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I got the following interview question:

Consider a digital option, it will be priced by using two approaches: 1)constant volatility; 2)local volatility. At the strike, both volatilities are equal. (See the image).

The question is: How to compute the price difference between both approaches? It is a pencil and paper question, should be solved algebraically.

enter image description here

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  • $\begingroup$ My guess is this involves replication arguments $\endgroup$ – James Spencer-Lavan Jun 18 at 8:31
  • $\begingroup$ looks like homework. What have you tried so far ? $\endgroup$ – Antoine Conze Jun 18 at 9:37
  • $\begingroup$ It is an interview question $\endgroup$ – John Jun 18 at 12:20
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    $\begingroup$ Write the digital as the derivative wrt strike of the vanilla, both in constant vol case and smiled vol case. use the chain rule in the second case. price difference will be vega * skew. $\endgroup$ – Antoine Conze Jun 18 at 12:34

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