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You can find the answers to most of your questions in the Taylor's series and/or approximation theory articles, but I will add a bit more detail below (in order): A simplistic example would be $y=a+bx$ vs $z=bx$, so greeks being equal does not necessarily mean that the prices will be equal. But you can use hedging/replicating argument, though it needs more ...

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Let's say the company was bankrupt (ie, stock price is 0). A put option effectively becomes a bond with face value equal to the strike and maturity equal to the expiration. With positive interest rates, zero coupon bonds generally become more valuable as time passes. In this extreme case, an American option is worth more because you could early ...

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I will answer in two parts: 1): Assuming this is meant in the Black Scholes sense (one dimensional diffusion), here is an alternative explanation motivated by the convexity of the option price. In simple terms, if you plot the Back Scholes Call price as a function of S, you get this convex curve (blue curve): Now if you draw the tangents at two different ...

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As @AlexC shows this is true in the Black Scholes model. However as the late Mark Joshi comments in the link, the result is not true in all models. For example , in the stochastic vol model , suppose implied vols fall if the underlying stock moves away from at the money in either direction. Perhaps the losses on implied vol exceed the gamma profits from the ...

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Here is the reasoning I use. (Assuming familiar facts from the standard BSM setup). The Delta of a Call is positive, as S goes up the Delta goes up towards 1. (Why? The call has more moneyness, more probability of exercise, so the option behaves more like the stock). The Delta of a Put is negative, as S goes up the Delta goes towards zero (less chance of ...

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Are you sure your rf values are right? If 15 is to mean 15%, then write it as 0.15.

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