So, in mathematical terms:. We know that the formulas for these options are the following: We also know that we are supposed to follow the derivation of Black-Scholes in order to derive these formulas but we are having trouble understanding how it differs from the derivation of Black-Scholes itself.
The value of an cash-or-nothing option is just the discounted expected payoff of the option. So you would need to use the lognormal stock price and integrate it with pdf of standard normal and "complete the square". You can derive these formulae by tweaking the black scholes derivation. If you are using PDE method, you will use different boundary conditions. If you are using integration over the risk neutral probability , you will use a different payoff function but the same risk neutral density.
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Derivation of the formulas for the values of European asset-or-nothing and cash-or-nothing options. So, in mathematical terms: Sertii 11 1 4. LocalVolatility 4, 3 9 Will Gu 1 In fact, it's the same idea as Black-Scholes. I get what you intend to say. However, even this is in my opinion not a satisfactory answer to the question. Keep in mind that Sertii knows the solution already and wants to know how to derive it.
For both the cases the d1 and d2 will be function of E not the strike price. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. We already know the formulas stated in the question , the OP was interested in how they were derived.More...