Hi As I understand it, there are three existing methods for calculation of Local Correlation :  1. Local in index volatility of the index (Lagnau 2010, Kovrizhkin 2012)  2. Local in index correlation matrix (Guyon & Henry-Labordère 2011)  3. "Building all admissible local correlation models...

Yes, Bergomi section 2.10 discusses exactly this problem, it seems, but it doesn't look promising since he explicitly says "the model is unusable"...

Haven't read Carr & Madan yet, but hopefully tonight!

Thanks for the links!
/Samuel, Stockholm, Sweden

Something like this. Definitions:     Logmoneyness = x     "Probability" p = CDF(x) = N(z)     Corresponding Normally Distributed Variable z = N^-1(CDF(x))   i.e. Inverse Normal Distribution     x = CDF^-1(p) = CDF^-1(N(z)) Simulation in One Dimension, Long Step:     Simulate p, rectangula...

Hi, thanks for answer! This is not for any particular product, but for a 3rd party system which must be consistent in the valuation. (I.e. analytical formulas, PDE & Monte Carlo must agree, when applied to same instrument.) The two Local Volatility functions are known, i.e. the individual Distri...

Hi First, two facts: 1. In a Local Volatility context for single underlying, it is possible to take a long first time step, by using the (pre-calculated) inverse of the density function to map (simulated) probabilities to logmoneynesses. (I.e. the volatility smile at time T is known --> we know the ...

You also need the expected value operator. The formula you've written is unfortunately no convexity adjustment at all. The Linear Swap Model is an approximation for a certain conditional expected value, and one of its components has a factor 1/S. This matters when the Swap rate is close to zero but...

Hi Does anybody know anything written on (CMS, in-arrear) convexity adjustment for models where the rates can be negative? And in particular "replication" models, taking the entire volatility smile into account. I have tested a Displaced Diffusion model (offset = -D = -0.5%) and used the &...

As I understand it (^ denoting transpose):In 1944, Kenneth Levenberg invented J^ J + eps * IIn 1963, Donald Marquardt improved the method to J^ J + eps * diag(J^ J)I don't know if the two ever met.../Samuel

<t>HiFon non-linear least squares:Is there any way one can one apply Broyden's rank-1 update of the Jacobian, and also utilize the Sherman?Morrison formula for rank-1 updates, in conjunction with Levenberg-Marquardt ??Broyden's rank-1 update can of course be used to update the Jacobian.However, util...

<t>Assume two futures (on e.g. a commodity) with maturities 10m and 16m.Options traded on the 10m future has expiries: 1m, 2m, 3m, 4m, 7m, 10m.We denote them 1->10, 2->10 etc.Options traded on the 16m future has expiries: 1m, 4m, 7m, 10m, 13m, 16m.We denote them 1->16, 4->16 etc.Now, there is an OTC...

Great!Exactly what I was looking for! I'll implement this and check it against my (slower) numerical FD solver.Thank you very much!/Samuel, Stockholm

<t>Yes, it becomes:[$]A_0\ \ \ \ =\ \ \ \ \int^T_0{\frac{dA_0}{dt}\ dt}\ \ \ \ =\ \ \ \ N\left(d_1\right)\ \ +\ \ {\left(\frac{H}{S}\right)}^{2µ}N\left(d_2\right)[$] = Value when RiskFreeRate is Zero[$]A_{PayAtExp}\ \ \ \ =\ \ \ \ e^{-rT}\int^T_0{\frac{dA_0}{dt}\ dt}\ \ \ \ =\ \ \ \ e^{-rT}\left[N\l...

<t>HiThe analytical formulas for One-Touch Options unfortunately doesn't work when the interest rate istoo negative, since there is a component sqrt(a^2 + 2r) where a = g/v+v/2; v = Vola; g = CarryCost;r = InterestRate. (It becomes the square root of a negative number.)So I'm trying to derive an ana...

<t>Yes, but I'm still deriving them and testing them. The trick is to derive them from parity conditions, and one also needs to "slice" the payoff into two parts, one part above and one part below the barrier (which barrier depends on which part of the formula). It's exactly like deriving the "stand...

<t>For the Down-In-Up-In Put, where X < U, exactly at knock-in at "first" barrier L:S = L, the formula then becomes "ordinary" Up-In (if L substituted to S) which is exactly what should happen.For the Up-In-Down-In Call, where L < X, exactly at if knock-in at "first" barrier U:S = U, the formula the...