I must emphasize again that they are not the same thing. We said that delta was closely related to the probability of finishing ITM and used it sometimes this way as it is quite intuitive for option rookies. Wrong models will typically result in wrong hedge ratios.ĥ.2.8 Delta as a hedge ratio, not a probability It is therefore fundamental that you understand well the model's assumptions and their implications. When pricing an exotic option, you will typically have to use some model. ![]() The parabolic approximation is almost undistinguishable unless we move substantially from the initial level. This simply gives us the various orders of sensitivities. The approximation generally gets better as we add more terms to it. Since option prices are convex with respect to some of their parameters, their linear approximations always lie below the exact option prices. The second order approximation means we are using a parabolic shape. The coefficients for this polynomial are determined by the derivatives at a single point (understand the current market conditions in this case).Ī first order approximation means that we are approximating the option price with a straight line. To understand the concept of sensitivity we must first mention the Taylor series.Īny function can be approximated by a polynomial function.
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