SETUP: You have 2 different European call options. They are the same except their expiration date. Based on this info, what can you say about their respective values?
The program stated that the correct answer was that the one that expires later has to be worth AT LEAST what the value of the earlier call option is. This makes sense on the surface. If they were both deep out of the money, they might be equal in value. If they were barely in the money, the longer one would be worth more.
HOWEVER, I disagree based on something I read from a book on derivatives. I would agree only if these were AMERICAN options. But if
A) they’re European options and
B) they’re REALLY deep in the money
C) one option is going to expire soon and one is going to expire much later
D) it’s a volatile security
then I can argue that it’s possible that the one expiring FIRST is worth more. Pretty sure this was covered in Frans De Weert’s “An Introduction to Options Trading”
I haven’t read De Weert’s book, but I believe that for European call options theta (= _d_price/_d_time-to-expiry) is always positive.
I have the B-S-M model in an Excel spreadsheet, so I tried a number of combinations of volatility and strike price vs. spot price: in all cases, theta was always positive for T = 0 to T = 1 (years).
In any case, in the CFA curriculum, Schweser’s answer is correct.
(Note that it wouldn’t be correct for deep in-the-money European _ put _ options, where it’s possible that the time value (and, therefore, theta) can be negative.)
Correct me if my logic is flawed, but I look at it like this:
European and American options are actually quite similar because to realize a profit one does not have to actually exercise the option, but rather enter an opposite transaction (i.e., write a call with the same terms). This is important in your example because the price you will sell the call for will be priced appropriately high given that the call is deep in the money. Given that options are, in theory, priced for zero arbitrage opportunity, there has to be positive time value in the call in order for the call to clear the market.
I believe there may be other situations involving securities with cashflows where the timing of the cashflows could further muddy the theta but that is a conversation for another day.
Well theta wouldn’t always be positive if it’s a volatile stock, right? Say for example you have shares of AMZN and the normal price is 400. The strike price is 400. Let’s say that the standard deviation is such that the value only goes up or down $30 a month. The shares shoot up to 650 on a big announcement. Wouldn’t you agree that the European option that expires tomorrow is worth more than the european option that expires in 6 months?
I have been thinking about this question and have come to the conclusion that the Schweser material was correct because the prompt asked for the most likely scenario, not “the scenario that is ALWAYS true”
A call option’s value has two components: Intrinsic Value and Time Value. Intrinsic value is simply the current stock price less the strike price. In your example, intrinsic value is $250 (650-400). If time value were negative, then the call would be priced below $250. This would allow for an arbitage opportunity. I could buy the call at say $249 (assume time value is negative -$1) and sell the stock at $650, locking in a riskless profit of $1. If my stock goes up by $5, my call goes up by $5 (as my delta would be 1 this deep in the money) and my short stock position declines by $5 and vice-vera for a drop in the stock’s price.
Markets price to no arbitrage and therefore your time value cannot be negative in this case.