Exotic option pricing question

[MarekB]

Hi guys, I thought that you might have faced with such a problem in the past and you’ll be able to give me some tips. I’m having a problem with pricing of an exotic contract which looks like an option with the following name: moving-strike barrier american option. The strike depends on the asset price on the market and the LIBOR rates.

Because this is OTC product, there are some non-trivial features here, naming the option buyer have the right to buy the underlying asset in a particular period of time, but if he won’t exercise it before the maturity (let’s call that maturity A), the option seller will then gain an option to sell it to the buyer for some small period of time until maturity B. The contract might be exercised before maturity A, but must be exercised until maturity B, so the contract will be settled, no matter what.

The first component (call option from the point of view of a buyer) is rather straight forward. I have priced that via binomial tree and Monte Carlo simulation and I’ve obtained almost the same results (positive value, difference 2 cents), but I’m thinking if I should somehow price the second feature and incorporate it in the final value (the one which will activate once the option buyer decides not to exercise the option before the maturity A)? To give you a better overview, I can tell you that under Monte Carlo simulation, the average option price from all values at particular dates are decreasing in time and at maturity A, in around 80% of cases the option value equals zero. Can I deal with such contract like in the case of an option contract (mainly in terms of pricing)? How to find fair value of that contract from the point of view of buyer and seller?

Any tips and feedback will be much appreciated.

Best,

Marek

 

[Keith Tan]

isn't this a compound option? taking conditional probability into account, you need another simulation to maturity B.

 

[MarekB]

Thanks for your input Keith!

Well, it doesn’t look like a compound option to me, at least not the standard one. After maturity B, the “option” to execute the contract changes from one counterparty to the another in contrast to the typical compound option. I put a quotation mark in a word of option, because we need to have in mind that the option before the maturity B must be exercised, it is just a matter of when it will be settled. The second part just doesn’t look like an option to me (more like a forward contract with option alike payoff), because the only one optionality here is when it will be settled.

How about that: can we assume that the counterparty which has a option to buy before the maturity A will be no matter what looking for executing the contract before the first maturity date? After the maturity A, it will lose the optionality to execute the option in favor of the other counterparty and both sides know that the contract will be settled. In such situation there is no need to price the second part of the contract.


Regards,

Marek

 

[ChrisDerick]

I'm just thinking out loud here:

Intuitively, I would think the structure consist of:
1) long american call, expiry at date A, with strike K.
2) short forward american put, from date A to date B, with strike K (assumably).

As the short american put is negative in value, it is always optimal to exercise on expiry A. if you would imagine it in a tree, any node beyond date A will have a value of min(S - K, df * future node value). This gives a max of S - K. Assuming df < 1, we then conclude at date A, max(S - K, min(S - K, df * future node value) * df) will always result in option exercise.

 

[MarekB]

That sounds like a reasonable explanation to me.
Thanks a million Chris.