The Research On CMS Interest Rate In Multi-Factor LIBOR Market Model

With the development of China's financial system,interest rate derivative products have gradually entered our field of vision.Interest rate derivatives with forward interest rates will become more prevalent in domestic financial markets.Based on the foundation of measure transformation theory and martingale theory,the second-order variance method is used to integrate the CMS interest rate into the framework of the LIBOR model,the analytical solution of the CMS interest rate is obtained and the negative situation of CMS interest rate is avoided.On this basis,the pricing formula of a series of CMS derivative products is derived by using the analytical solution of CMS interest rates,including the CMS digital range notes,CMS spread notes and simplified by using the Girsanov formula to simplify the analysis.In the process of research using Girsanov formula,the paper uses two different methods to compare,which provides investors with a choice of pricing process,which will help investors get a better return on investment.There are some innovations in my paper.Compared with the single factor LIBOR market model,the multi-factor LIBOR market model can better fit the market fluctuation rule.The paper uses the multi-factor LIBOR model to obtain the analytical solution of the CMS interest rate,and cleverly solves the problem that the CMS interest rate does not satisfy the logarithm Normal distribution of the problem,which for the latter part of the pricing of CMS derivatives provides a convenient.At the same time,the analysis formula of CMS derivatives is obtained,which avoids the Monte Carlo simulation in the process of pricing and saves investors time and energy.The use of Girsanov formula makes the relevant categories of products can be priced through the method in the paper,extending the scope of the model.The comparison of the two different forms of the Girsanov formula also makes it possible for investors to have a better choice in case of difficult parameter acquisition.At last,several fitting methods of model parameters are put forward,and the model can be finished better through parameter correction.