The Pricing Of Financial Securities Based On SVI-AJD Process

The pricing model of financial assets is the foundation of asset pricing and calculation of credit portfolio VaR(value at risk)and ES(expected shortfall).The setting of pricing model needs to take into account the characteristics of financial asset price fluctuation.Generally,there are four significant phenomenon in financial asset price fluctuation.First,the probability density function of financial asset return exhibits leptokurtosis;Secondly,time series of financial asset returns shows heteroscedasticity:the variance changes over time stochastically and uncontrollably.The representative phenomenon is the volatility smile.Furthermore,there exist rare events(like a financial crisis)in financial markets that affect asset prices;In the end,the impact of stochastic interest rate has become increasingly prominent.As more and more structured financial products have been created in the financial market,the financial asset pricing model should not only take into account the above four points,but also has a wide range of pricing capabilities and multi-dimensional expansion capabilities.This article includes the stochastic volatility(SV),stochastic interest rate(SI)and double exponential jump into the affine jump diffusion(AJD)framework and proposes the SVI-AJD(Stochastic Volatility&Interest rate-AJD)model.The model has the effective parameter estimation method,which can integrate the market risk,credit risk,and have strong ability of multidimensional expansion.Starting from the SVI-AJD model,this paper obtained the pricing characteristic function of financial derivatives,which can achieve accurate pricing be of European options,bonds and other financial derivatives.The pricing characteristic function has analytic expression,some simple financial assets,such as bonds,can be directly carried out by pricing characteristic function;but other complex financial derivatives,like European options,have the pricing formula which is derived by the Fourier transform of the pricing characteristic function.In this aritcle,the pricing formula of European option is deduced.The formula is solved using numerical method of Fourier transform,with high speed and accuracy.In order to test model accuracy,this article deduces the higher-order moments of basic state process variation and K-S test formula.The derivation of higher order moments is similar to the derivation of VaR and ES.The conclusion can be directly applied to the calculation of VaR and ES in credit portfolio through multidimensional expansion and proper modification.The parameter estimation of S VI-AJD model is a significant part of actual pricing and risk measurement.This article deduced Hidden-Variable MCMC parameter estimation method which can effectively solve the problems that stochastic volatility and double exponential jump brings.As is proved,this method has unique.In order to test model accuracy,this article deduces the higher-order moments of basic state process variation and K-S test formula.Based on the pricing formula and the Hidden-Variable MCMC,this article chooses SSE(Shanghai Stock Exchange)50ETF and Overnight(O/N)SHIBOR as the original data,and carries out the pricing of all 50ETF call and put options expiring in June 2016.The pricing accuracy of SVI-AJD model is much higher than that of Black-Scholes and Kou(2002)[1]models.Then,this article studies the goodness-of-fit of SVI-AJD model from three perspectives:Higher-order moments of the basic state process variation,K-S test and the curve features of probability density functions of underlying asset return.It finds out that the SVI-AJD model has the highest goodness-of-fit and the best leptokurtosis feature compared with BS and Kou model.Effectively measuring the credit risk of credit portfolio with large amount of correlations is a difficult task.At the end of this article,credit risk is incorporated into the SVI-AJD model,and it is used in Credit Portfolio VaR and ES value measurement,which enhances the scope of the application of the model.The VaR and ES can be calculated by the Fourier transform of the pricing characteristic function,which greatly improves the efficiency of risk measurement.