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I want to implement a function which is passed two inputs: a strike and a time to maturity (which can be arbitrary within a specified range) and returns an FX volatility for this strike and maturity from a volatility surface estimated from FX data.

To give you context, I was given volatilies for 10delta put & call, 25delta put and call, ZDS/ATM for various tenors (O/N, 1W, 1Y etc). So using these and expiries I calculated my strike prices (using flat yield curve for both currencies) for each of the delta call and puts. Now I am asked to create a function to interpolate volatilities for any strike price and expiry

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    $\begingroup$ This is mission impossible, as an FX forward does not involve a volatility. $\endgroup$ – Gordon Jun 19 '20 at 16:08
  • $\begingroup$ Actually, I would like to edit the question and say just any Strike and Time to Maturity $\endgroup$ – Srini Jun 19 '20 at 16:42
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    $\begingroup$ Just to give you context, I was given volatilies for 10delta put & call, 25delta put and call, ZDS/ATM for various tenors (O/N, 1W, 1Y etc). So using these and expiries I calculated my strike prices (using flat yield curve for both currencies) for each of the delta call and puts. Now I am asked to create a function to sort of backsolve for volatilities for any strike price and expiry $\endgroup$ – Srini Jun 19 '20 at 19:34
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    $\begingroup$ Please see if you like my edits or if you would like to revert to previous question. $\endgroup$ – noob2 Jun 19 '20 at 19:50
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    $\begingroup$ @noob2. Thanks sounds very clear now based on your edit. $\endgroup$ – Srini Jun 19 '20 at 20:03

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