New Approach for the Pricing of Bond Option Using the Relation between the HJM Model and the BGM Model

In this paper, we propose a new approach for the pricing of bond options using the relation between the Heath-Jarrow-Morton (HJM) model and the Brace-Gatarek-Musiela (BGM) model. To derive a closed-form solution (CFS) of bond options on the HJM model with the BGM model, we first consider about basic concepts of the HJM model in which is hard to achieve the CFS of bond options. The second obtains the bond pricing equation through the fact that the spot rate is equal to the instantaneous forward rate. Furthermore, we derive the formula of the discount bond price using restrictive condition of Ritchken and Sankarasubramanian (RS). Finally, we get a CFS of bond options using the relation between the HJM volatility function

σ

f

(

t

,

T

) and the BGM volatility function

λ

(

t

,

T

) and give the analytic proof of bond pricing. In particular, we can confirm the humps in the pricing of bond call option occur while the graph of bond put option are decreasing functions of the maturity as the value of

δ

(tenor) and

σ

r

(volaitility of interest rate) are increasing with two scenarios. This result means a simple and reasonable estimate for the pricing of bond options under the proposed conditions.