II. AN APPROXIMATION FORMULA Here we derive an approximation formula for near-the-money call options. It makes use of the following approximation to the normal distribution function:¹ that for small $z$, $\Phi(z) \approx \frac{1}{2} + 0.4z$. Now consider a call is near the money, so $S \approx K$ and suppose that the risk-free rate $r$ is close to zero (or at least small compared to $\sigma$).
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We are given an approximation for the normal distribution function: $d(z) \approx 0.42z$ for small $z$. Show more…
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