Pricing of Asian options on interest rates in the CIR model
In this paper, we study the integral over time of the instantaneous rate, i.e. the interest rate accrual, in the Cox Ingersoll Ross model. We derive distributional results for this process, including series representations for the density and probability distribution function. Applications to the valuation of derivatives, including Asian options prices in closed form, are presented here. Numerical examples are included to demonstrate the speed of convergence of the series. We also find that the series provide a more robust tool than numerical Laplace transform inversion for regions of high maturity and volatility. Given the versatility of the square-root process, the results derived in this paper are also of value for various others areas of finance, among which stochastic volatility and credit derivatives.
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- Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-36.
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- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
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