Markets: A Rigorous Course

M14 · Problem 25 ★★ Check

Probability of a call

For the position of Worked example 14.18.1 (trigger fall 17.24%, no interest), use (14.23) to compute the probability of a margin call within three months when μ=12%\mu = 12\% and (a) σ=30%\sigma = 30\%, (b) σ=40%\sigma = 40\%. (c) Compute the driftless value 2Φ(b/(σT))2\Phi(b/(\sigma\sqrt T)) for σ=30%\sigma = 30\% and explain why it exceeds (a).

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Commas, ₹, % and 1e-3 notation are accepted.

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