# Tag Info

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The exercise is really not about replicating a call with asset or nothing. It is simply about the PDE of the delta of a call. The usual derivation of the BS equation starts by considering a portfolio short the option $$\Pi_t = \delta^0_t B_t + \delta_t S_t - V(t,S_t)$$ Assuming the portfolio is selfinancing (and interest rate = 0), we get  d\Pi_t ...

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I think the title here is misleading. Let's go back to the BS world with $r=0$ to $a(S_t)=S_t \sigma.$ In that case, all you are saying is that you can replicate a call option by holding $N(d_1)$ units of stock at time $t.$ What does this have to do with the second equation? I am guessing that this is the price process of an asset of nothing option with ...

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Without getting into all the Math one thing should be clear that: Call option is equivalent to: long asset or nothing AND short cash or nothing options. You cannot replicate a call option without asset or nothing since replicating portfolio for long call requires holding N(d1) quantity of the underlying. Asset or nothing gives you this exposure directly. ...

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