Partial Differential Equation Approach

Pricing a derivative usually means computing the expectation of the discounted option’s payoff.

It is Pde approach1 , where Pde approach2 is a certain payoff function and the stock price follows a stochastic process. 

Assuming such a process and using a no-arbitrage argument, it is often possible to find a self-financing strategy that replicates the particular option. This will imply a PDE which the option’s price must satisfy. In this case, pricing on option amounts to solving the PDE. 



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