Pricing and hedging interest rate caps: With the LIBOR, Hull-White, and G2++ interest rate models - Evidence from the Danish market

Lenn Bloch Mikkelsen

Student thesis: Master thesis


This thesis investigates the pricing and hedging accuracy of alternative interest rate models. The models include the LIBOR market model, the Hull-White model and the G2++ model. Based on market data of Danish interest rate caps this thesis provides empirical evidence on the relative performance of the interest rate models and, moreover, investigates how the instantaneous volatility in the LIBOR market model should be specified and whether an additional stochastic factor improves the performance of the Hull-White model. The LIBOR market model is represented using three different volatility parameterizations counting the Rebonato, Exponential and Constant volatility parameterizations. The G2++ model represents the two-factor Hull-White model. Inspired by the works of Gupta & Subrahmanyam (2005) the models are compared based on their ability to fit current market prices, price interest rate caps out-of-sample and hedge interest rate caps. The hedging accuracy is measured using a replicating portfolio strategy based on zero-coupon bonds. The results of the calibration to market prices show that the most accurate in-sample estimation is achieved with the LIBOR market model which is able to exactly fit market prices of interest rate caps. In addition, when pricing interest rate caps out-of-sample the LIBOR market model is more accurate at predicting future prices of interest rate caps compared to the Gaussian models (Hull-White and G2++). However, when measuring the hedging ability the results indicate that the Hull-White and the G2++ model provide more accurate hedging of interest rate caps than the LIBOR market model but on average the difference between the models is less than 1 basis point for a one-day rebalancing interval. Compared to the Hull-White model the two-factor model (G2++) provides more accurate calibration to interest rate caps as well as more accurate out-of-sample pricing. Furthermore, when hedging interest rate caps the G2++ model produces smaller errors compared to the Hull-White model. The results also show that the Hull-White model is consistently over-hedging short maturity caps. In relation to the LIBOR market model this thesis finds that specifying instantaneous volatility using the Rebonato parameterization produces the most accurate in-sample estimation and out-of-sample pricing of interest rate caps. The ability of the Rebonato parameterization to fit both humped and decreasing shapes of the term structure of volatilities leads to more accurate pricing compared to the Exponential and Constant volatility parameterizations. However, when measuring the hedging performance the results are inconclusive. The investigative work in this thesis involves a number of methodological considerations and the results are tested for robustness towards calibration method and bias in sample data. Two criteria are applied for model calibration; standard least squares and percentage least squares. The results show superior calibration using the standard criterion. Conclusively, the empirical evidence of out-of-sample pricing and hedging are in accordance with Gupta & Subrahmanyam (2005) who find that a LIBOR market model provides more accurate pricing and, moreover, that more efficient hedging is achieved with multifactor interest rate models

EducationsMSc in Applied Economics and Finance, (Graduate Programme) Final Thesis
Publication date2010
Number of pages94