I am a newbee in Quantive finance.

supposing I calibrate a smoothing implied volatility surface with cubic spline now.

A minute later I want to price K=100,t=1 option, can I just find the point on the volatility surface which K=100 and t=(1-1/24*60*360)?

Many thanks.

  • $\begingroup$ Can you clarify what do you mean by: t=(1-1/24*60*360)? If it is a minute later the observation K=100, t=1 should be close enough $\endgroup$ – phdstudent Dec 3 '15 at 10:45
  • $\begingroup$ @volcompt actually I don't know how people using market data to get implied volatility and then use this to price vanilla. Yes, we can use it to calculate the illiquid strikes, but as far as I known,market makers using this to price liquid strikes $\endgroup$ – Tim Dec 3 '15 at 14:14
  • $\begingroup$ @Tim, "to price" here is a bit misleading. If there is a market, there is a price. Fair value may be a better term, but really all this is for the purpose of hedging - delta, and gamma through inventory management. $\endgroup$ – onlyvix.blogspot.com Dec 7 '15 at 17:41

If you have 2-dimensional model (spline or otherwise) of vol surface vol = f(t,K), and assuming that vol is sticky-strike, that is changes in moneyness have no effect on strike vol, then you can use your function with K=100 and t=1-1/(24*60*360) - note the parenthesis.

  • $\begingroup$ so if I use some models such as SABR and SVI, I calibrate their parameters perfectly to the present market volatility. Then what should I do to price one minute later?do I just use this volatility surface and then change the spot and expiry? $\endgroup$ – Tim Dec 3 '15 at 14:44
  • $\begingroup$ It appears that you need to make choice between sticky-strike and sticky-delta. Under the sticky strike, you do not take your new spot into consideration and look up the volatility based on the strike. Under the sticky delta, the new strike used for look up the volatility can be set to $\frac{K}{S_{new}}×S_{old}$. $\endgroup$ – Gordon Dec 3 '15 at 15:30
  • $\begingroup$ @Tim Yes @ Gordon, yes, or just use delta directly. The choice of "basis" is unlikely to have any major difference for one-minute interval. $\endgroup$ – onlyvix.blogspot.com Dec 5 '15 at 14:37

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