A. Dassios and J. Nagaradjasarma (UK)
Derivatives, valuation, Square-root process, average-rate claims.
In this paper, we study the integral over time of the ins tantaneous rate, i.e the interest rate accrual, in the Cox In gersoll Ross model. We derive distributional results for this process, including series representations for the den sity 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 ro bust tool than numerical Laplace transform inversion for regions of high maturity and volatility. Given the versa tility 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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