Pricing Correlation Options: from the P. Carr And D. Madan Approach to the New Method Based on the Fourier Transform

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Abstract

Pricing of options plays an important role in the financial industry. Investors knowing how to price derivative contracts quickly and accurately can beat the market. On the other hand market participants constructing their investment strategies with the use of options based on techniques that do not assure the highest computational speed and efficiency are doomed to failure. The aim of the article is to extend the existing methodology of pricing correlation options based on the Fourier transform. The article starts with a presentation of Carr and Madan’s concept (Carr & Madan, 1999). Then other methods of pricing options with the use of the Fourier transform are summarized. Finally, a new approach to pricing derivative contracts is derived and then applied to the correlation options.

Attari, M. (2004). Option pricing using Fourier transforms: A numerically efficient simplification. Retrieved from http://papers.ssrn.com/sol3/papers.cfm?abstract_id=520042. doi:

Bakshi, G., & Madan, D. (2000). Spanning and derivative - security valuation. Journal of Financial Economics, 55(2), 205-238. doi:

Bates, D. (2006). Maximum likelihood estimation of latent affine processes. Review of Financial Studies, 19(3), 909-965. doi:

Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. The Journal of Political Economy, 81(3), 637-654. doi:

Carmona, R., & Durrleman, V. (2003). Pricing and hedging spread options. SIAM Review, 45(4), 627-285. doi:

Carr, P., Geman, H., Madan, D., & Yor, M. (2002). The fine structure of asset returns: An empirical investigation. Journal of Business, 75(2), 305-332. doi:

Carr, P., & Madan, D. (1999). Option valuation using the fast Fourier transform. Journal of Computational Finance, 2(4), 61-73. doi:

Dempster, M. A. H., & Hong, S. S. G. (2000). Spread option valuation and fast Fourier transform. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.27.9431&rep=rep1&type=pdf. doi:

Fan, K., & Wang, R. (2017). Valuation of correlation options under a stochastic interest rate model with regime switching. Frontiers of Mathematics in China, 12(5), 1113‑1130. doi:

Feunou, B., & Tafolong, E. (2015). Fourier inversion formulas for multiple-asset option pricing. Studies in Nonlinear Dynamics & Econometrics, 19(5), 531-559. doi:

Heston, S. L. (1993). A closed form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6(2), 327‑343. doi:

Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42(2), 281-300. doi:

Kirkby, J. L. (2017). Robust barrier option pricing by frame projection under exponential Levy dynamics. Applied Mathematical Finance, 24(4), 337-386. doi:

Kou, S. G. (2002). A jump-diffusion model for option pricing. Management Science, 48(8), 1086-1101. doi:

Lewis, A. (2001), A simple option formula for general jump-diffusion and other exponential levy processes. Retrieved from http://papers.ssrn.com/sol3/papers.cfm?abstract_id=282110. doi:

Madan, D. B., Carr, P., & Chang, E. C. (1998). The variance gamma process and option pricing. European Finance Review, 2, 79-105. doi:

Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1-2), 125-144. doi:

Orzechowski, A. (2016). Analiza efektywności obliczeniowej opcji na przykładzie modelu F. Blacka i M. Scholesa. Finanse, 9(1), 137-154.

Stein, E., & Stein, J. (1991). Stock price distributions with stochastic volatility. Review of Financial Studies, 4(4), 727-752. doi:

Zhu, J. (2000). Modular pricing of options. An application of Fourier analysis. Heidelberg: Springer-Verlag. doi:

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