I have attended a conference where one speaker mentioned that the market standard to price FX and Equity derivatives is now the Local-Stochastic volatility model. I understand this class of model is a mix of local volatility and stochastic volatility models but is the pricing done always via Monte Carlo simulation?

Can you point me to an example of how this model is used to price for example FX american barrier options?

  • $\begingroup$ You do not need MC for American Barriers. See for example Bloomberg's OVML for Barriers. It can price with SLV (default is VV if you do not change that setting but SLV is recommended). This is not MC (if you price a TARF it would be - to see that it would read MC SLV in OVML). It is done via solving the PDE numerically. Examples are hard to find, as there aren't many non proprietary models that complex around. I think Quantlib (I never used quantlib personally) may have an implementation as shown here. $\endgroup$
    – AKdemy
    Jul 16, 2022 at 22:18
  • $\begingroup$ I believe Bloomberg uses the Douglas finite (one of the options in Quantlib) for its SLV PDE solver (or Crank Nicholson - should be written in the whitepaper). Overall, implementing and solving a full fledged SLV model is very complex and there is no simply way to show how its done. If you have access to Bloomberg, the white paper for the SLV model is relatively detailed. I guess your best choice is to delve into the details of Quantlib's implementation if you want a working example. That said, I am not sure American barrier options are implemented for FD in quantlib. $\endgroup$
    – AKdemy
    Jul 16, 2022 at 22:21


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