The Valuation of Bond Futures and Implied Quality Options

The thesis mainly based on the concept of exchange options combining the martingale pricing theory to deduce the valuation of bond futures and quality options under risk neutral probability, and then adopted the Hull-White two-factor model to introduce the pricing process of the bond futures and quality options on interest rate tree.
Since the paper published by Ritchken, and Sankarasubramanian(1992) which used HJM model to compute the value of the quality options, the restriction of constant interest rate has been removed. However, the operating elasticity is limited due to the lack of Markovian property with HJM model. Therefore, in 1997, Lin and Chou chose Hull-White single factor model to implement the computation of the quality options. The drawbacks of this method is that the single factor model can not fit some sophisticated volatility term structures. In addition, it is not proper to use the zero coupon bond formula which derived by Kijima and Nagayama(1994) combining the Hull-White single-factor model. Only when the volatility parameter( ) is set to be constant, the framework would be correct. In other words, the zero coupon bond formula which derived by Kijima and Nagayama is the special case of the one(Lee and Hsieh) in the Hull-White single-factor model when the volatility parameter ( ) is set to be constant.
On the interest rate model, the Hull-White single factor model with time-dependent volatility parameter can fit the initial volatility term structure, but it causes the non-stationary problem instead. Hence, this study opts the Hull-White two-factor model to proceed the valuation under the conditions of the stationary property and the abilities of fitting the term structures of interest rate and volatility.
To sum up, there are two conclusions in this study:

1.According to the results of proposition 1 and 2 in section 3.2, it can show that the zero coupon bond formula derived by Kijima and Nagayama(1994) is not the general case. In fact, it is the special case of the one in the Hull-White single- factor model when the volatility parameter( ) is set to be constant.
2.Because the Hull-White two-factor model possess the stationary property and the abilities of fitting the term structures of interest rate and volatility, it can improve the accuracy and efficiency of the pricing; furthermore, in the sensitivity analysis, it found that the parameters of the second interest rate factor in Hull-White two- factor model have more significant effects on the value of the quality options than the first one.