Risk Sensitivities of Bermuda Swaptions
Bank of America Working Paper
45 Pages Posted: 24 Mar 2003
Date Written: November 1, 2002
We present new theoretical results for risk sensitivities of Bermuda swaptions, and derive new representations for them. We apply these results to the problem of risk sensitivities computation and derive algorithms that perform the task much faster and more accurately than the traditional approach. Computation of risk sensitivities to market and model parameters (deltas, gammas, vegas) is one of the most important applications for any model. In most practical situations, the Greeks are computed numerically by shocking appropriate inputs and revaluing the instrument. The time needed to execute such a scheme grows linearly with the number of Greeks required. Our approach allows one to compute any number of Greeks for a Bermuda swaption in nearly constant time. Computational advantages versus the standard approach are significant, with time needed to compute a large number of sensitivities reduced by orders of magnitude. Our approach explores symmetries in the structure of Bermuda swaptions, and is essentially model-independent. The approach is based on a newly discovered set of recursive relations between different sensitivities. The recursive relations allow us to represent sensitivities in a number of interesting ways, in particular as integrals over the "survival" density. The survival density is obtained as a solution to a forward Kolmogorov equation. This representation is the basis for practical applications of our approach.
Keywords: Bermudan swaptions, fast greeks, risk sensitivities, interest rate derivatives valuation and hedging, BGM, Cheyette, PDE methods
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