<t> For the purpose of this question a local vol model is a 1d SDE which specifies the price process and we have a contingent claim that depends on those prices (in general, at multiple times). e.g. [$]dX_t = \sigma(X_t, t)dW_t[$]. A stochastic vol model is an at least 2d SDE where one of the equati...

Definitely the flavor of what I was looking forThe Recovery TheoremRisk, Return, and the Recovery Theorem

In case you want the formula. Assuming the joint density is continuous (which it doesn't have to be) [$]f_Z(z) = \int_{-\infty}^\infty p(x, z/x) \frac{1}{|x|}dx[$]

Are you looking for the formula in terms of the joint density of [$]X[$] and [$]Y[$]. In general, the marginals alone won't be sufficient to determine how [$]XY[$] is distributed.

You're welcome. Was fun. Not sure about marking threads as answered.

<t>QuoteOriginally posted by: mAgentaI just reread part of the 2nd paper and found equation (3.9), p. 20 which seems odd to me. I thought D and B should be different zero coupon bonds (differing in their maturity), but if they have the same maturity as in this formula they should be the same bond an...

<t> Yes, I would choose to pay more attention to the second paper. However, it very well may just be an incorrect derivation of the correct Radon-Nikodym derivative in the first paper. Regarding the point about [$]\frac{D(0, T_i)}{D(0, T_{i+1})} = 1 + \alpha_iL_i(t)[$]. Above he defined [$]D(0, i) =...

<t>I see that he defines [$]P(.,T_i)[$] as numeraire for [$]Q^{T_i}[$]. Theorem 2.1.5 states the Radom-Nikodym derivative is [$]\frac{N(S)/N(t)}{M(S)/M(t)}[$] where I replaced T with S. I calculate the value of [$]\frac{dQ^{T_i}}{dQ^{T_{i+1}}}[$] to then be [$]\frac{P(S,T_i)/P(t,T_i)}{P(S,T_{i+1})/P...

Yes you are right. I thought P stood for something else.

<t>It looks to me like formula (2.8) is wrong [$]P(t,T_i) - P(t,T_{i+1}) = \delta_iL_iP(t,T_{i+1})[$] Written like that, it says that the price of a bond that expires a bit later than another is proportional to the later value. It probably was supposed to be [$]P(t,T_i) - P(t,T_{i+1}) = -\delta_iL_i...

<t>Not that I will most likely have an answer, but I am somewhat confused by your question. My understanding is, you go through the process specified in the paper to build a complete volatility surface. Known expirations are fit to SABR and then an interpolation of some form is performed for paramet...

<t>QuoteI'm looking for a sound method to account for implied sentiment due to the quantity/distribution/moneyness/etc of option contracts traded across the strike range for the nearest several expirations along the forward curve, and model the aggregate impact of this activity for its underlying in...

Does it have both local caps and a global floor?

<t>QuoteOriginally posted by: AllanqunziQuoteOriginally posted by: DavidJNThere is no reason why one cannot formulate an option model that can be inverted to back out the expected return on the underlying. One needs to introduce some appropriate model into the formulation. Stephen Ross and Peter Car...

<t> I compared your values to mine for SPY in that expiration and Date range and they are pretty similar. I'm not quite sure how to read your last question. I find that the volatility surface tends to become pretty extreme within a week to expiration. But as to your original question, I don't person...