hard · Quantitative Finance qf-core
A foreign equity index S follows dS/S=μ,dt+σ_S,dW^S in its own (foreign) currency, and the domestic-per-foreign FX rate X follows dX/X=μ_X,dt+σ_X,dW^X, with dW^S,dW^X=ρ,dt. A quanto forward pays, in domestic currency at time T, the value S_T converted at a FIXED contractual FX rate (not the realized X_T).
Under the domestic risk-neutral measure, what is the correct drift of S used to price this quanto payoff, given foreign rate r_f and dividend yield q?
- r_f-q-ρ,σ_S,σ_X
- r_d-q-ρ,σ_S,σ_X, using the domestic rate r_d in place of the foreign rate
- r_f-q+ρ,σ_S,σ_X, adding the covariance rather than subtracting it
- r_f-q, since a fixed conversion rate removes any FX dependence from the drift
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