Explain how European options on currencies and equities are valued with the Black–Scholes–Merton model
The idea
For an equity paying a continuous dividend yield δ, c = S × e^(−δT) × N(d1) − X × e^(−rT) × N(d2), with d1 = [ln(S ÷ X) + (r − δ + σ²/2)T] ÷ (σ√T) and d2 = d1 − σ√T. Dividends lower the call and raise the put: p = X × e^(−rT) × N(−d2) − S × e^(−δT) × N(−d1). For currencies, quote the spot as domestic per unit of foreign currency and replace δ with the foreign continuously compounded risk-free rate, with r as the domestic rate. A call on the foreign currency then gains when that currency strengthens. The trap is swapping the domestic and foreign rates, or ignoring the dividend yield.
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