Strike price decrease

Determine the Value of an Embedded Call Option After determining the value of an option-free bond, we calculate the value of the option element. On the maturity, the value of the option is 0 because the bond s ex coupon value is 100 and equal to the strike price. In other nodes, the option has value if the strike price is less than bond s price. The strike price for each node is shown in Table 11.3. Consider also that the value of the option decreases as the bond approaches maturity due to the decreasing probability to redeem the bond. Figure 11.10 shows the value of a call option. The holder of the option has substantially the choice to exercise the option or wait a further period. Therefore, the value of the option if exercised is given by (11.7) ... 

Several factors affect the decision if exercising the option or not. The first one is the asymmetric profit-loss profile. The potential gain of the option holder is unlimited when the price of the underlying asset rises, and losing only the initial investment if the price decreases. The second one is the time of value. In fact, in callable bonds, usually the price decreases as the bmid approaches maturity. This incentives the option holder to delay the exercise for a lower strike price. However, coupon payments with lower interest rates can favour the early exercise. 

Determine the Value of a Callable Bond Since the option is held by the issuer, the option element decreases the value of the bond. Therefore, the value of a callable bond is found as an option-free bond less the option element according to Formula (11.3). For the hypothetical bond, the price is 106.13-2.31 or 103.82. This is shown in Figure 11.11. The binomial tree shows that at maturity the option free and callable bond have the same price, or 100. Before the maturity, if the interest rates go down, the callable bond s values are less than an option-free bond, and in particular when the embedded option is deeply in the money, the callable values equal the strike price according to the caU schedule. Conversely, when the interest rates go up, the option free and callable bonds have the same price. 

A number of factors dictate whether an option is exercised or not. The first is the asymmetric profit-loss profile of option holders their potential gain is theoretically unlimited when the price of the underlyir asset rises, but they lose only their initial investment if the price falls. This asymmetry fevors runnir an option position. Another consideration favorir holdir is the fact that the options time value is lost if it is exercised early. In callable bonds, the call price often decreases as the bond approaches mamriry. This creates an incentive to delay exercise until a lower strike price is available. Coupon payments, on the other hand, may fevor earlier exercise, since, in the case of a normal, nonembedded option, this allows the holder to earn interest sooner. 

The buyer has the right to buy the spread and benefits from the spread decreasing in value. The payoff has the form max (strike - spread, 0). This option pays out if the spread tightens below the strike level, a tightening spread would result in an increasing bond price. Therefore the credit spread call option provides a payout should the underlying bond position increase in value. 

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