Model[Multi_Asset_Option]__Pricing_Method__BlenmanClark

Arbitrage-free analytical formula for pricing primarily European options of type Power Exchange Option

The Power Exchange Option price is given by

*V(S1,S2,t,r,ρ,σ1,σ2,δ1,δ2;λ1,λ2,α1,α2) = Y1*N(d1) - Y2*N(d2)*

where

*S1* is the initial price of the first underlying

*S2* is the initial price of the second underlying

*t* is the time to option expiry in annual units

*r* is the effective flat continuously compounded interest rate.

*ρ* is the flat correlation between the two underlying prices.

*σ1* is the flat lognormal volatility of the price of the first underlying.

*σ2* is the flat lognormal volatility of the price of the second underlying.

*δ1* is the flat continuously compounded dividend yield of the first underlying.

*δ2* is the flat continuously compounded dividend yield of the second underlying.

*d1 = {ln[(λ1*S1^α1)/(λ2*S2^α2)] + [α1(r-δ1)-α2(r-δ2)-α1(1-α1)σ1²/2+α2(1-α2)σ2²/2+υ²/2]t}/(υt^½)*

*d2 = d1 - υt^½*

*υ² = α1²σ1²+α2²σ2²-2α1*α2*σ1*σ2*ρ*

*Y1 = λ1*S1^α1*exp{[(α1-1)r-α1*δ1-α1(1-α1)σ1²/2]t}*

*Y2 = λ2*S2^α2*exp{[(α2-1)r-α2*δ2-α2(1-α2)σ2²/2]t}*

and *N(.)* denotes the cumulative standard normal distribution function.

The following features are currently not supported:

American exercise, barriers, discrete dividends/storage costs.