On the Cheyette short rate model with stochastic volatility

Abstract

The purpose of this thesis is to compare the Hull-White short rate model to the Cheyette short rate model. The Cheyette short rate model is a stochastic volatility model, that is introduced to improve the fit of the implied volatility skew to the market skew. Both models are implemented with piecewise constant parameters to match the term structure. We calibrate the Cheyette model to the EURO, USD and KRW swaption markets and compare the calibration results to the Hull-White model. We propose an efficient implementation method to speed up the calibration process. In general we see that the Cheyette model gives indeed a better fit, in particular for the EURO and KRW markets. The models with calibrated parameters are used to price exotic interest rate derivatives by Monte Carlo simulation. Comparing the results of the Cheyette model to the results of the Hull-White model, can give insight in the skew and curvature impact on exotic interest rate derivatives. We consider digital caplets, digital caps, range accrual swaps, callable range acrruals and a callable remaining maturity swap. The price impact on digital caplets and digital caps are in line with static replication. By this we mean that the prices computed with static replication are better matched by the Cheyette model than by the Hull-White model. For the callable range accrual on LIBOR we have to be more careful, since a one-factor model cannot be calibrated to two market skews per option maturity. This implies that the price of the underlying range accrual is not in line with static replication, since we calibrate to co-terminal swaptions, while the underlying depends on the cap market. For the callable remaining maturity swap we do not encounter this issue, since the underlying depends on the same co-terminal swaption skews. For a callable RMS we observe that the Hull and White model underestimates the option price, compared to the Cheyette model.