Sample Question #211 (finance – option pricing)

For an at-the-money stock option, how many shares of the underlying stock should you long or short in order to hedge the option? Does your answer depend on whether the option is American or European?

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ANSWER

Easy. At the money, the delta of an option (call or put) is 0.5, so the equivalent stock position is 0.5 shares. The answer does not depend on whether the option is American or European.

not so …what about the term (r+(sigma^2)/2)(T-t) in the definition of d1?

You probably read too much into the question. The question was very straightforward, and my answer is correct. 🙂

-brett

OK, I might have been wrong, I’m ready to learn .. so please explain your answer a bit more.Here’s my a little bit longer answer. Several things should be mentioned:1. you assumed delta hedging2. the answer will obviously depend on the model …3. even if one assumes the BS model, the answer is not 0.5 (it is close to 0.5). This is because for example call’s delta is N(d1), and d1 is not zero when stock equals strike.4. obviously, put’s delta is negative … so writing that delta of ATM option is 0.5 for call or put, … you certainly wouldn’t make it to the next round if I was an interviewer …