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record

Margrabe

Margrabe's (1978) closed form for a European option to exchange asset 2 for asset 1 — payoff max(S1_T - S2_T, 0). The option is on the ratio, so only the effective volatility sqrt(vol1^2 + vol2^2 - 2 rho vol1 vol2) and the two carry rates enter; there is no strike and no separate discount term for the spread itself.

sigma = sqrt(vol1^2 + vol2^2 - 2 rho vol1 vol2)
d1 = (ln(S1/S2) + (q2 - q1 + sigma^2/2) T) / (sigma sqrt(T))
d2 = d1 - sigma sqrt(T)
price = S1 e^{-q1 T} N(d1) - S2 e^{-q2 T} N(d2)

Record components

price
double
delta1
double
delta2
double

Methods

static Margrabe of(double s1, double s2, double vol1, double vol2, double rho, double yield1, double yield2, double maturity)
s1
spot of the asset received
s2
spot of the asset given up
vol1
lognormal vol of asset 1
vol2
lognormal vol of asset 2
rho
correlation of the two Brownians
yield1
carry / convenience yield on asset 1
yield2
carry / convenience yield on asset 2
maturity
time to expiry in years