Pricing European Options in the Variance Gamma Model

• Autorzy: Arkadiusz Orzechowski
• Języki publikacji: EN

Abstrakty

EN

The purpose of the article was to investigate if it is possible to speed up the process of pricing European options in the variance gamma setting. The analysis carried out for this purpose refers to the choice of the Fourier transform scheme, which allows to obtain accurately and fast the final result (theoretical value of the European option). The issues being discusses that refer to other methods of pricing options via Fourier transform are also briefly discussed.(original abstract)

Słowa kluczowe

EN

European options; Fourier Transform; Options pricing

PL

Opcje europejskie; Transformacja Fouriera; Wycena opcji

• Czasopismo: Metody Ilościowe w Badaniach Ekonomicznych / Szkoła Główna Gospodarstwa Wiejskiego
• Rocznik: 2019
• Tom: 20(XX)
• Numer: nr 1
• Strony: 45--53

Twórcy

autor

Arkadiusz Orzechowski

• Warsaw School of Economics, Poland

Bibliografia

• Attari M. (2004) Option Pricing Using Fourier Transform: A Numerically Efficient Simplification. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=520042, [dostęp: 1.07.2018].
• Bakshi G., Madan D. (2000) Spanning and Derivative-Security Valuation. Journal of Fin10 ancial Economics, 2(55), 205-238.
• Barndorff-Nielsen O. E. (1991) Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling. Scandinavian Journal of Statistics, 24(1), 1-13.
• Bates D. S. (2006) Maximum Likelihood Estimation of Latent Affine Processes. Review of Financial Studies, 19(3), 909-965.
• Black F., Scholes M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.
• Carr P., Geman H., Madan D. B., Yor M. (2002) The Fine Structure of Asset Returns: An Empirical Investigation. Journal of Business, 75(2), 305-332.
• Carr P., Madan D. B. (1999) Option Valuation Using the Fast Fourier Transform. Journal of Computational Finance, 2(4), 61-73.
• Eberlein E., Keller U., Prause K. (1998) New Insights into Smile, Mispricing and Value at Risk: The Hyperbolic Model. Journal of Business, 71(3), 371-405.
• Kou S. G. (2002) Jump-Diffusion Model for Option Pricing. Management Science, 48(8), 1086-1101.
• Lewis A. (2001) A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy Processes. SSRN Electronic Journal, 1-25.
• Lipton A. (2002) The Vol Smile Problem. http://www.math.ku.dk/~rolf/Lipton_ VolSmileProblem.pdf [access date: 8.12.2017].
• Madan D. B., Carr P., Chang E. (1998) The Variance Gamma Process and Option Pricing Model. European Finance Review, 2(1), 79-105.
• Madan D. B., Milne F. (1991) Option Pricing with VG Martingale Components. Mathematical Finance, 1(4), 39-55.
• Merton R. C. (1976) Option Pricing When Underlying Stock Returns Are Discontinuous. Journal of Financial Economics, 3(1-2), 125-144.
• Orzechowski A. (2018) Pricing Correlation Options: from the P. Carr and D. Madan Approach to the New Method Based on the Fourier Transform. Economics and Business Review, 4(1), 16-28.
• Schoutens W. (2003) Lévy Processes in Finance: Pricing Financial Derivatives. John Wiley & Sons, Chichester.

Identyfikatory

DOI

https://doi.org/10.22630/MIBE.2019.20.1.5