Interview Question at HAP Capital - Delta of the option

While recently interviewing at HAP capital, I received a question that I stumbled on. Went something like this: If one knows a stock price, a strike price and the premium, estimate the delta of the option. Anyone have any clue?

 

might be mistaken but not sure you have suficient information. delta is change in option price for a given change in assets price. so you probably need what the call/put & asset was trading at time t and t+1 to calculate delta. but hey I am not an option trader....

 
Best Response
intuit2k2:
thanks edtkh.. Your formula just seems to be %OTM * premium... any intuition for this?

I have kind of updated the formula. Bear in mind this is purely an estimate and that this estimate would not work for a case where the Strike=Stock Price though..

Let's consider an ITM call for the following for illustration: A) Strike = 34, Stock Price = 104 and Delta = 0.95. Then Premium at this point would be 1.41. B) Strike = 34, Stock Price = 100 and Delta = 0.92 Then Premium at this point would be 1.39.

Since Case A is more in the money than Case B, the delta would necessarily be closer to 1 in the former than the latter (delta for call tends to 1.00 as its moneyness increases). Similarly, the premium for Case A would also be higher than that for Case B.

In the event that the strike > stock (ie. OTM call), you'd get a negative value for (Stock Price - Strike Price). However, you could still pretty much extrapolate by using the above formula after switching your delta.

Let's consider an OTM call for the following for illustration: C) Strike = 34, Stock Price = 14 and Delta = 0.25. Then Premium at this point would be 0.525. D) Strike = 34, Stock Price = 10 and Delta = 0.15 Then Premium at this point would be 0.354.

In Case C, your actual Delta is actually 1-0.25=0.75 (we compute using the delta from the perspective of an ITM put instead). By taking the absolute value in difference between Strike and Stock (ie.34-14=20), Premium in Case C = 0.525.

Similarly for Case D, your actual Delta would be 1-0.15=0.85. Premium in Case D would then yield 0.354.

Take note that when Strike > Stock Price, you would necessarily need to compute the premium by using the ITM put delta as opposed to the OTM call delta (given). Since the "put delta + call delta = 1" holds at all times (put-call parity), this can be done easily.

Clearly, this would then make sense as the premium increases as the stock price increases...

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