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The linear/non-linear classification is concerned about the dependent variables, and its derivatives. To verify whether the equation is linear, you should be checking that the equation is linear in each of these variables, and the coefficients of these are functions of the independent variables (t and x in your example). In your example, the dependent ...


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"Whose price function $V$ fluctuates according to the actual market price of that derivative"—this is not true. The reason being that we are 'modeling' the derivative price (where a model is a simplified version of reality). So $V$ tells us what the derivative price would be under our model—and since this model doesn't use the actual derivative price as an ...


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I think I have found the answer to my question: While deriving the Black-Scholes PDE, we write out the derivative price $f$ as a function of 2 things—the current time $t$ and the price of the underlying $S_t$. This is not to say that $f$ doesn't depend on other factors; it clearly depends on 5 other inputs $(r, \sigma, q, K, T)$. But the reason for writing ...


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