Libor Market Models With Stochastic And Regime-Switching Volatility And CMS Spread Option Pricing

With the development of interest rate marketization and the liberalization offinancial system, the forward interest rate derivative products will become more andmore prevalent in the domestic financial market. Therefore, the effective modeling ofthe stochastic process which forward interest rate obeys, and the pricing for its relatedderivatives is worth to study. And most of the stochastic process which forward interestrates obeys is mainly used Libor market model. As the defects of standard Libor marketmodel, as well as the limitations of extended model of existing literature, the defects ofexisting forward interest rate model is corrected to make it closer to the market volatilitycharacteristics, is the focus of the current forward rate pricing model studies. CMSspread options as an important class of options in the CMS product, the productstructure were analyzed in this study are derived using forward rate pricing model tostudy its practical significance.Therefore, this paper discusses the contents of the following sections:Firstly, the background and significance of the object were studied, and the existingliterature at home and abroad were reviewed. Thus the Libor market model withstochastic and regime-switching volatility was introduced.Secondly, the standard Libor market model and the swap rate market model wereintroduced. This model is the basic model in this paper. After the introduction of thestandard Libor market model and the standard interest rate swap market model, theLibor market model with stochastic and the regime-switching volatility were introducedas well as the swap rate market model.Third, using the market quotes of interest rate caps and interest rate swaptions forlocal volatility and instantaneous correlation parameters calibration were discussed.Meanwhile, after the models were discreted, using the Markov chain Monte Carlosimulation method for stochastic and regime-switching volatility parameter estimationwere introduced.Fourth, under the assumption of the standard interest rate swap market model andstochastic volatility swap rates and stochastic volatility regime-switching market modelrespectively, using the Feynman-Katz theorem for solving characteristic function of CMS and the use of inverse fast Fourier transform method eventually solved the CMSspread options pricing formula were discussed.Fifth, the empirical part of this study. In this part, the results of theoreticalderivation were tested by market data, simulation results were compared and thetheoretical price of CMS spread options were solved.Finally, this study summarizes the research results and prospects. Summarizes thetheoretical derivation and empirical analysis in this paper. The future research directionsare suggested.By summarizing the existing literature and the relevant results of theoretical andempirical analysis, this study eventually drew the following conclusions:First, the effect of empirical results which were used by Monte Carlo simulationshow that the Libor Market Model with stochastic and regime-switching volatility isobviously better than the standard Libor market model. Secondly, using the marketquotes of interest rate caps and interest rate swaption for local volalitity parameterscalibration introduced the current information in the market; using Markov chain MonteCarlo simulation approach for stochastic and regime-switching volatility parametersestimation introduced the history information in the market. The empirical results alsoshow that this method generates a good fitting effect. Finally, using Feynman-Katztheorem and fast inverse Fourier transform method solved the theoretical CMS spreadoptions pricing formula. Compared with the Monte Carlo simulation method, theanalytic methods for solving options prices obviously have advantages in computingtimes. The empirical results also show that the CMS spread options pricing formulasolved by this study has a good empirical results.