This is a revised version of Discussion Paper CIRJE-F-129 (September 2001), Graduate School of Economics, University of Tokyo. We thank the referees, the co-editor of this journal and Roger Smith for their useful and detailed comments. We also thank Nakahiro Yoshida, Hideo Nagai and the participants of Finance Workshop at the Osaka University for their helpful comments on the earlier versions.
EFFECTS OF STOCHASTIC INTEREST RATES AND VOLATILITY ON CONTINGENT CLAIMS*
Version of Record online: 8 FEB 2007
The Japanese Economic Review
Volume 58, Issue 1, pages 71–106, March 2007
How to Cite
KUNITOMO, N. and KIM, Y.-J. (2007), EFFECTS OF STOCHASTIC INTEREST RATES AND VOLATILITY ON CONTINGENT CLAIMS. Japanese Economic Review, 58: 71–106. doi: 10.1111/j.1468-5876.2007.00345.x
- Issue online: 8 FEB 2007
- Version of Record online: 8 FEB 2007
- Final version accepted 29 October 2004.
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.