>MCarrelraThanks. I read through the thread. It's interesting and the book is well-written. But I suppose some comments in the thread are a bit too positive.

<t>Hi stringtheory. I agree. Adding to what you commented, it gives wired results for digital products such as european digitals or barriers even around ATM strikes. Actually, it could have very shin density around the ATM strike. And if no-touch-conditional, the density sometimes becomes negative d...

<t>Maybe each trader has one's own view, I suppose it works in some case.However I do not recommend Vanna-Volga methods in the following reasons.1) It does not fit highly skewed vol curve. esp, JPY 10 delta.2) Far strike imp. vol. converges to the reference vol rapidly.3) Marginal density (the 2nd d...

x(t) changes and the relation holds. but it is short rate under fwd meas. see B&M 3.2.1 and 3.8.

It works.I suppose LSM smoothes the exercise boundary but this is surprisingly good.Nice result from simple algorithm.

Thanks. I'm looking forward to.

<t>Amin, thank you for your reply.Ah, I forgot to count up / down calc. Correctly, central difference delta calc = 8,000,000.Since one could restrict delta calc to some set of shifts, e.g. principal components of zero bond yield curve, and regress if one likes, the number is a bit exaggerated. But s...

As all said, XLOPER could point a range object.I don't remember exactly, but the following might work,(1) set the target argument reference type(2) write a function with XlfOper argument(3) get reference of XlfRef from the XlfOper arg via XlfOper::AsRef().

<t>So they are supposed to converge to the same value if the shift for both deterministic and random delta are appropriately small.Maybe you're right. Digital payoff could create bumpy exercise boundary.I personally think it is better to see the effect of "large jump" on pv, but is not for delta,to ...

Sorry, a bit confusing expression. I mean the regression parameters of Longstaff-Schwartz Least Square Monte Carlo. It is fixed in the regression delta case.

Thanks Amin.I see. Did you also fix the regression coefficients for central difference delta calculation?

<t>Thank you for presenting very interesting result.It works for non-differentiable payoff cases where Piterbarg's pathwise greeks method cannot be applied.I could not figure out the reason why the method works for CMS spread TARN digital payoff but does not for CMS digital bermuda.Do you have any i...

Sorry. I supposed it's about implicit type FDM solver.boost.thread could work but OpenMP seems easier.Maybe writing a couple of #pragma like directive is enough.OpenMP library also automatically pools thread handles in an optimized way.

<t>VC++ compliers do less optimization generally.1. Try Intel C++ complier and set -O5. You can use it free in trial period.This is sometimes twice as fast.2. Profile with Intel V-Tune.This gives you the performance profile.3. Use fixed length array only.Maybe the bottle-neck is tridiagonal inversio...