Valuation of Callable Options and Structures
February 10, 2010
Over the last ten years callable structures and options have become quite popular with both the banks as well as the investors. This has especially been the case with interest rate options and structured products. What was amazing was that even though most interest rate callable structures lost money for the investors, they loved them simply because they were cheap - the callable structures were sometimes a lot cheaper than their non-callable counter-parts.
So, what are callable options and how do we value them? If the writer (seller) of the option has the right to cancel the option at a pre-determined price and time in future then the option becomes a callable option.
In essence, the buyer of the option enters into a second contract with the same counter-party whereby the contract requires the buyer to give up the option for a fixed amount (which the seller pays to the buyer) as well as it gives the seller the right to cancel that deal when it matures.
What happens is that when the value of the option goes down the seller will cancel the contract but if the value of the option keeps going up then the seller will let the contract mature and will buy back the option from the buyer for the fixed amount. Therefore, the seller is exchanging the fixed amount for an option and hence this second (option) contract is for exchanging a fixed amount for an option. It is an option on an option. Thus, in the second contract the buyer of the option is receiving a fixed amount for selling the "option on the first option" to the seller.
In short, a callable option can be decomposed into a vanilla call plus a short compound call option.
The buyer of a callable structure - the investors' position - is going long a call option on the underlying (equity index, interest rate, etc.) and simultaneously short a compound call option on the same underlying. He is buying a vanilla call (on the underlying) from the seller and at the same time selling a compound call, i.e. call option on the call option, (on the same underlying) to the seller. The premium he receives from selling a compound call option to the seller cheapens the price of the vanilla call option that he buys on the underlying.
It is pretty straight forward to value a compound call option. One can use closed for solution or any of the numerical techniques.
Essentially - and this point is quite obvious from the above construction of the payoff - by giving the seller of the option the opportunity to buy it back from him at a per-determined price the option buyer implicitly forgoes his profit. Obviously, if the option moves in the money there is a great chance, if not a certainty, that the option seller will call the option back. Of course, ultimately the strike price of the compound call will influence the decision of the seller to call back the option.
References: Structured Equity Derivatives by Harry M. Kat
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