Probability Distribution and Option Pricing for Drawdown in a Stochastic Volatility Environment

Kyo Yamamoto, Seisho Sato and Akihiko Takahashi
Additional contact information
Kyo Yamamoto: Graduate School of Economics, University of Tokyo
Seisho Sato: Department of Prediction and Control, Institute of Statistical Mathematics
Akihiko Takahashi: Faculty of Economics, University of Tokyo

No CIRJE-F-625, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper studies the probability distribution and option pricing for drawdown in a stochastic volatility environment. Their analytical approximation formulas are derived by the application of a singular perturbation method (Fouque et al. [7]). The mathematical validity of the approximation is also proven. Then, numerical examples show that the instantaneous correlation between the asset value and the volatility state crucially affects the probability distribution and option prices for drawdown.

Pages: 23 pages
Date: 2009-06
New Economics Papers: this item is included in nep-ore
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