Bond Option
We present a pricing model for bond options. Assuming that the bond price at the maturity of the option is lognormal, the model adopts the Black’s analytical closed-form solution. In market, both the underlying spot price of bond and the strike price are clean prices (quoted prices), while dirty prices are used in the price dynamic and the closed-form solution.
Let B(t) be a price process of a given bond, and T be a payoff maturity date. The bond option with the underlying B is a European type derivative security whose matured payoff at the settlement date is given by
Assuming that the bond price at the maturity of the option is lognormal, the prices of bond options at time zero are given by using the Black’s formula
Equation (6) actually calculates both cash forward price and cash futures price. Let A denote the accrued interest since last coupon date on bond delivered, and let C denote the conversion factor for delivering bond.
We test the bond option model in several different cases.
Case 1/2: present value of the coupons that will be paid during the life of the option is zero; Case 3/4: present value of the coupons that will be paid during the life of the option is not zero;
References: