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Forward contract initial condition
In a recent lecture on derivatives pricing, we used Laplace transform for determining the value function of a forward contract.Our lecturer said the initial condition was [$]V(S,T-t=0)=S[$]. To be honest, I don't understand why that would be. After all, forward contracts are not marked to market like futures, so shouldn't the condition be [$]V(S,0)=S-K[$]?I looked it up in PW's books and his formulation is in disagreement with my lecturer's, too.Thanks in advance for helping a student out!
Forward contract initial condition
The confusion seems to be whether you are trying to determine the value of a forward contract with a contractually fixed forward price of K, in which case you are right, or whether you are trying to solve for the forward price as a function of spot price and remaining time to maturity, in which case your lecturer may be right.
Forward contract initial condition
Thanks for your helpful reply! I understand that differentiation now.