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I have a finite difference pricing model and would like to factor in a volatility surface for each underlying equity. However, I have limited data. Essentially I'm just pulling a few implied volatilities from Bloomberg for each underlying equity. As such, I would like to postulate a functional form and simply fit it to my data. I was thinking of something like $$ \sigma(S_t/K, t) = \alpha + \beta \exp(-\gamma S_t/K) - \delta t. $$ I'm not familiar with any sort of theory for the functional form, so I don't know if this is the right approach.

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    $\begingroup$ Directly interpolating carries risk of arbitrage $\endgroup$
    – Arshdeep
    Apr 2 at 22:24
  • $\begingroup$ @Arshdeep Yeah, a functional form probably also invites arbitrage. However, they're probably both better than a constant volatility assumption. $\endgroup$ Apr 3 at 0:40
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    $\begingroup$ What about Gatheral's SVI arbitrage-free implied volatility parameterization? $\endgroup$
    – Kevin
    Apr 4 at 22:07
  • $\begingroup$ @Kevin Maybe. I should read the paper. $\endgroup$ Apr 8 at 16:17

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