Relevant bibliographies by topics / Martingale approach in option pricing

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Academic literature on the topic 'Martingale approach in option pricing'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Martingale approach in option pricing"

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Gerber, Hans U., and Elias S. W. Shiu. "Martingale Approach to Pricing Perpetual American Options." ASTIN Bulletin 24, no. 2 (November 1994): 195–220. http://dx.doi.org/10.2143/ast.24.2.2005065.

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AbstractThe method of Esscher transforms is a tool for valuing options on a stock, if the logarithm of the stock price is governed by a stochastic process with stationary and independent increments. The price of a derivative security is calculated as the expectation, with respect to the risk-neutral Esscher measure, of the discounted payoffs. Applying the optional sampling theorem we derive a simple, yet general formula for the price of a perpetual American put option on a stock whose downward movements are skip-free. Similarly, we obtain a formula for the price of a perpetual American call option on a stock whose upward movements are skip-free. Under the classical assumption that the stock price is a geometric Brownian motion, the general perpetual American contingent claim is analysed, and formulas for the perpetual down-and-out call option and Russian option are obtained. The martingale approach avoids the use of differential equations and provides additional insight. We also explain the relationship between Samuelson's high contact condition and the first order condition for optimality.
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Wang, Ming-Chieh, Li-Jhang Huang, and Szu-Lang Liao. "Option Pricing Using the Martingale Approach with Polynomial Interpolation." Journal of Futures Markets 33, no. 5 (May 14, 2012): 469–91. http://dx.doi.org/10.1002/fut.21557.

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Yu, Xisheng, and Li Yang. "Pricing American Options Using a Nonparametric Entropy Approach." Discrete Dynamics in Nature and Society 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/369795.

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This paper studies the pricing problem of American options using a nonparametric entropy approach. First, we derive a general expression for recovering the risk-neutral moments of underlying asset return and then incorporate them into the maximum entropy framework as constraints. Second, by solving this constrained entropy problem, we obtain a discrete risk-neutral (martingale) distribution as the unique pricing measure. Third, the optimal exercise strategies are achieved via the least-squares Monte Carlo algorithm and consequently the pricing algorithm of American options is obtained. Finally, we conduct the comparative analysis based on simulations and IBM option contracts. The results demonstrate that this nonparametric entropy approach yields reasonably accurate prices for American options and produces smaller pricing errors compared to other competing methods.
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Nowak, Piotr, and Maciej Romaniuk. "A fuzzy approach to option pricing in a Levy process setting." International Journal of Applied Mathematics and Computer Science 23, no. 3 (September 1, 2013): 613–22. http://dx.doi.org/10.2478/amcs-2013-0046.

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Abstract In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets.We assume that some parameters of the financial instrument cannot be precisely described and therefore they are introduced to the model as fuzzy numbers. Application of fuzzy arithmetic enables us to consider various sources of uncertainty, not only the stochastic one. To obtain the European call option pricing formula we use the minimal entropy martingale measure and Levy characteristics.
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Liu, Guoxiang, Quanxin Zhu, Zhaowei Yan, and Yuanyao Ding. "The martingale approach for vulnerable binary option pricing under stochastic interest rate." Cogent Mathematics 4, no. 1 (January 1, 2017): 1340073. http://dx.doi.org/10.1080/23311835.2017.1340073.

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Lee, Jun Hui, and Kook Hyun Chang. "Volatility Smile Surface for Levy Option Pricing Model." Journal of Derivatives and Quantitative Studies 12, no. 1 (May 30, 2004): 73–86. http://dx.doi.org/10.1108/jdqs-01-2004-b0004.

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This paper discusses theoretical extensions of the implied volatility method of Dupire (1994) when the stock prices follow the Geometric Levy process. For the extensions of Kolmogorov forward equation for Levy process, this paper uses adjoint operator in L² spaces. This paper obtains similar results of Dupire (1994) and Andersen and Andreasan (2001). However, our results can be applied to more general semi-martingale processes such as well-known VG (Variance Gamma) model and NIG (Normal Inverse Gaussian) model with diffusion processes. This paper also applies the approach to the case of stochastic time changed Levy process, which generates the stochastic volatility models.
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Li, Qing, Songlin Liu, and Misi Zhou. "Nonparametric Estimation of Fractional Option Pricing Model." Mathematical Problems in Engineering 2020 (December 15, 2020): 1–8. http://dx.doi.org/10.1155/2020/8858821.

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The establishment of the fractional Black–Scholes option pricing model is under a major condition with the normal distribution for the state price density (SPD) function. However, the fractional Brownian motion is deemed to not be martingale with a long memory effect of the underlying asset, so that the estimation of the state price density (SPD) function is far from simple. This paper proposes a convenient approach to get the fractional option pricing model by changing variables. Further, the option price is transformed as the integral function of the cumulative density function (CDF), so it is not necessary to estimate the distribution function individually by complex approaches. Finally, it encourages to estimate the fractional option pricing model by the way of nonparametric regression and makes empirical analysis with the traded 50 ETF option data in Shanghai Stock Exchange (SSE).
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Siu, Tak Kuen. "Regime-Switching Risk: To Price or Not to Price?" International Journal of Stochastic Analysis 2011 (December 27, 2011): 1–14. http://dx.doi.org/10.1155/2011/843246.

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Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.
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ELLIOTT, ROBERT J., TAK KUEN SIU, and LEUNGLUNG CHAN. "OPTION PRICING FOR GARCH MODELS WITH MARKOV SWITCHING." International Journal of Theoretical and Applied Finance 09, no. 06 (September 2006): 825–41. http://dx.doi.org/10.1142/s0219024906003846.

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In this paper we develop a method for pricing derivatives under a Markov switching version of the Heston-Nandi GARCH (1, 1) model by using a well known tool from actuarial science, namely the Esscher transform. We suppose that the dynamics of the GARCH process switch over time according to one of the regimes described by the states of an observable Markov chain process. By augmenting the conditional Esscher transform with the observable Markov switching process, a Markov switching conditional Esscher transform (MSCET) is developed to identify a martingale measure for option valuation in the incomplete market described by our model. We provide an alternative approach for the derivation of an analytical option valuation formula under the Markov switching Heston-Nandi GARCH (1, 1) model. The use of the MSCET can be justified by considering a utility maximization problem with respect to a power utility function associated with the Markov switching risk-averse parameters.
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Hainaut, Donatien. "Calendar Spread Exchange Options Pricing with Gaussian Random Fields." Risks 6, no. 3 (August 8, 2018): 77. http://dx.doi.org/10.3390/risks6030077.

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Most of the models leading to an analytical expression for option prices are based on the assumption that underlying asset returns evolve according to a Brownian motion with drift. For some asset classes like commodities, a Brownian model does not fit empirical covariance and autocorrelation structures. This failure to replicate the covariance introduces a bias in the valuation of calendar spread exchange options. As the payoff of these options depends on two asset values at different times, particular care must be taken for the modeling of covariance and autocorrelation. This article proposes a simple alternative model for asset prices with sub-exponential, exponential and hyper-exponential autocovariance structures. In the proposed approach, price processes are seen as conditional Gaussian fields indexed by the time. In general, this process is not a semi-martingale, and therefore, we cannot rely on stochastic differential calculus to evaluate options. However, option prices are still calculable by the technique of the change of numeraire. A numerical illustration confirms the important influence of the covariance structure in the valuation of calendar spread exchange options for Brent against WTI crude oil and for gold against silver.
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Dissertations / Theses on the topic "Martingale approach in option pricing"

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Harr, Martin. "Option Pricing in the Presence of Liquidity Risk." Thesis, Umeå University, Department of Physics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-35100.

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The main objective of this paper is to prove that liquidity costs do exist in option pricingtheory. To achieve this goal, a martingale approach to option pricing theory is usedand, from a model by Jarrow and Protter [JP], a sound theoretical model is derived toshow that liquidity risk exists. This model, derived and tested in this extended theory,allows for liquidity costs to arise. The expression liquidity cost is used in this paper tomeasure liquidity risk relative to the option price.

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Lei, Ngai Heng. "Martingale method in option pricing theory." Thesis, University of Macau, 2003. http://umaclib3.umac.mo/record=b1447303.

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Dranev, Yury. "Equivalent Martingale measures and option pricing in jump-diffusion markets." Thesis, University of Ottawa (Canada), 2004. http://hdl.handle.net/10393/10794.

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One of the key questions in financial mathematics is the choice of an appropriate model for the financial market. There are a number of models available, such as Geometrical Brownian motion and different types of Levy processes, that are not general enough to reflect all the characteristics of fluctuations in stock price but for which the parameters can be estimated with relative ease. There are more general semimartingale models for which parameter estimation and numerical calculation become very difficult questions. The goal of this thesis is to present a tractable model for which we can carry out computations, and it seems that by varying the parameters this model can be related to real market data. We will use the equivalent measure approach to obtain estimates of the price of European call options for our model. Since our market is incomplete, a consequence of the inclusion of jump processes in the model, we will choose the "best" equivalent martingale measure by applying various techniques and compare the results for different choices. We will also illustrate how this theory works on particular examples. We consider applications not only to the cases of continuous and Levy process markets but also to cases that reflect the main advantages of our jump diffusion model. Finally we numerically illustrate option pricing in our setting.
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Matsumoto, Manabu. "Options on portfolios of options and multivariate option pricing and hedging." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.324627.

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Hao, Wenyan. "Quantum mechanics approach to option pricing." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/43020.

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Options are financial derivatives on an underlying security. The Schrodinger and Heisenberg approach to the quantum mechanics together with the Dirac matrix approaches are applied to derive the Black-Scholes formula and the quantum Cox- Rubinstein formula. The quantum mechanics approach to option pricing is based on the interpretation of the option price as the Schrodinger wave function of a certain quantum mechanics model determined by Hamiltonian H. We apply this approach to continuous time market models generated by Levy processes. In the discrete time formulization, we construct both self-adjoint and non selfadjoint quantum market. Moreover, we apply the discrete time formulization and analyse the quantum version of the Cox-Ross-Rubinstein Binomial Model. We find the limit of the N-period bond market, which convergences to planar Brownian motion and then we made an application to option pricing in planar Brownian motion compared with Levy models by Fourier techniques and Monte Carlo method. Furthermore, we analyse the quantum conditional option price and compare for the conditional option pricing in the quantum formulization. Additionally, we establish the limit of the spectral measures proving the convergence to the geometric Brownian motion model. Finally, we found Binomial Model formula and Path integral formulization gave are close to the Black-Scholes formula.
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Chen, Si S. M. Massachusetts Institute of Technology. "Robust option pricing : An [epsilon]-arbitrage approach." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/55108.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009.
In title on title-page, "[epsilon]" appears as the lower case Greek letter. Cataloged from PDF version of thesis.
Includes bibliographical references (p. 59-60).
This research aims to provide tractable approaches to price options using robust optimization. The pricing problem is reduced to a problem of identifying the replicating portfolio which minimizes the worst case arbitrage possible for a given uncertainty set on underlying asset returns. We construct corresponding uncertainty sets based on different levels of risk aversion of investors and make no assumption on specific probabilistic distributions of asset returns. The most significant benefits of our approach are (a) computational tractability illustrated by our ability to price multi-dimensional options and (b) modeling flexibility illustrated by our ability to model the "volatility smile". Specifically, we report extensive computational results that provide empirical evidence that the "implied volatility smile" that is observed in practice arises from different levels of risk aversion for different strikes. We are able to capture the phenomenon by appropriately finding the right risk-aversion as a function of the strike price. Besides European style options which have fixed exercising date, our method can also be adopted to price American style options which we can exercise early. We also show the applicability of this pricing method in the case of exotic and multi-dimensional options, in particular, we provide formulations to price Asian options, Lookback options and also Index options. These prices are compared with market prices, and we observe close matches when we use our formulations with appropriate uncertainty sets constructed based on market-implied risk aversion.
by Si Chen.
S.M.
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Chuang, Chienmin. "Multi-asset option pricing problems : a variational approach." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/3917/.

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Options are important and frequently traded products in the modern financial market. How to price them fairly and reasonably is always an interesting issue for academia and industry. This research is performed under the classical multi-asset Black-Scholes-Merton (BSM) model and can be extended to other exotic models. We show how to reformulate the multi-asset Black-Scholes-Merton partial differential equation/inequality (BSM PDE/PDI) and provide theorems to justify the unique solution of reformulations. In terms of discretization, we adopt the finite element method (FEM) in space and finite difference method (FDM) in time. Moreover, we develop the closed-form formulas for the elemental matrices used in the finite element assembly process in a general high-dimensional framework. The discrete systems of option pricing problems are presented in the form of linear system of equations (LSE) and linear complementary problems (LCP) for European and American/perpetual options respectively. Up to six different algorithms for the LCP are introduced and compared on the basis of computational efficiency and errors. The option values of European, American and perpetual types are calibrated when given various payoffs and up to three assets. Particularly, their numerical free boundaries are identified and presented in the form of (d - 1)-dimensional manifold in a d-assetframework. In the last chapter, we conclude our research with our contributions and potential extension.
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Liu, Lu. "Pricing energy path-dependent option using tree based approach." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.512006.

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Grandits, Peter, and Werner Schachinger. "Leland's approach to option pricing. The evolution of a discontinuity." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/1448/1/document.pdf.

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A claim of Leland (1985) states that in the presence of transaction costs a call option on a stock S, described by geometric Brownian motion, can be perfectly hedged using Black-Scholes delta hedging with a modified volatility. Recently Kabanov and Safarian (1997) disproved this claim, giving an explicit (up to an integral) expression of the limiting hedging error, which appears to be strictly negative and depends on the path of the stock price only via the stock price at expiry ST . We prove in this paper that the limiting hedging error, considered as a function of ST, exhibits a removable discontinuity at the exercise price. Furthermore, we provide a quantitative result describing the evolution of the discontinuity, which shows that its precursors can very well be observed also in cases of reasonable length of revision intervals. (author's abstract)
Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
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Bart, Adde Tiffany, and Kadek Maya Sri Puspita. "American Option pricing under Mutiscale Model using Monte Carlo and Least-Square approach." Thesis, Mälardalens högskola, Utbildningsvetenskap och Matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-35848.

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In the finance world, option pricing techniques have become an appealing topic among researchers, especially for pricing American options. Valuing this option involves more factors than pricing the European style one, which makes it more computationally challenging. This is mainly because the holder of American options has the right to exercise at any time up to maturity. There are several approaches that have been proved to be efficient and applicable for maximizing the price of this type of options. A common approach is the Least squares method proposed by Longstaff and Schwartz. The purpose of this thesis is to discuss and analyze the implementation of this approach under the Multiscale Stochastic Volatility model. Since most financial markets show randomly variety of volatility, pricing the option under this model is considered necessary. A numerical study is performed to present that the Least-squares approach is indeed effective and accurate for pricing American options.
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Books on the topic "Martingale approach in option pricing"

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Pascucci, Andrea. PDE and Martingale Methods in Option Pricing. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1781-8.

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Chorro, Christophe, Dominique Guégan, and Florian Ielpo. A Time Series Approach to Option Pricing. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-45037-6.

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Page, H. A practical approach to option pricing theory. Dublin: University College Dublin, 1994.

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Risk-adjusted lending conditions: An option pricing approach. Chichester: John Wiley & Sons, 2002.

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Rosenberger, Werner. Risk-adjusted lending conditions: An option pricing approach. Chichester: John Wiley, 2003.

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Lee, Jaewoo. Insurance value of international reserves: An option pricing approach. [Washington D.C.]: International Monetary Fund, Research Dept., 2004.

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Baranzini, Andrea. Uncertainty and global warming: An option-pricing approach to policy. Washington, D.C: World Bank, Latin America and the Caribbean, Country Dept. I, Country Operations Division, 1995.

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Katz, Jeffrey Owen. Advanced option pricing models: An empirical approach to valuing options. New York: McGraw-Hill, 2005.

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Claessens, Stijn. An option-pricing approach to secondary market debt: Applied to Mexico. Washington, DC: Data and International Finance Division, International Economics Dept. and the Country Operations Division, Latin America and the Caribbean Country Dept. II, World Bank, 1990.

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Estache, Antonio. Evaluating the minimum asset tax on corporations: An option pricing approach. London: Centre for Economic Policy Research, 1992.

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Book chapters on the topic "Martingale approach in option pricing"

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Kallianpur, Gopinath, and Rajeeva L. Karandikar. "Arbitrage and Equivalent Martingale Measures." In Introduction to Option Pricing Theory, 137–67. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-0511-1_8.

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Pascucci, Andrea. "Derivatives and arbitrage pricing." In PDE and Martingale Methods in Option Pricing, 1–13. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1781-8_1.

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Rogers, Jamie. "Option Pricing Methods." In Strategy, Value and Risk — The Real Options Approach, 74–84. London: Palgrave Macmillan UK, 2002. http://dx.doi.org/10.1057/9780230513051_11.

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Platen, Eckhard, and David Heath. "Introduction to Option Pricing." In A Benchmark Approach to Quantitative Finance, 277–318. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-47856-0_8.

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Pascucci, Andrea. "Continuous market models." In PDE and Martingale Methods in Option Pricing, 329–87. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1781-8_10.

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Pascucci, Andrea. "American options." In PDE and Martingale Methods in Option Pricing, 389–401. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1781-8_11.

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Pascucci, Andrea. "Numerical methods." In PDE and Martingale Methods in Option Pricing, 403–28. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1781-8_12.

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Pascucci, Andrea. "Introduction to Lévy processes." In PDE and Martingale Methods in Option Pricing, 429–95. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1781-8_13.

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Pascucci, Andrea. "Stochastic calculus for jump processes." In PDE and Martingale Methods in Option Pricing, 497–540. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1781-8_14.

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Pascucci, Andrea. "Fourier methods." In PDE and Martingale Methods in Option Pricing, 541–76. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1781-8_15.

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Conference papers on the topic "Martingale approach in option pricing"

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Chen, Hung-Ching (Justin), and Malik Magdon-Ismail. "Learning Martingale Measures From High Frequency Financial Data to Help Option Pricing." In 9th Joint Conference on Information Sciences. Paris, France: Atlantis Press, 2006. http://dx.doi.org/10.2991/jcis.2006.126.

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Miyahara, Yoshio, and Naruhiko Moriwaki. "Option Pricing Based on Geometric Stable Processes and Minimal Entropy Martingale Measures." In Proceedings of the 2008 Daiwa International Workshop on Financial Engineering. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814273473_0007.

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Yeyou Xu. "Notice of Violation of IEEE Publication Principles - Empirical martingale method of option pricing." In 2010 2nd International Conference on Advanced Computer Control (ICACC 2010). IEEE, 2010. http://dx.doi.org/10.1109/icacc.2010.5486915.

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Mostafa, F., and T. Dillon. "A neural network approach to option pricing." In COMPUTATIONAL FINANCE 2008. Southampton, UK: WIT Press, 2008. http://dx.doi.org/10.2495/cf080081.

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Hajizadeh, Ehsan, Abbas Seifi, Ilias Kotsireas, Roderick Melnik, and Brian West. "A hybrid modeling approach for option pricing." In ADVANCES IN MATHEMATICAL AND COMPUTATIONAL METHODS: ADDRESSING MODERN CHALLENGES OF SCIENCE, TECHNOLOGY, AND SOCIETY. AIP, 2011. http://dx.doi.org/10.1063/1.3663498.

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Aimi, A., L. Diazzi, and C. Guardasoni. "Integral approach to Asian barrier option pricing." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114486.

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Liu, Shu-Ing, and Yu-Chung Liu. "Threshold-GARCH Option Pricing: A Trinomial Tree Approach." In Second International Conference on Innovative Computing, Informatio and Control (ICICIC 2007). IEEE, 2007. http://dx.doi.org/10.1109/icicic.2007.597.

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Min, Zhang. "An actuarial approach to foreign currency option pricing." In 2015 Conference on Informatization in Education, Management and Business (IEMB-15). Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/iemb-15.2015.179.

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Jizba, Petr. "Option pricing and generalized statistics: density matrix approach." In Recent Advances in Stochastic Modeling and Data Analysis. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709691_0068.

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Palupi, Irma. "Pricing bermudan option via evolutionary Discrete Morse Flow approach." In 2015 3rd International Conference on Information and Communication Technology (ICoICT ). IEEE, 2015. http://dx.doi.org/10.1109/icoict.2015.7231493.

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Reports on the topic "Martingale approach in option pricing"

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Das, Sanjiv Ranjan. An Efficient Generalized Discrete-Time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model. Cambridge, MA: National Bureau of Economic Research, June 1997. http://dx.doi.org/10.3386/t0212.

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