Given two options with equal strike price on the same underlying, one with an exercise date in a month, the other in three months, which is more valuable?
What is the answer to this question and why?
Is it because of Theta and the value of an option deteriorating the closer it gets to its expiration date?
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This question is very interesting. You didn't mention in the question, but I'll assume that you mean that we have two European options, one is a put and one is a call (based on your title about "hedging").
The simple answer is the one with the exercise in 3 months is more valuable due a longer time to maturity, hence a greater chance of the underlying asset going "into the money".
Now the thing about theta is quite strange. You didn't mention which option (call or put) is associated with which time frame but regardless the following holds:
For a call option, theta (or the value of the option with respect to time to maturity) is always negative. A European call option is always worth more than its payoff (can be proven with no arbitrage argument) and as maturity approaches the option value must converge to it. We are losing what is known as the ”time value” of a European call option.
Now for a put option, this gets interesting: theta can be positive or negative. In most cases, just like the European call options, the put is losing what is known as the ”time value” as maturity approaches. However, when the put is deep in the money and the time to maturity is short, the sign of theta can be positive. The put is more likely to be deep in the money at maturity because of the short time to maturity. As time goes by, the holder of the put has higher probability of exercising the put. Thus, the put should has higher value when time approaches the maturity. If you have matlab, you can plot this and see the relationship.
Hope this helps!
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