I had a bid volatility data that had a concave shape. my question is how can I extrapolate for the the extreme strikes, and does the bid volatility goes to zero when strike->0 and strike-> infinity. I tried to approximate the smile by the following polynomial $(k,t)\rightarrow a_1+a_2k+a_3k^2+a_4t+a_5kt$ but I do not know if this approximation is accurate.
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$\begingroup$ Why do you have a $kt$ term with weight $a_5$, if you say you want only extrapolation in strike? I presume $k$ is strike or log-moneyness? $\endgroup$– fwd_TCommented Jan 15, 2023 at 22:56
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$\begingroup$ Why do you have a kt term with weight a5, if you say you want only extrapolation in strike? I presume k is strike or log-moneyness? $\endgroup$– fwd_TCommented Jan 15, 2023 at 22:56
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