A comparison of interest-rate models, application of range accrual note pricing

Abstract

The objective of this thesis is to apply the Hull-White model and CIR++ model to price the range accrual note by using Monte Carlo simulation practically. This thesis also studies the behavior of the model by providing the sensitivity of the note’s price, when changing the model’s parameters. As a conclusion, the method used in this thesis is well applied to price the range accrual note by using Monte Carlo simulation. Models’ parameters can be practically computed from the interpolated historical data which are daily 6M USD LIBOR and weekly U.S. swap curve. These models’ prices are little affected by changing their mean reversion and speed of mean reversion in case of low volatility, but they are highly affected by changing them in case of high volatility. In addition, the changing of range of strike rates highly affects the prices of range accrual note. The narrow range provides the note’s prices are lower than the wide range for all volatility cases. Moreover, range of strike rates which is near the movement of reference rate makes the note’s prices more sensitive than other ranges. Therefore, the initial short rate highly affects the range accrual note’s prices too. Lastly, the normal distribution function of Hull-White model makes the range accrual note’s prices are higher than the chi-squares distribution function of CIR++ model.