Risk Sensitivities of Bermuda Swaptions
Bank of America Working Paper
45 Pages Posted: 24 Mar 2003
Date Written: November 1, 2002
Abstract
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
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Computing Deltas of Callable Libor Exotics in Forward Libor Models
-
Partial Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks
By Christian P. Fries and Mark S. Joshi
-
Localized Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks
-
By Mark S. Joshi and Terence Leung
-
Fast Monte-Carlo Greeks for Financial Products with Discontinuous Pay-Offs
By Jiun Hong Chan and Mark S. Joshi
-
Conditional Analytic Monte-Carlo Pricing Scheme of Auto-Callable Products
By Christian P. Fries and Mark S. Joshi
-
Fast and Robust Monte Carlo Cdo Sensitivities and Their Efficient Object Oriented Implementation
By Marius G. Rott and Christian P. Fries
-
Minimal Partial Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks
By Jiun Hong Chan and Mark S. Joshi
-
First and Second Order Greeks in the Heston Model
By Jiun Hong Chan, Mark S. Joshi, ...