Many financial derivatives contain the provision of the callable feature which allows the issuer to buy back the derivative at a predetermined call price, while the holder of a derivative with American early exercise privilege may choose to exercise his derivative rather than selling it back to the issuer upon call price. In the thesis, we examine the optimal calling policy for the issuer so that the value of the derivative is minimized among all possible calling policies. Also, we examine the effects of the callable feature on the early exercise policy for the callable American call option....[ Read more ]

Many financial derivatives contain the provision of the callable feature which allows the issuer to buy back the derivative at a predetermined call price, while the holder of a derivative with American early exercise privilege may choose to exercise his derivative rather than selling it back to the issuer upon call price. In the thesis, we examine the optimal calling policy for the issuer so that the value of the derivative is minimized among all possible calling policies. Also, we examine the effects of the callable feature on the early exercise policy for the callable American call option.

In the thesis, we focus on the case that the call back provision is activated in the whole option's life or limited to the part of the life. For the cases where the call provision ends at expiration, we found that the American call with callable feature is a hybrid of the American option and the European barrier option. The model can be divided into different time intervals. The formula of the option price in each time interval is expressed in integral form and can be fully analyzed. Also, the early exercise policy is constructed. The critical asset value of the callable American option is a composite function of the critical asset value of the non-callable American option and the value K + X where K is the call price and X is the strike price. In the case that the period of call provision ends before the expiration (at τlow), the critical asset price increases and the option value may overshoot K before τ = τlow. Once at τ = τlow, the call option will be called back whenever the asset value reaches S̃ which is below K + X. The critical asset price at which the option will be called back at K increases monotonically until it hits K + X at τ = τ̃. For the valuation of the option price, we cannot obtain an analytic formula for the option price in [τlow, τ̃]. It is interesting to observe that the option price with longer time to expiration may worth less than that of shorter life counterpart.

The numerical algorithms for the valuation of American call with callable fea-ture, the recursive integration method, the Crank-Nicolson scheme and binomial method are also presented. We found that they all show a significantly high level of accuracy. However, the Crank-Nicolson scheme and binomial scheme show better advantages over the recursive integration method in terms of programming efficiency and ease of implementation.