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Fourier Inversion Formulas for Multiple-Asset Option Pricing

Listed author(s):
  • Bruno Feunou
  • Ernest Tafolong

Plain vanilla options have a single underlying asset and a single condition on the payoff at the expiration date. For this class of options, a well-known result of Duffie, Pan and Singleton (2000) shows how to invert the characteristic function to obtain a closed-form formula for their prices. However, multiple-asset and multiple-condition derivatives such as rainbow options cannot be priced within this framework. Utilizing inversion of the Fourier transform - and resorting to neither the Black-Scholes framework nor the affine models settings - the authors provide an analytical solution for options whose payoffs depend on two or more conditions. Numerical experiments based on the multiple-asset and multiple-condition derivatives are provided to illustrate the usefulness of the proposed approach.

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File URL: http://www.bankofcanada.ca/wp-content/uploads/2015/03/wp2015-11.pdf
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Paper provided by Bank of Canada in its series Staff Working Papers with number 15-11.

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Length: 47 pages
Date of creation: 2015
Handle: RePEc:bca:bocawp:15-11
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  1. Gourieroux, Christian & Sufana, Razvan, 2010. "Derivative Pricing With Wishart Multivariate Stochastic Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 438-451.
  2. Adrian Buss & Grigory Vilkov, 2012. "Measuring Equity Risk with Option-implied Correlations," Review of Financial Studies, Society for Financial Studies, vol. 25(10), pages 3113-3140.
  3. Patrick Navatte & Christophe Villa, 2000. "The information content of implied volatility, skewness and kurtosis: empirical evidence from long-term CAC 40 options," European Financial Management, European Financial Management Association, vol. 6(1), pages 41-56.
  4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
  5. Feunou Bruno & Tafolong Ernest, 2015. "Fourier inversion formulas for multiple-asset option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 531-559, December.
  6. Christoffersen, Peter & Feunou, Bruno & Jacobs, Kris & Meddahi, Nour, 2014. "The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(03), pages 663-697, June.
  7. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
  8. Chang, Chuang-Chang & Chung, San-Lin & Yu, Min-Teh, 2006. "Loan guarantee portfolios and joint loan guarantees with stochastic interest rates," The Quarterly Review of Economics and Finance, Elsevier, vol. 46(1), pages 16-35, February.
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