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Keywords:

  • G13

We investigate the effects of stochastic interest rates and the volatility of the underlying asset price on contingent claim prices including futures and options prices. The futures price can be decomposed into the forward price and an additional term; the options price can be decomposed into the Black-Scholes formula and several additional terms by applying the asymptotic expansion approach of the small disturbance asymptotics developed by Kunitomo and Takahashi (1995, 1998, 2001, 2003a, 2003b). The technical method is based on a new application of the Malliavin-Watanabe Calculus or the Watanabe-Yoshida Theory on Malliavin Calculus in stochastic analysis. We illustrate our new formulae and their numerical accuracy.