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Quantitative Finance

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    $\begingroup$ How exactly would you use a forward to imply an implied vol smile? $\endgroup$ Commented Apr 10, 2023 at 15:55
  • $\begingroup$ I meant using the forward curve to infer the parameters and then use the usual methods of pricing once you have the parameters $\endgroup$ Commented Apr 10, 2023 at 16:13
  • $\begingroup$ Yes, but how would you infer the parameters of a vol surface from a forward? As shown here, the parameters control the height, skew and smile of the vol surface. $\endgroup$ Commented Apr 10, 2023 at 16:18
  • $\begingroup$ Thanks for your response. Given observations of the forward rate, the MCMC method I'm using can simulate the most likely latent volatility process values that would cause those observations and then infer the parameters from that. Very similar to this: arxiv.org/abs/2009.05318 $\endgroup$ Commented Apr 10, 2023 at 19:17
  • $\begingroup$ I have verified the scheme by forward simulating the SDE system and feeding a thinned set of forward rates into the scheme. The posterior means of the Parameters seem to be very close to the true values used to forward simulate. So, I am basically asking if would be valid to use these values to input into the formulas for pricing under SABR. I.e getting the 3M LIBOR curve and doing a similar process $\endgroup$ Commented Apr 10, 2023 at 19:20