Yes. It turns out that there's a bug in the boundary condition, and more importantly, my min/max nodes are not far apart enough when local vol on both ends are very high! (about 400% at 3sd from current spot)

Thanks!

<t>. which FDM are you using? implicit scheme, using the Black-Scholes PDE with underlying variable = log(S). relative sizes of vol versus drift? implied vol goes from 50% to 85% across strikes, which makes local vol roughly 50% to 170%. Interest rate and cts div are zero, so drift of log(S) is -sig...

<t>Hi guys,I wonder if there is any experience in troubles using finite difference (just implicit scheme) when local vol is used. I'm only solving for European style options using log(S) as underlying variable. When I passed in a flat surface, the price and every thing looks fine. But when I pass in...

<t>But won't it be the same as simulating a forward start option using small dt steps? My goal is not to get a forward starting price. It is to find an algorithm that can avoid simulating a long dated option without resorting to tiny time steps, yet the distribution remains the same. I don't see how...

<t>Hi Alan,Actually, I am assuming the local vol process holds until the maturity of my option.dS / S = (r-q)dt * sigma(S, t) dWUnder this assumption, I think we can indeed back out the forward starting option from the generated local vol surface, in a sort of "Sticky Surface" way.If we simulate the...

<t>My idea is that we can convert the local vol surface to implied vol surface at any time and any stock price level.For instance, say we're simulating the process at T1, T2, T3, ... , Tn, given S0 and vanilla prices at all strikes and maturities (basically, the local vol function). In order to simu...

Does all these discussion imply that although we can find the law of S from T_0 to T_1, we still can't find the law of S from T_1 to T_2, given S_1? My information, of course, is all vanilla prices over all strikes and maturities.

<t>first one:long 0.1 B1, long 1.1 B2, short 1 B3at day zero, cost is0.1 * 95 + 1.1 * 90 - 100 = 8.5cashflow at 1yr:0.1 * 100 - 10 = 0cashflow at 2yr:1.1 * 100 - 110 = 0So riskfree profit = 8.5 at day zero.The idea of the rest is the same. Two of the bonds can give the zero bond price. The third can...

<t>Hi guys,I wonder if anyone can enlighten me on simulating a local volatility process without resorting to small time step sizes.In a flat surface, we can simulate from time t1 to t2 directly by sqrt(int(sigma^2, t=t1... t2)) * Z as the random term because it has the same distribution as int(sigma...

<t>I believe you meantdA(t)=mu A(t)dt+sigma A(t) dW_tSince A(t)=A(0) exp[(mu -0.5 sigma^2)t + sigma W_t].E[A(t)] = A(0) exp[(mu -0.5 sigma^2)t] E[exp(sigma W_t)].Now sigma W_t ~ N(0, sigma^2 t), soE[A(t)] = A(0) exp[(mu -0.5 sigma^2)t] exp[0.5 sigma^2 t].= A(0) exp[mu*t]Similarly,E[A(t)^2] = A(0)^2 ...

<t>This topic has been raised multiply times already, but I still haven't found a satisfying solution! The problem is:Consider a basket to be a weighted average of underlying assets with fixed weights. Given the implied volatility surfaces of the assets and a fixed correlation matrix, how can we app...

Hi Daniel,You've mentioned that you have the code for your MADE (very fast FDM) in your book? Are you referring to "FMD in FE, a PDE approach"?I have the book but no CD with me, but I don't seem to find such info even in the text.

<t>Suppose the stock S follows a geometric Brownian motion. Assume zero interest rate and dividend. Consider the two options:Option A: Pays $1 at the end of 2nd year if stock > 100, nothing otherwiseOption B: Pays $1 at any time from now until the end of 2nd year when stock > 100. Once this is paid ...

If I'm dealing with very large matrices, what kind of common operations that would reasonably implemented with parallel programming?In that regard, how does the performance of QR factorization compare to that of SVD in computing the inverse of a matrix?