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While recently interviewing at a prestigious bank, 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.

Can I estimate other greeks given these information ?

szd116
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  • You do not tell us if you want to estimate delta assuming the Black-Scholes model. If it is so, this may be useful: https://quant.stackexchange.com/questions/1150/what-are-some-useful-approximations-to-the-black-scholes-formula – mlc Apr 21 '17 at 22:34
  • I don't see where they are estimating delta. I guess my interview questions implies that you could use B.S. – szd116 Apr 24 '17 at 14:21

1 Answers1

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One way to price a call option is to use the Black Scholes formula. $$ \begin{align} C(S_t, t) &= N(d_1)S_t - N(d_2) Ke^{-r(T - t)} \\ d_1 &= \frac{1}{\sigma\sqrt{T - t}}\left[\ln\left(\frac{S_t}{K}\right) + \left(r + \frac{\sigma^2}{2}\right)(T - t)\right] \\ d_2 &= d_1 - \sigma\sqrt{T - t} \\ \end{align} $$ You know the price $C$, so you solve for $\sigma$, which would be called the implied volatility.

The greeks can obtained by differentiating the Black Scholes formula.

In the Black Scholes model, the delta has a closed form: $$ \Delta = \frac{\partial C}{\partial S} = N(d_1) $$

msitt
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  • I understand the BlackScholes and I also understand the delta is just the first derivative of the call option with respective to the stock price. But during the interview, the interviewer asked to estimate the delta If one knows a stock price, a strike price and the premium. He was looking for a quick shortcut to estimate the delta. This is where I stumbled on. – szd116 Apr 17 '17 at 14:30