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I have the option price at a rate which is much smaller than the rate at which I have tick data for the underlying. If I have option price at times $t_1, t_3, t_5$ and I have tickdata at $t_1, t_2, t_3, t_4, t_5$ can I find the option price at $t_2, t_4$ ?

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Why not? You can back out implied vol from the times you do have for the underlier price and then use that to price the options for the times you do not have. (This is assuming you are taking about pricing one particular options, not using options of one strike and expiry to price options at an other time, strike, and expiry.)

You could even do a linear interpolation and probably get very close.

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  • $\begingroup$ I thought implied volatility is calculated fom the option price. If I dont have the option price I cant find the implied volatility. $\endgroup$ – roller Sep 13 at 18:35
  • $\begingroup$ You said you had the option prices for some of the times. Implied vols do not change rapidly. So, back out implied vols for prices you have and use those to find prices you do not have. $\endgroup$ – kurtosis Sep 13 at 22:15
  • $\begingroup$ I was thinking if the stock price falls implied volatiltiy changes but I dont have that price. I could do what you are suggesting but I am trying to find the relation between stock price and implied volatility $\endgroup$ – roller Sep 13 at 22:39
  • $\begingroup$ The implied vol will change more due to the change in option moneyness. So if you have some option prices, you can estimate a vol curve for that option using the implied vols for various %ITM values for your strike -- probably a constant, linear, and quadratic component will work fine. Then use that for the times you do not have option prices by looking up the implied vol for the %ITM at that time. $\endgroup$ – kurtosis Sep 13 at 23:28

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