Greetings Wilmotters!I had the following practical question related to Gyongy's lemma and also to the topic of Markovian projections that has many applications.In practice if one wants to map a "complicated" process Y to a "simpler" process X one can use the results sited in link * for example.In case there is (no easy way) to approximate closed form solutions for the time dependent mapping, can someone do a monte carlo of the complicated process and calibrate naively local parameters of a simpler model based on the simulated paths? *http://finmath.stanford.edu/seminars/do ... dfmerci!pb

Hi,You can have a look at V. Piterbarg's works on stochastic local vol model calibration, based on Markovian projection. See for instance Modern Approaches to Stochastic VolatilityCalibration or Markovian Projection Method for Volatility Calibration (this one is quoted in your link).

Thanks VivienB the first link is all what I was looking for.I have one question related to this subject,I applied the results for swaptions prices in loc-stoch vol HJM models, the approximation (Markovian-Projection + Taylor Developpment to linearise the local + Parameters Avreaging) has some problems for long maturities and deep OTM strikes. And I suspect that the approximation fails in the second step.Did any one tried to use quadratic Taylor development instead of linearising locale volatility and solve the quadratic stochastic volatility model (QLSV) in closed-form (Andersen) ?Regards,

Hi quantiquequant, you're welcom.I didn't knew the closed form for QSLV. Is the corresponding article Andersen, Hutchings, Parameter Averaging of Quadratic SDEs With Stochastic Volatility ? Do you know other references about it ? It seems to be interesting, in particular for FX modeling. Thank you to mentioned it.About your problem, the parameters averaging is another candidate to explain your problems I think. You can also have a look at the second order term of the Taylor expansion to verify if it is big enough to impact the approximation.I implemented too a slv HJM model (one factor quasi gaussian with linear local vol / CIR variance), and remarked that a term structure on the eta (variance volatility) don't improve enough the calibration to justify a less precise approximation (due to the parameters averaging on one more parameter) in my cases. Maybe it can help you.

Hi VivienB,For the QLSV, yes it is Andersen and Hutchings for closed form approximations (I have already implemented it for equity modelling, however I don't share the idea, page 25 of linearising the quadratic term by a linear term that depends on the strike !!). I don't see other reference to this in closed-form except the general loc-stoch vol by J. Andreasen and B. Huge using PDE.Yes, I have noticed also that: one "vol-of-volatility" term-structure is not strong enough and sufficient to match many curvatures of the smiles in closed-form (sometimes with wise choice of cir mean-reversion this works, however it is not guaranteed). I don't have the time to wait for a full Monte-Carlo calibration to judge the ability of the model.About the P. Averaging you can avoid averaging the "eta" and keep averaging only the time dependent skew to get a solvable model (ODE for Time dependent Heston) this can also be improved if you specify the HJM volatility in such way to make the time-dependant skew of the swap-rate vary less.

Any thoughts on implementing this approach to simplify models from various asset classes and then copulate them together for CVA calculation purposes ?One plausible reason to do so would be to be able to map and track hedging from various models to simpler ones that need to be copulated after.regards

For Parameter averaging (or other moments matching techniques), I think it can boost your CVA calculations. However, the markovian projection will give you wrong values of future expected exposure (correct me if I am wrong !).Unless, if the CVA starts to be a liquid asset and has to be marked. You don't need a consistent smile model like SV-Cheyette to get a "proxy" of the credit risk exposure ? You have to be more concerned more about the impact of the recovery rate rather than matching the smile.