Valuation and hedging of loan prepayment risk: an options pricing approach

Abstract

This thesis discusses loan prepayment risk and describes a binomial model that can be used to value and hedge this risk. Borrowers have an option to repay lenders before the respective loans reach maturity. In the particular case of fixed rate loans and mortgages, this poses risks to lenders. If prepayment occurs when market interest rates have declined, lenders are forced to replace the high interest loans with low interest ones, thereby reducing their net interest margin. The option to repay loans early is an American call option on a bond. Bonds with embedded options can be valued using a binomial interest rate tree. In this thesis, the Black Derman Toy binomial model is calibrated to the South African continuous term structure of interest rates and interest rate cap volatilities. Prepayment risk is then valued as the embedded call option for fixed rate loans of various maturities. Option greeks delta, vega and gamma are described and calculated. Various instruments that exist in the South African fixed income market and can be used to hedge prepayment risk are presented.