Description: We consider Libor market model and calibration process. We estimate some interest rate derivatives such as Caps and Swaptions. We use Monte Carlo methods with appropriate dynamics under spot measure and forward measure. Imposing martingale discretization property, the same quantities are estimated again to see a contrast or discrepancy in light of confidence interval. Based on algorithms discussed in the paper, “Arbitrage-free discretizations of lognormal forward Libor and swap rate models” by Glasserman, P and Zhao, X 2000, the algorithms are implemented in excel VBA. Starting with current market data such as FRAs and Bond Prices, we describe steps involved to estimate the price of interest rate derivatives such as Caps and Swaptions, which would be beneficial to the practitioners in the industry.

Description: Constant maturity credit default swaps [CMCDS] are useful as hedging tools. In intensity model approach, the default time is defined as the first arrival time of the Poisson process. From the market quotes of CDS forward rates and bonds, we are able to numerically compute the default probabilities. Approximating CMCDS price depends largely on CDS forward rates’ volatilities and their correlations. This paper implements the price algorithm based on Brigo’s work [2006]. Starting with current market data such as CDS forward rates and nondefaultable bond prices, the paper describes steps involved to obtain the price CMCDS. The paper demonstrates the impact of convexity on the CMCDS price structure.