Asian And American Option Pricing Problem And Its Application

Firstly,in this paper the model of Asian option pricing is applied to electricity territory.The stochastic volatility model of a class of one dimension electricity Asian option pricing with single parameter is discussed.The volatility of the model adopts the fast stochastic volatility mean reversion model.Introducing no risk neutral probability measure and using Radon-Nikodym derivative,a transformation between expected return rate and no risk interest rate is realized.By using Feynman-Kac's formula,parabolic differential equation in which the risky asserts of electricity Asian option prices is obtained.Applied the singular perturbation method,the asymptotic solution to its Black-Scholes equation is obtained;Secondly,the single parameter model is extended to two parameters case and a stochastic volatility model of a class of the general one-dimensional Asian option pricing with two parameters is discussed.The volatility is based on the fast time scale and the slow time scale which is used to conform the fast and slow system.The asymptotic solution of the one dimensional two parameters Asian option pricing and its consistent effective error estimates are obtained;Thirdly,the one-dimensional stochastic volatility model of Asian option pricing is extended to the high dimensional case.A type of stochastic volatility model which includes fast-slow alternate multiple scales of high dimension Asian option pricing problem is discussed.By Feynman-Kac's formula,the generalized Black-Scholes equation of high dimension Asian option pricing is derived.Acorrding to singular perturbation method,the asymptotic solution of high dimension Asian option pricing and its consistent effective error estimates are obtained by making higher-order expansion.Further,the type of stochastic volatility model which includes fast-slow alternate multiple scales of perpetual American option pricing problem is discussed.The elliptic equations satisfied by option pricing is obtained by using Feynman-Kac formula.Applied the singular perturbation method,the asymptotic expansion of perpetual American option pricing and the uniformly valid error estimation is achieved;Furthermore,extended to the case of general American options,the stochastic volatility model of the general two-parameters American Option Pricing is discussed.The volatility is based on the fast time scale and the slow time scale which is used to conform the fast and slow system.By Feynman-Kac formula,the parabolic differential equation of the general two-parameters American Option Pricing is derived.Acorrding to the singular perturbation method,the asymptotic solution of the general American option pricing with two parameters and the uniformly valid error estimation by making higher-order expansion is achieved.The main contents are as follows:1.The model of Asian option pricing is applied to electricity territory and a stochastic volatility model of a class of one dimension electricity Asian option pricing with single parameter is discussed.The singular perturbation method and making higher-order expansion is applied to improve the accuracy of the solution.Acorrding to De Giorgi method,the asymptotic solution to its Black-Scholes equation and its uniformly valid error estimation is obtained.2.In the case of scalar,the two parameters model is introduced to better describe the real futures transaction.The pricing problem of a kind of two parameters Asian option is discussed.Taking the mutual influence between the parameters into account,the singular perturbation method is applied to option pricing by using the multi parameter combined asymptotic expansion.The asymptotic solution of the one dimensional two parameters Asian option pricing and its consistent effective error estimates are obtained by applying De Giorgi iterative technique.3.The model of the Asian option pricing with two parameters is extended to higher dimensional case.The pricing problem of a class of two parameters high dimension Asian option pricing is discussed.In the vector case,the Asian option path dependent way in the sense of scalar is no longer applicable.Assuming all risky assets without coupling conditions,high dimension Asian option path dependent way is defined for the first time in the vector case.The Asian option path dependent type way is generalized to the vector case.A parabolic partial differential equation satisfied two parameters high dimension Asian option pricing is obtained by using Feynman-Kac's formula.Acorrding to singular perturbation method,the asymptotic solution of high dimension Asian option pricing and its consistent effective error estimates are obtained by making higher-order expansion and using De Giorgi iterative technique.4.A class of perpetual American option pricing problem with two parameters is discussed,which is the free boundary problem for the permanent American option pricing.On the problem of the inner layer of the solution generated by the combined use of the option price,the multi parameter and higher order expansion of the option price is obtained by the free boundary.The asymptotic solution of the dual parameter permanent American option pricing is obtained.5.The model of permanent American option pricing problem with two parameters is extended to the general dual parameter American option.The pricing problem of a class of two parameters American option is discussed.The solution of the option pricing is existing in the inner layer,while the boundary layer is shown.By using the singular perturbation method,the asymptotic solution of the option price and the uniform effective error estimate are obtained.The complete structure of the option pricing problem is obtained,and the complexity of the solution is demonstrated.