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For Black-Scholes, $\Delta_C=\partial_{S} C=N(d_1)$, $d_1= \frac{\ln\left(\frac{S_t}{K}\right) + \left(r + \frac{\sigma^2}{2}\right)(T - t)}{\sigma\sqrt{T - t}}$ You may fit the volatility $\sigma$ to this term by $$\Delta_C({\hat{\sigma}})=0.25$$Note that $\Delta_P=1-\Delta_C$ by Put-Call-Parity.


Found a nice source, hopefully someone can verify: http://www.elitetrader.com/vB/showthread.php?p=3482827 The trick is to back into the strike by using the delta formula (of course). Here is the R code posted at the site above: BSStrikeFromDelta <- function(S0, T, r, sigma, delta, right) { strike <- ifelse(right=="C", S0 * exp(-qnorm(delta * ...

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