELS." International Journal of Theoretical and Applied Finance 04, no. 01 (2001): 91–119. http://dx.doi.org/10.1142/s0219024901000882.

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A general approach for calibrating Monte Carlo models to the market prices of benchmark securities is presented. Starting from a given model for market dynamics (price diffusion, rate diffusion, etc.), the algorithm corrects price-misspecifications and finite-sample effects in the simulation by assigning "probability weights" to the simulated paths. The choice of weights is done by minimizing the Kullback–Leibler relative entropy distance of the posterior measure to the empirical measure. The resulting ensemble prices the given set of benchmark instruments exactly or in the sense of least-squa

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Zhu, Qinwen, Grégoire Loeper, Wen Chen, and Nicolas Langrené. "Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing." Mathematics 9, no. 5 (2021): 528. http://dx.doi.org/10.3390/math9050528.

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The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate a more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its non-Markovianity brings mathematical and computational challenges for model calibration and simulation. To overcome these difficulties, we show that the rBergomi model can be well-approximated by the forward-variance Bergomi model with wisely chosen weights and mean-reversion speed parameters (aBergomi), which has the Markovian property. We establish an exp

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Hsu, Chih-Chen, Chung-Gee Lin, and Tsung-Jung Kuo. "Pricing of Arithmetic Asian Options under Stochastic Volatility Dynamics: Overcoming the Risks of High-Frequency Trading." Mathematics 8, no. 12 (2020): 2251. http://dx.doi.org/10.3390/math8122251.

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This research extended the model developed by Hull and White by integrating Taylor-series expansion into the model for deriving approximate analytical solutions for stochastic volatility forward-starting Asian options. Numerical experiments were performed to compare the proposed model with the Monte Carlo model over numerous simulations and demonstrated that the developed model has a pricing accuracy greater than 99%. Furthermore, the computation time was approximately 10−5 s for each simulation. The model’s outstanding computational performance demonstrates its capability to address the chall

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Yin, Xiao Cui. "Estimation of SV Model with Leverage Effect Based on MCMC Technique." Applied Mechanics and Materials 530-531 (February 2014): 605–8. http://dx.doi.org/10.4028/www.scientific.net/amm.530-531.605.

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This paper is to study the estimation of stochastic volatility model with leverage effect using Bayesian approach and Markov Chain Monte Carlo (MCMC) simulation technique. The data used is China's Shenzheng stock index. Estimations of model parameters are achieved by using MCMC technique in Openbugs Software, results show that there is leverage effect in Shenzheng stock series, convergence diagnostics suggest that parameters of the model are convergent.

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Rambharat, Bhojnarine R., and Anthony E. Brockwell. "Correction: Sequential Monte Carlo pricing of American-style options under stochastic volatility models." Annals of Applied Statistics 5, no. 1 (2011): 604. http://dx.doi.org/10.1214/11-aoas462.

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Klepáč, Václav, Petr Kříž, and David Hampel. "Real options analysis in the engineering company practice." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 61, no. 7 (2013): 2303–9. http://dx.doi.org/10.11118/actaun201361072303.

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In this paper, we deal with the real options analysis of selected investment projects. This approach is supplemented and compared to calculations of the net present value (NPV). Two research problems are analyzed: acquisition of the simulation software for the foundry industry in the sense of the expansive options and options on leaving the project in the case of acquisition of the spectrometer. For the option valuation, there were used analytical and numerical methods like the Black-Scholes model, binomial model and Monte Carlo simulations. In the case of binomial pricing model we used modifi

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KREMER, MARCEL, FRED ESPEN BENTH, BJÖRN FELTEN, and RÜDIGER KIESEL. "VOLATILITY AND LIQUIDITY ON HIGH-FREQUENCY ELECTRICITY FUTURES MARKETS: EMPIRICAL ANALYSIS AND STOCHASTIC MODELING." International Journal of Theoretical and Applied Finance 23, no. 04 (2020): 2050027. http://dx.doi.org/10.1142/s0219024920500272.

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This paper investigates the relationship between volatility and liquidity on the German electricity futures market based on high-frequency intraday prices. We estimate volatility by the time-weighted realized variance acknowledging that empirical intraday prices are not equally spaced in time. Empirical evidence suggests that volatility of electricity futures decreases as time approaches maturity, while coincidently liquidity increases. Established continuous-time stochastic models for electricity futures prices involve a growing volatility function in time and are thus not able to capture our

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31

Choi, Byungwook. "Overpriced Puts Puzzle in KOSPI 200 Options Market." Journal of Derivatives and Quantitative Studies 17, no. 3 (2009): 23–65. http://dx.doi.org/10.1108/jdqs-03-2009-b0002.

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The purpose of this paper is to examine the argument that the put options traded in the exchanges are too high, compared to the asset prices based on the classical CAPM model, and thus the short position of the put option would make a significant profit from trading. In order to explore the earlier report, this paper, using the KOSPI 200 index options market price, estimates the historical rate of return on several option trading strategies such as naked option, protective put, covered call, straddle, and strangle. Secondly this paper compares the historical rates of return on the option tradi

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Mi, Yanhui. "A modified stochastic volatility model based on Gamma Ornstein–Uhlenbeck process and option pricing." International Journal of Financial Engineering 03, no. 02 (2016): 1650017. http://dx.doi.org/10.1142/s2424786316500171.

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Stochastic volatility model of the Gamma Ornstein–Uhlenbeck possess authentic capability of both capturing some stylized features of financial time series and pricing European options. In this work we modify the Gamma OU model from the viewpoint of Monte Carlo simulation, which is crucial in both model inference and exotic option pricing. We discuss topics related to the measure transformation between objective and risk-neutral measures, arbitrage-free and market incompleteness of the new model. Furthermore, we investigate the performance of this model in European options pricing and an empiri

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La Bua, Gaetano, and Daniele Marazzina. "On the application of Wishart process to the pricing of equity derivatives: the multi-asset case." Computational Management Science 18, no. 2 (2021): 149–76. http://dx.doi.org/10.1007/s10287-021-00388-7.

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AbstractGiven the inherent complexity of financial markets, a wide area of research in the field of mathematical finance is devoted to develop accurate models for the pricing of contingent claims. Focusing on the stochastic volatility approach (i.e. we assume to describe asset volatility as an additional stochastic process), it appears desirable to introduce reliable dynamics in order to take into account the presence of several assets involved in the definition of multi-asset payoffs. In this article we deal with the multi asset Wishart Affine Stochastic Correlation model, that makes use of W

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34

Renò, Roberto. "NONPARAMETRIC ESTIMATION OF THE DIFFUSION COEFFICIENT OF STOCHASTIC VOLATILITY MODELS." Econometric Theory 24, no. 5 (2008): 1174–206. http://dx.doi.org/10.1017/s026646660808047x.

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In this paper, new fully nonparametric estimators of the diffusion coefficient of continuous time models are introduced. The estimators are based on Fourier analysis of the state variable trajectory observed and on the estimation of quadratic variation between observations by means of realized volatility. The estimators proposed are shown to be consistent and asymptotically normally distributed. Moreover, the Fourier estimator can be iterated to get a fully nonparametric estimate of the diffusion coefficient in a bivariate model in which one state variable is the volatility of the other. The e

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MERINO, RAÚL, JAN POSPÍŠIL, TOMÁŠ SOBOTKA, TOMMI SOTTINEN, and JOSEP VIVES. "DECOMPOSITION FORMULA FOR ROUGH VOLTERRA STOCHASTIC VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 24, no. 02 (2021): 2150008. http://dx.doi.org/10.1142/s0219024921500084.

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The research presented in this paper provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple nonlinear financial derivatives as vanilla European options are typically priced by means of Monte–Carlo (MC) simulations which are more computationally demanding than similar MC schemes for standard stochastic volatility models. In this pa

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Xi, Yanhui, Hui Peng, and Yemei Qin. "Modeling Financial Time Series Based on a Market Microstructure Model with Leverage Effect." Discrete Dynamics in Nature and Society 2016 (2016): 1–15. http://dx.doi.org/10.1155/2016/1580941.

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The basic market microstructure model specifies that the price/return innovation and the volatility innovation are independent Gaussian white noise processes. However, the financial leverage effect has been found to be statistically significant in many financial time series. In this paper, a novel market microstructure model with leverage effects is proposed. The model specification assumed a negative correlation in the errors between the price/return innovation and the volatility innovation. With the new representations, a theoretical explanation of leverage effect is provided. Simulated data

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Mrázek, Milan, and Jan Pospíšil. "Calibration and simulation of Heston model." Open Mathematics 15, no. 1 (2017): 679–704. http://dx.doi.org/10.1515/math-2017-0058.

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Abstract We calibrate Heston stochastic volatility model to real market data using several optimization techniques. We compare both global and local optimizers for different weights showing remarkable differences even for data (DAX options) from two consecutive days. We provide a novel calibration procedure that incorporates the usage of approximation formula and outperforms significantly other existing calibration methods. We test and compare several simulation schemes using the parameters obtained by calibration to real market data. Next to the known schemes (log-Euler, Milstein, QE, Exact s

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Ibrahim, Siti Nur Iqmal, Adan Diaz-Hernandez, John G. O'Hara, and Nick Constantinou. "Pricing holder-extendable call options with mean-reverting stochastic volatility." ANZIAM Journal 61 (May 6, 2020): 382–97. http://dx.doi.org/10.21914/anziamj.v61i0.12090.

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Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility. The option price is expressed in integral forms which have known closed-form characteristic functions. We price these options using a fast Fourier transform, a finite difference method and Monte Carl

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IBRAHIM, S. N. I., A. DÍAZ-HERNÁNDEZ, J. G. O’HARA, and N. CONSTANTINOU. "PRICING HOLDER-EXTENDABLE CALL OPTIONS WITH MEAN-REVERTING STOCHASTIC VOLATILITY." ANZIAM Journal 61, no. 4 (2019): 382–97. http://dx.doi.org/10.1017/s1446181119000142.

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Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility. The option price is expressed in integral forms which have known closed-form characteristic functions. We price these options using a fast Fourier transform, a finite difference method and Monte Carl

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Ma, Jingtang, Wenyuan Li, and Harry Zheng. "Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model." European Journal of Operational Research 280, no. 2 (2020): 428–40. http://dx.doi.org/10.1016/j.ejor.2019.07.041.

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TADJOUDDINE, EMMANUEL M. "MODELING AND SIMULATION OF SEQUENTIAL AUCTIONS: PRICING AND CALIBRATION ALGORITHMS." International Journal of Modeling, Simulation, and Scientific Computing 03, no. 03 (2012): 1250009. http://dx.doi.org/10.1142/s1793962312500092.

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We consider sequential auctions wherein seller and bidder agents need to price goods on sale at the 'right' market price. We propose algorithms based on a binomial model for both the seller and buyer. Then, we consider the problem of calibrating pricing models to market data. To this end, we studied a stochastic volatility model used for option pricing, derived, and analyzed Monte Carlo estimators for computing the gradient of a certain payoff function using Finite Differencing and Algorithmic Differentiation. We then assessed the accuracy and efficiency of both methods as well as their impact

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DE GRAAF, CORNELIS S. L., QIAN FENG, DRONA KANDHAI, and CORNELIS W. OOSTERLEE. "EFFICIENT COMPUTATION OF EXPOSURE PROFILES FOR COUNTERPARTY CREDIT RISK." International Journal of Theoretical and Applied Finance 17, no. 04 (2014): 1450024. http://dx.doi.org/10.1142/s0219024914500241.

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Three computational techniques for approximation of counterparty exposure for financial derivatives are presented. The exposure can be used to quantify so-called Credit Valuation Adjustment (CVA) and Potential Future Exposure (PFE), which are of utmost importance for modern risk management in the financial industry, especially since the recent credit crisis. The three techniques all involve a Monte Carlo path discretization and simulation of the underlying entities. Along the generated paths, the corresponding values and distributions are computed during the entire lifetime of the option. Opti

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Huang, Shoude, and Xunxiang Guo. "A Fourier-Cosine Method for Pricing Discretely Monitored Barrier Options under Stochastic Volatility and Double Exponential Jump." Mathematical Problems in Engineering 2020 (October 12, 2020): 1–9. http://dx.doi.org/10.1155/2020/4613536.

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In this paper, the valuation of the discrete barrier options on the condition that the underlying asset price process follows the GARCH volatility and double exponential jump is studied. We derived an analytical approximation of the characteristic function for the underlying log-asset price. Then, a quasianalytical approximate formula of the price of the discrete barrier option is obtained based the on Fourier-cosine method. Numerical examples show that the Fourier-cosine method is fast and efficient for pricing discrete barrier options compared with the Monte Carlo simulation method. Finally,

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HE, XIN-JIANG, and SONG-PING ZHU. "Pricing European options with stochastic volatility under the minimal entropy martingale measure." European Journal of Applied Mathematics 27, no. 2 (2015): 233–47. http://dx.doi.org/10.1017/s0956792515000510.

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In this paper, a closed-form pricing formula in the form of an infinite series for European call options is derived for the Heston stochastic volatility model under a chosen martingale measure. Given that markets with the stochastic volatility are incomplete, there exists a number of equivalent martingale measures and consequently investors face a problem of making a choice of appropriate measure when they price options. The one we adopt here is the so-called minimal entropy martingale measure shown to be related to the expected utility maximization theory (Frittelli 2000 Math. Finance10(1), 3

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ANTONELLI, FABIO, and VALENTINA PREZIOSO. "RATE OF CONVERGENCE OF MONTE CARLO SIMULATIONS FOR THE HOBSON–ROGERS MODEL." International Journal of Theoretical and Applied Finance 11, no. 08 (2008): 889–904. http://dx.doi.org/10.1142/s021902490800507x.

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The Hobson–Rogers model is used to price derivative securities under the no-arbitrage condition in a stochastic volatility setting, preserving the completeness of the market. Here we are studying the rate of convergence of the Euler/Monte Carlo approximations, when pricing European, Asian and digital type options. The aim of the present work is to express the approximation error in terms of the time step size, denoted by h, used for the Euler scheme. We recover an already known result, obtained by other authors using PDE approximations, for European options. Namely we show that for a Lipschitz

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Doffou, Ako. "Testing derivatives pricing models under higher-order moment swaps." Studies in Economics and Finance 36, no. 2 (2019): 154–67. http://dx.doi.org/10.1108/sef-04-2018-0106.

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Purpose This paper aims to test three parametric models in pricing and hedging higher-order moment swaps. Using vanilla option prices from the volatility surface of the Euro Stoxx 50 Index, the paper shows that the pricing accuracy of these models is very satisfactory under four different pricing error functions. The result is that taking a position in a third moment swap considerably improves the performance of the standard hedge of a variance swap based on a static position in the log-contract and a dynamic trading strategy. The position in the third moment swap is taken by running a Monte C

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Zhang, Xin, Hong Liu, and Li Mei Zhou. "The Probabilistic Reliability Assessment of Distribution Network Containing Distributed Generation." Applied Mechanics and Materials 448-453 (October 2013): 2503–6. http://dx.doi.org/10.4028/www.scientific.net/amm.448-453.2503.

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The access of distributed renewable energy enhances the uncertainty of the distribution network reliability, whereas the distribution network reliability evaluation using existing methods cannot fully reflect the stochastic volatility of islanding power supply and loads. For this reason the approach of active distribution network probabilistic reliability evaluation based on point estimation method was proposed. In the framework of Monte Carlo simulation, the islanding random variable was sampled and processed firstly; then the islanding probabilistic reliability was assessed with a nonlinear

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ALÒS, E., F. ANTONELLI, A. RAMPONI, and S. SCARLATTI. "CVA AND VULNERABLE OPTIONS IN STOCHASTIC VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 24, no. 02 (2021): 2150010. http://dx.doi.org/10.1142/s0219024921500102.

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This work aims to provide an efficient method to evaluate the Credit Value Adjustment (CVA) for a vulnerable European option, which is an option subject to some default event concerning the issuer solvability. Financial options traded in OTC markets are of this type. In particular, we compute the CVA in some popular stochastic volatility models such as SABR, Hull et al., which have proven to fit quite well market derivatives prices, admitting correlation with the default event. This choice covers the relevant case of Wrong Way Risk (WWR) when a credit deterioration determines an increase in th

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BOYARCHENKO, SVETLANA, and SERGEI LEVENDORSKIĬ. "SINH-ACCELERATION: EFFICIENT EVALUATION OF PROBABILITY DISTRIBUTIONS, OPTION PRICING, AND MONTE CARLO SIMULATIONS." International Journal of Theoretical and Applied Finance 22, no. 03 (2019): 1950011. http://dx.doi.org/10.1142/s0219024919500110.

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Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around [Formula: see text]. The Fourier transform techniques reduce calculation of probability distributions and option prices in the evaluation of integrals whose integrands are analytic in domains enjoying these properties. In the paper, we suggest to use changes of variables of the form [Formula: see text] and the simplified trapezoid rule to evaluate the integrals accurately and fast. We formulate the general scheme, and apply the scheme for cal

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El Aoud, Sofiene, and Frédéric Abergel. "A Stochastic Control Approach to Option Market Making." Market Microstructure and Liquidity 01, no. 01 (2015): 1550006. http://dx.doi.org/10.1142/s2382626615500069.

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This paper presents a model for the market making of options on a liquid stock. The stock price follows a generic stochastic volatility model under the real-world probability measure [Formula: see text]. Market participants price options on this stock under a risk-neutral pricing measure [Formula: see text], and they may misspecify the parameters controlling the dynamics of the volatility process. We first consider that there is a risk-neutral agent who is willing to make markets in an option on the stock, with the aim of maximizing the expected terminal wealth at maturity. Using standard tool

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