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delta sensitivity to strike
Using B/S as a starting point, I derived the sensitivity of delta to the strike price in order to resolve some pricing model issues with far OTM and ITM strikes. The formula I came up with is very similar to that for Gamma, except replacing the S with (-K):ddC/dSdK = -exp(-qt)*phi(d1)/K*sigma*root(t), where d1 is the standard (ln(S/K) + (r - q - sigma^2/2)t / sigma * root(t)), and phi(x) = exp(-x^2/2)/sqrt(2pi)Has anyone ever seen this particular sensitivity published? I'd like to check that I did my derivatives correctly. Thanks.
Last edited by ronnotel on December 2nd, 2010, 11:00 pm, edited 1 time in total.
delta sensitivity to strike
Since Delta only depends on (S,K) through x = log S/K, its almost immediate that your derivative is -S/K x Gamma, so you're good to go.
Last edited by Alan on December 2nd, 2010, 11:00 pm, edited 1 time in total.
delta sensitivity to strike
Yes, that was my intuition as well. Thanks for the second opinion. My freshman-level calculus is a bit rusty.