# 3 - S 1 S 2 If we let S 3 = S 1 S 2 you may think that S 3...

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Product option and power option Question: Suppose S 1 and S 2 are two stocks which follow geometric brownian motion with correlation ρ . Standard Black Scholes assumptions apply. How to price European product call option ( S 1 S 2 - K ) + ? I will try to answer this question, ﬁrst let us make some assumptions: 1 . ρ = 1.(There is only one brownian motion.) 2 . dS i ( t ) = u i S i ( t ) dt + σ i S i ( t ) dW t , i = 1 , 2 Generally, we may use the ito’s product and get that d ( S 1 S 2 ) = ( u 1 + u 2 + σ 1 σ 2 ) S 1 S 2 dtd + ( σ 1 + σ 2
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Unformatted text preview: ) S 1 S 2 If we let S 3 = S 1 S 2 , you may think that S 3 is a geometric brownian motion and we want to get the call price with ( S 3-K ) + , we may just use the standard Black scholes formula to get the price. In fact, I think this is wrong! Let try to make our problem much easier, assume that S 1 = S 2 = S . Then we get that dS 2 = (2 u + σ 2 ) S 2 dt + 2 σS 2 dW t [email protected]
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