Parameter Estimation And Timer Option Pricing Based On Stochastic Volatility Model

In this paper,we study the log-transition density function of the time-varying stochastic volatility model.Under stochastic volatility model,we discuss the timer option pricing method under the condition of paying dividends and stochastic interest rate.Firstly,the approximate log-transition density function of the reducible and irreducible are obtained by using the Hermite method and Kolmogorov method.We prove the asymptotic properties of the approximate log-transition density of the time-varying stochastic volatility model,and the maximum likelihood estimations of the parameters in the model are studied.Secondly,under the Heston stochastic volatility model,the risk-free assets are constructed by using the Δ-hedging principle of portfolio,and the partial differential equations are obtained which satifies the timer option pricing.The explicit formulas of the joint density function related to Bessel processes are studied by using Laplace inverse transform.The Black-Scholes-Merton formula for the time-varying option pricing under the pay dividends is derived.Finally,motivated by analytical valuation of timer options,we explore their novel mathematical connection with stochastic volatility and stochastic interest rates under the CIR stochastic interest rate model.By introducing the first-passage time problem on realized variance and using the Δ-hedging method,we obtain the four-dimensional partial differential equation of the timer option with interest rate risk.By using the dimensionreduction technique to derive the two-dimensional partial differential equation of timer option,the explicit approximation expression of option pricing is obtained.