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So rather than a call option C(S_t,t) we have some type of asset with asset price is given by S(x,t) where x is any type of variable that the asset price depends on. I.e Price of wooden desks, W(x,t) where x is price of wood. Or price of bitcoin, B(x,t) where x is price of electricity.

Could the FK equation be used if their PDEs were of the required format? Or does it only work will call options? I’m basically asking if we can find solutions to the price of the asset , not it’s derivatives

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  • $\begingroup$ The way you describe the setting suggests that desks are a derivative written on wood (ie it’s value is derived from wood). That allows you treat desks like options. Traditionally, stock prices (equity prices) have been interpreted as call options written on underlying (but unobservable) asset values (such that stock options are really compound options). You can apply valuation theory in these settings. New questions arise though including spanning, market completeness and tradability of the underlying. $\endgroup$
    – Kevin
    Jun 10 at 18:44
  • $\begingroup$ That is kind of what I was getting at. Could the stock price be the contract price and x be some other random variable. Essentially, you’re solving the price of the stock. $\endgroup$
    – Xerium
    Jun 10 at 19:08
  • $\begingroup$ Seems to me you just want to price derivatives, is it a requirement to use Feynman-Kac? $\endgroup$
    – Bob Jansen
    Jun 10 at 19:20

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