Model[MultiAsset_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{[(α₁-1)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.