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The value of an cash-or-nothing option is just the discounted expected payoff of the option. So the value of such a call should be exp[-r(T-t)]NP(S>K), where P(S>K) = N(d2), and N is the cash agreed to be paid. The asset-or-nothing is a bit more complicated since it is exp[-r(T-t)]E[S|S>K]. The last term is the expected value of stock price given that S > ...


the negative and positives in the same series are a result of negative convexity. stated differently, the asymmetry in the series is a result of negative convexity. These relationships, however, are not permanent and may flip.

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