CFAI Mock Exam AM: Valuing Option

Hi everyone,

Regarding CFAI Mock Exam 2015 Morning Session - Question 34

I’m having troubles understanding the solution of question 34. The IIG option on LAT Transport was described as ''having the right to purchase 50% of LAT Transport for EUR 30 million at any time for over the next 2 years". This sounds like a American call option to me.

Then if its a American call option, why the solution even cares about the option value at t = 2? We could have just exercised the option at t = 1 and lock in the profit.

Anyone? :smiley:

Hi Phu,

I think the reason we should consider the option value at t=2 is because the option’s price derived from binomial model makes sure no arbitrage txn can occur (between t=1 to t=2).

Consider 50% Latvia project as a stock which has the value at the end of year 2 is 39,675 or 27,6. A porfolio combining long position in n stocks and short position in one call option with exercise price = 30 has the value at the end of year 2 as follows:

n.39.675 - 9,675 (the index moves up) and n.27,6 (index moves down)

For the porfolio being hedged, we set the two values equal and solve for n, we then have n=0,8012.

A hedged profolio should earn risk-free rate only, so its value (or its cost) at the end of year 1 must be: n.39,675 - 9,675 (or n.27,6) divided by 1,02. We have cost of n stocks at the end of year 1, so it’s easy to calculate the value of the option, 5,96. At t=1, if the option value < 5,96, the porfolio is overprived and we should short it to earn more than risk-free rate, if the option value >5,96, the portfolio is underpriced and we should long it.

Just my thought:)

American call options must be worth at least Max (0, Spot Price at time zero - Exercise price). With the exception of expiration, the European lower bound would therefore be greater than the minimum value of the American call option value. We could not expect an European call to be worth more than an American call option.

"In theory, early exercise is never optimal for American call option on non-dividend stocks. Hence, early exercise has zero value. " (@ohai, http://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91310380).

Therefore treat American calls as European calls.

@phutruongsy

Wow…be honest I was surpised since I thought no one asked the question. I guess you studied and prepared very well. Without that much understanding, you cannot ask that question. The answers above are not right I believe. And your guess is right. It is American option, which can be executed early. The reason why there is no early execution is as below: When you value American option you have to compare the payoff coming from the next node and the early execution payoff. And choose the greater one. For example, the discounted payoff from the next node in this question is .6286*9.675/1.02=5.96. You have to compare the early execution payoff with 5.96. In this question, the early execution payoff is 34.5-30=4.5. 5.96 vs 4.5–>5.96 is greater. Therefore, we should not do early execution. Since waiting another period will generate more profit, you should not execute at t=1. This is a tip. In the exam, they can ask American option valuation at anytime, the simple trick. Make sure you check if it asks American option or European option. If it is American option, step 1 is to calculate payoff of each node like European option. step2. compare it with Early execution payoff. Do not fall into the easy trap in the exam!! Good luck!

I agree with Justin1217. Learned at uni, before looking at the CFA program, that at least assuming no dividends, exercising an American option before expiration never makes sense in theory, because you lock in the intrinsic value but give up the remaining option value by exercising it.

Exercising early an American put option that is deep in the money can make sense, as the time value can be negative.