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In the B&S world, interest rates are constant and thus deterministic. In particular, they are not correlated to the stock price whatsoever. Thus, firstly interest rates don’t change in the first place in the B&S world. You can generalise the model and allow for time dependent (but still deterministic) interest rates. The interest rates are then ...


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When you’re short an American option, the buyer of that option may wish to exercise that option early - at any time point. You have no control about that. So there is no terminal payoff, the payoff can occur at any time. For an European-style option it is clear that it may only be exercised on maturity date. If you have a portfolio of several options with ...


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