Research On The Pricing Of Option

In this paper we consider three problem on option pricing: the pricing of options in a financial market model with transaction costs, dividends and uncertain volatility ; return of the stocks follows a mean reversion Ornstein–Uhlenbeck process and volatilities are correct with stock return to evaluate option prices; American call option with stochastic market model.Considering the pricing of options with transaction costs, dividends and uncertain volatility.Ⅱw hich depended on the work of Nikolai.G.Dokuchaev(1998 )[ 32], Chance(2002 )[ 33]recreated self-financing strategy and reformed B-S model. finally we get a closed-solution for European option pricing.Ⅲexten Stein and stein stochastic volatility model(S&S),which suppose that return of the stocks follows a mean reversion Ornstein–Uhlenbeck process and volatilities are correlate with stock return .a closed-form pricing solution is derived.And the correlate between stock return and volatilities are show by using Fourier inversion.In theⅣ,American call Option is generalized to the case where the riskless asset earns a time-dependent interest rate r (t ),a stochastic rate of returnμ(t ),a-time-dependent dividend yieldρ(t )and stochastic volatilityσ(t ).Using Fourier transform method, closed-form solutions of American call option claim.otherwise we give the formula to American option pricing with transaction costs.