Effects of Callable Feature on Early Exercise Policy

Convertible bonds and American warrants commonly contain the provision of the callable feature which allows the issuer to buy back the derivative at a predetermined recall price. Upon recall, by virtue of the early exercise privilege embedded in an American style derivative, the holder may choose either to exercise his derivative or to sell it back to the issuer. Normally, there is a notice period requirement on the recall, that is, the decision of the holder to exercise or to receive the cash is made at the end of the notice period. Also, the period of recall provision may cover only part of option's life. In this article, we examine the effect of the callable feature (with the notice period requirement) on the early exercise policy of a callable American call option. The optimal calling policy for the issuer is explored where the value of the American option is minimized among all possible recall policies. Without the notice period requirement, the critical asset price boundary of the callable American call is identical to that of the American capped call. When the notice period requirementis imposed, the critical asset price (considered as a function of time to expiry τ) first increases with τ,reaches some maximum value, then decreases with τ. Several approaches of designing numerical algorithms for the valuation of the callable American option are also presented. This revised version was published online in November 2006 with corrections to the Cover Date.