Valuation of mortgage backed securities (MBSs) and collateralized mortgage obligations (CMOs) is the big science of the financial world. There are many moving parts, each one drawing on expertise in a different field. Prepayment modeling draws on statistical modeling of economic behavior. Data...

Exotic interest rate derivatives are hard to value. Care must be taken to make sure that sources of volatility that impact the contingent claim are properly modeled, and that appropriate relationships are maintained between the underlying rates involved.In this presentation, we outline the...

We review and detail the causes of errors in numerical differentiation, including roundoff error, convexity error, cancellation error and correlated errors. We discuss methods for improving accuracy, including step size selection and smoothing techniques, as well as a number of approaches...

Lecture notes for a short course on FX option valuation. Includes: - Mathematical framework for FX valuation - Handling the smile and term structure for vanilla options (calls and puts): --- Interpolation issues and techniques --- Handling business time --- Handling market conventions - Pricing...

Tutorial on valuation of mortgage backed securities and collateralized mortgage obligations, including: - Structure of the mortgage market - Prepayment modeling - OAS analysis - Interest rate modeling - Numerical methods - Parallelization

We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of at-the-money and out-of-the-money options as the option maturity approaches zero. We show that these prices converge...

We consider the hedging of derivative securities when the price movement of the underlying asset can exhibit random jumps. Under a one factor Markovian setting, we derive a spanning relation between a long term option and a continuum of short term options. We then apply this spanning relation to...