The Valuation Of Swaption With Counterparty Risk Under A Markov Chain

Recently, with the development of China’s economy and the upgrading ofindustrial structure, the financial derivatives market is growing rapidly. Derivativespricing and risk management become more and more important, what’s more, we payclose attention to credit risk. Above all, combining with her professional backgroundin mathematics and the interest of financial engineering, the author deeply study thecomplex model, which is used to describe the changing economic environment. Thespecific contents of this paper are as follows:Firstly, we studied the theory of the European option pricing. Then we use theBSM option pricing model and the two binomial tree option pricing model as theresearch object, and do the empirical analysis on the influence of parameters ofEuropean option pricing.Secondly, in order to describe the relationship between spot rate andmaturity, the author analyses the affine term structure of interest rates on assetpricing, hedging and risk management. In this paper, we use the static NSS affineterm structure model to produce the spot rate of each periods:1year,2years,3years,4years,5years,7years,10years. Next, we use the two factor CIR affine termstructure model and combine with Kalman filter and the maximum likelihood methodto process the spot rates data. As a result, we have estimated Parameters，likes i, i,i, i.Then, based on two factor CIR affine term structure model, we use the datagenerated by Kalman filtering method to achieve comparison of the spot interest rateand real interest rate. Generally speaking, we can find that the short rate isproportional to the real rate, and the estimation of1years,2years and7years effectswell. Therefore, the CIR model can accurately describe the behavior of the affine termstructure of interest rates in China’s bond market.Finally, we study the valuation of swaption with counterparty risk. Based on theShanghai stock exchanges’panel data fixed rate bond transaction information fromJuly29,2005to July30,2010in each month of the last trading day and rating agency-Moody’s credit rating data, we introduce the model of common and rating specificfactors as an affine term structure process, and build the valuation model of swaptionwith counterparty risk under a Markov chain model. At last, we show the impact ofcredit rating of counterparty on the price swaption. Due to the professional span and time limitation, we can’t deal with the paneldata for transition probability matrix in the Markov model, which will affectthe empirical analysis. Above all, we will finish the data processing for transitionmatrix in Markov model for my future work.