The Pricing Of Extreme Option Under Wishart Stochastic Volatility Model

The rational pricing of options has been one of the core subjects of the financial industry,while the option pricing model is the most common and important method to study option pric-ing.The earliest option pricing model is the classic Black-Scholes option pricing model.In this pricing model,it is assumed that the yield of the underlying asset is obey the logarithmic nor-mal distribution and its instantaneous volatility is constant.However,a large number of empirical results confirm that the pricing model is not in line with the actual market movement behavior characteristics,and has great limitation,especially the instantaneous volatility is not observable in practice.So it is imperative to improve the Black-Scholes option pricing model,one of the typical improvements is to assume that the instantaneous volatility satisfies another stochastic volatility process associated with the underlying asset,namely the stochastic volatility model.The widely used stochastic volatility model is set up by Heston,which use the mean square root process to describe the process of the instantaneous volatility.Because the real financial market is changeable,it will cause the underlying asset returns to occur,such as the time when the time is fast,and the time is small.therefore,it is difficult to describe these phenomena in a simple transient volatility process.Therefore,to study the volatility and risk characteristics between multiple factors,it is particularly important to construct a multivariate volatility model.In this paper,the used pricing model is multidimensional Wishart stochastic volatility model(WSVM),the random volatility of the set assets in the model is a covariance matrix obeying the Wishart process,and the parameters in the model are multidimensional matrices.Extremum Option is an option with a multi-asset portfolio,compared to standard options,the biggest feature is that investors can get the maximum benefit or minimize the losses,that is why investors love it,however,it is very important to study the pricing and analyze the price changes of Extremum Option.This paper mainly studies the pricing of Extremum Option under Wishart stochastic volatility,using Ito? formula,Feynman-Kac theorem,partial differential equation,the joint characteristic function of multidimensional random variables,Girsanov measure transformation and other random analysis methods,and the Fast Fourier transform(FFT)inverse transform,Derive the strike price of the same two assets Minimum European call Option,two assets Maximum European call Option and large n assets European call option pricing formula.On the numerical simulation,we use matlab software calculate and analyze two assets European call option price about volatility,mean reversion,the volatility of dependencies,etc.The result shows that the price of the European maximum price is increase function of the fluctuation factor,the average recovery speed,the volatility of the fluctuation rate,the impact of the four volatility factors more than the two on option pricing,Compared with the Black-Scholes model,the price of this model is larger,and the impact is relatively small.This indicates that the model adopted in this paper is more able to describe the random characteristics of volatility in financial markets.Secondly,the two asset European extremum options were extended to the form of power extremum options,and the pricing formula was derived and the dependence of the power index on the option price was derived.The results showed that the smaller the ? value,the more favorable the investors were to hedge their hedging and avoid the risk.In addition,the long-termvolatility and short-term volatility are different from the impact of the price of European maximum call option.So in the real financial market,and investors should not only pay attention to long-term volatility,but also should pay attention to short-term volatility and other related parameters caused by the share price volatility,and choose the appropriate option.The Wishart Stochastic Volatility Model under the extreme value option pricing problem is suitable for the actual financial market,which provide a more powerful theoretical basis and methods for extremum option pricing research,as well as it provide stronger theory basis for risk managers to make effective judgment.