Efficient Monte Carlo simulations of pricing captions using Libor market models

Includes bibliographical references.The cap option (caption) is one of common European exotic options discussed in literature. This (interest rates) exotic option has no closed form solution and its accurate pricing and hedging in a volatile market is a challenge for traders. The reason for this is that, comparatively, the behaviour on an individual interest rate is more complex than that of a stock price. To price any interest rate product, it is essential to develop an interest rates model describing the behaviour of the entire zero coupon yield curve. The equity and yield curve, respectively, relate to the difference in the dynamics of a scalar variable and vector variable. Moreover, captions are second order with respect to the discount bonds in that they are options on caps (which are also options on bonds). These reasons make it of particular interest to study efficient numerical solutions to price captions. Monte Carlo simulation provides a simple method for pricing this option, and a suitable interest rate model to use is the Libor market model. The approach of describing the behaviour of the entire zero coupon yield curve, in the era post the 2007 credit crunch crisis, is what is called a standard single-curve market practice, and Part l of this work is based on it. . After introducing the framework for option pricing in the interest rate market, the theory and implementation procedure for Monte Carlo simulation using Libor market models is described. A detailed analysis of the results is presented together with a sensitivity analysis, and finally suggestions for efficient pricing of captions are given. In Part II we review the recent financial market evolution, triggered by the credit crunch crisis towards double-curve approach. Unfortunately, such a methodology is not easy to build. In practice an empirical approach to price and hedge interest rate derivatives has prevailed in the market. Future cash flows are generated through multiple forwarding yield curves associated to the underlying rate tenors, and their net present value is calculated through discount factors front a single discounting yield curve