Mathematical Models For Timer Option Pricing Under The Stochastic Interest Rates

The timer option is a kind of exotic options traded in the OTC market. Instead of being exercised at a fixed maturity date as a vanilla option, the timer option has a random exercise date, which depends on the level of the accumulated variance of the underlying assets. When the cumulative variance reaches to the pre-set level, the timer option is exercised automatically; otherwise the timer option will not be exercised until the maturity date.In the previous studies, it is assumed that the risk-free interest rate is constant and thus the risk caused by the interest rates is ignored, In fact the changes in the interest rates will affect the volatility of the underlying asset, thus affect the exercise dates and prices for the time options. Therefore it is highly needed to investigate the correlations between the stochastic interest rates and the volatility of the underlying assets.In this thesis we study the timer option pricing under Vasicek models. We derive the closed-form formulas for valuation of the timer options under the stochastic interest rate models using martingale methods and stochastic analysis.