Valuation of Exotic Interest Rate Derivatives - Bermudans and Range Accruals

Abstract:     
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 issues involved in valuing exotics. We review valuation issues for interest rate derivatives in general, and for caps, floors and swaptions. We outline a pricing methodology and apply it to Bermudan swaptions, range accruals, callable range accruals, spread options and callable spread range accruals.

Outline:
- Review of interest rate modeling
- Handling of vanilla options
- - Forward Libor and swap rates
- - Caps and Floors
- - Swaptions
- - Cap stripping
- - Smile lifting
- Bermudan valuation
- - Hedging Bermudans
- - LGM model specification of the HW model
- - Pricing cashflows and options under the LGM model
- - Model calibration
- - Numerical methods
- Digital options
- - Pricing via vanillas.
- Range accruals
- - Pricing as a portfolio of digitals
- - Convexity adjustment - Change of measure and approximation
- Callable range accruals
- - Pricing under the one factor LGM model
- - - Model calibration.
- - - Use of control variates (adjusters).
- - Calibration and pricing under the two factor LGM model
- - - Model calibration.
- Spread range accruals
- - Pricing under the two factor LGM model.

Keywords: HJM, LGM, HW, Gaussian, linear, Markovian, Hull-White, swap, swaption, Bermudan, range, range accrual, cap, caplet, floor, digital, stripping, convexity, convexity adjustment, adjustment, adjusters, control variate, interest rate modeling, interest rate exotics

JEL Classifications: C63, E43, G12, G13

Working Paper Series