Zero-coupon bond call option, example

Example of a Zero-Coupon Bond Call Option with Ibslcok... 

Assume now that the one-year zero-coupon bond in the example has a call option written on it that matures in six months (at period 1) and has a strike price of 97.40. FIGURE 11.5 is the binomial tree for this option, based on the binomial lattice for the one-year bond in figure 11.4. The figure shows that at period 1, if the six-month rate is 5.50 percent, the call option has no value, because the bond s price is below the strike price. If, on the other hand, the six-month rate is at the lower level, the option has a value of 97.5562 - 94.40, or 0.1562. 

We now revisit the earlier Vasicek example for short interest rates to consider the case where the underlying bond pays an annual coupon at a 5% rate (p = 0.05), all the other characteristics remain as before. In order to calculate the call price of the coupon-bond European option first we need to calculate the interest rate such that the present value at the maturity of the option of all later cash flows on the bond equals the strike price. This is done by trial and error using equation (18.48) and the value we get here is = 22.30%. Next, we map the strike price into a series of strike prices via equation (18.50) that are then associated with coupon payments considered as zero-coupon bonds and calculate the value of the European call options contingent on those zero-coupon bonds as in the above example. The calculations are described in Exhibit 18.7. 

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