Using Sabr-Libor Market Modelto Pricing CMS Spread-Rrange Note

With the development of financial liberalization, interest rate structured products, especially development of CMS spread-range note is particularly rapid spread. This product plays a significant role in the finance and investment, hedging, etc., so is developing rapidly all over the world. However, investors observed that the product has good returns, while often overlooked huge risk that the product contains potentially, especially in times of economic downturn, adverse changes in interest rates cause the product difficult to reach the expected benefits, often bring investor losses. Meanwhile, in terms of issuers, the kind of product structure is more complex, temporarily does not have a complete and effective pricing system, resulting in a potential loss. It would also make investors underestimate the risk of the products. So studying these products right valuation methods and techniques for the pricing and risk management applications have important theoretical and practical significance.For research products valuation, this paper selected complex European CMS spreads-range note as objects of pricing studies, decomposing the intrinsic value of the products. At the same time the study of the underlying assets of these products, we use SABR-LIBOR model to simulate changes in the path of the underlying assets and use the MCMC methods of parameter estimation, while using the Monte Carlo simulation technique to price the value, and introduce Monte Carlo methods number of simulations to convergence analysis. On this basis, through sensitivity analysis, we discuss research methods to assess the product’s risks and make recommendations to investors and issuers.First, the previous literature about European CMS spreads-range note commonly use method of pricing analytical solutions. And this paper use copy decomposition financial engineering principles, decomposing the value of that type of product and obtaining conclusion:CMS spread-range note is usually composed of a digital options and a zero-coupon bond.Secondly, based on the decomposition of the pricing, we need study the characteristics of the underlying asset LIBOR rates. The feature of LIBOR rate is added to the interest rate model and to fit the term structure of interest rates by entering the beginning of the interest rate curve. On the basis of the interest rate model, price and historical data on the use of products in the market, we use the Blank backstepping formula and MCMC methods to estimate model parameters. Then based on Interest rate model, simulate changes paths in interest rates through the Monte Carlo simulation method. And compare the fact that stochastic volatility is not added to the normal Libor Market model with the fact that the stochastic volatility is added to the normal Libor Market model and obtain conclusion:LIBOR market model based on stochastic volatility can better fit the reality of value than stochastic volatility not join the LIBOR market model, and more authenticity, so pricing.is more accurate. Then we use Monte Carlo simulation method to price CMS spread-range note, and use simulation number to analyze the convergence of Monte Carlo simulation method, then concluded:In the simulation times of more than ten thousand times, this product value tends to converge.The last study is parameter sensitivity analysis based on the use of the pricing method, which means that the changes in the parameters affect the value of the product. The article select the beginning of this forward rates, the volatility of local as parameter to sensitivity analysis, obtaining the following conclusions:First, changes in the value affected by parameter change is not obvious, showing that the model has a certain stability and practicality. Second, investors need to predict changes in parameters according to the changes in the market environment, to select the appropriate investment strategy.According to literature from all over the world plus theoretical and empirical research can draw the following conclusions:Join stochastic volatility LIBOR market model can better describe the LIBOR rate variation, more accurately reflect the true path of interest rate changes; With increase the number of simulations, product value tend to convergent, indicating that the pricing method has good stability; the change of parameters based on changes of environment has significant impact on market value of the product and it will thus offer investors a good investment advice.