Option Q

“The call option price will decrease as the time to expiration decreases or the exercise price decreases; and is very sensitive to changes in the risk free rate” The statement is correct with respect to which position? A exercise price B time to expiration C risk free rate

I’ll go with A. As far as I know exercise prices dont decrease during an option’s life.

My bad. Read it wrong. C?

The answer is B. Options have negative theta aka time decays the value of your option. A is wrong because lower exercise price is good for a call option…if it was already in the money, it’s more in the money if the strike is lowered. C is tricky. Technically call options have positive rho. Your option is worth more in a high interest rate environment cause it’s letting you forgo holding the asset and park your cash in a juicy money market while still capturing the upside of the stock. However, your interest rate needs to go up a lot for this portion of the option value to really make a big difference. Most of the value of the option has to do with the volatility of your stock and the moneyness of your option…so it’s hardly “very” sensitive to rho.

…time… Its not exercise price I think saying it is VERY sensitive to rfr is a bit too much

B - the exercise price doesn’t change during the life of an option. only the value.

I agree with cere, that’s spot on



The correct answer is B. Good explanations guys. The stuff about the RFR threw me off.

fyi…You can use the put call parity and change the different values to what happens to what. Not sure its not heavily emphasized in the notes. c+x/(1+rf)t=P + S If you increase the RF, bond worth less call worth more. If there is less time to expiration, you discount the bond less, Call Value down.

I’m not sure there’s a simple answer to this one, unless there’s more to the question? Clearly not A - a lower exercise price makes a more attractive call option. Call options are sensitive to the risk-free rate, but necessarily very much so. As call options near expiration their time-value declines. Imagine a deep out-of-the-money option with one month to go or one minute to go - the latter is worth less, all else being equal. That’s because its value is mostly time-value. On the other hand, an option deep-in-the-money is priced almost entirely on the arbitrage-basis of its underlying discounted at the risk-free - because you know it has intrinsic value, can discount it. The discount will get smaller as the time nears, so the option will grow in value. So it seems possible for an option to either gain or lose value, even holding all else constant, as time gathers. I guess because it isn’t necessarily true, the answer would be C, but it’s a silly question.

It’s a stupid question and I threw my pen across the room when I was grading my answers. The question is not put in good context. Say you were holding a 1 Yr Call on the S&P 500 Index. Let’s say that on day 364 interest rates moved up, let’s say the FOMC raised rates or something. As the call holder I lost a minimal amount of value on my call due to time decay, but the increase in the RFR should have made up for that minuscule loss and increased the overall value of my contract.