Asian Vulnerable Option Pricing Based On Heston Stochastic Volatility

With the increasing trend of economic globalization,the risk management of financial markets has become an increasingly important and non-negligible issue.As an important tool for risk management in the modern financial market,option pricing theory and application have also developed rapidly.In addition to the traditional well-known European options and American options,a large number of derived exotic options have emerged,such as lookback options,barrier options,Asian options,Bermuda options and so on.The Asian option is one of the very important exotic options.This paper will also mainly consider the pricing of Asian options under the condition of credit risk.This paper will review the classic Asian vulnerable option model,weigh and compare two classic credit risk models—the structured model and the reduced model,and choose the structured model to model the pricing of Asian options under credit risk.In the calculation process of the Asian vulnerable option pricing formula,the mathematical knowledge of financial stochastic analysis,probability theory and measure theory,etc.,such as measurement transformation,the mutual transformation relationship between probability distribution function and characteristic function,etc.is used to solve the problem,and finally the explicit solutions for Asian vulnerable options under risk neutral measure is obtained.Asian option is a path-dependent exotic option,which makes it difficult to solve its pricing problem,and the process and result of solving the pricing formula are quite complicated.Although there have been many researches on Asian vulnerable options and many solutions have been proposed,such as partial differential equation method,Monte Carlo method and arithmetic mean Asian option approximate solution method,there is still no consensus expression.Starting from the expression of the pricing formula,this paper adopts the method of measure transformation to transform the expressions under various measures to facilitate the final solution,and also converts various distribution functions and probability sizes into the solution of characteristic functions,which further simplifies the calculation of the pricing formula of Asian options,the results of Asian vulnerable options are deduced,which provides a new method and new idea for the pricing of Asian options under credit risk.At the same time,the numerical calculation and correlation analysis of the model in this paper are carried out to obtain the variation of the pricing formula of the geometric mean Asian vulnerable option with the parameters in the model,which proves that the model is effective in the actual display market.And it has great performance and feasibility.Different from the previous pricing of Asian vulnerable options,the restriction of constant volatility is released,and the Heston stochastic volatility process is introduced into the price process equations of stock and company values.At the same time this makes the model of Asian vulnerable options more in line with the reality of modern financial markets,and the results obtained are more in line with the real market conditions.In the process of solving the Asian vulnerable pricing formula,this paper abandons the commonly used partial differential equation solution method,thereby avoiding the dimensionality reduction of partial differential equations and various complex mathematical processing,and instead adopts the method of solving the characteristic function to solve the pricing results.Each part in is associated with the corresponding characteristic function,which simplifies the calculation.