You are absolutely right, Alan! I talked to Lorenzo Bergomi myself and he clarified that he is actually using a CEV model where the local volatility is capped (see picture attached). Unfortunately, he didn't mention that at all in his published paper (only in his book "Stochastic Volatility Mod...

Thanks for all your input, Alan! As I mentioned briefly in the beginning, I am trying to implement the Bergomi forward variance model (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1493302). Here a quick overview of what I am trying to do: Given a discrete tenor structure, I simulate discrete f...

Good point, Alan. I didn't treat this case in any special way. If you calculate the expected payoff, then these instances will just contribute zero to the sum. Can this have such a huge impact? If yes: Is there a way to alleviate this issue?

I implemented the approximation and the calibration seems to work fine now. However, if I use constant values for sigma_0 and beta, I get a non-stationary forward skew. In other words, the n months forward skew with, say, maturity 4 months seems to be a (linearly) decreasing function of n (see chart...

Looks great! Thanks, Alan, this will be really helpful!

The perturbation starts looking odd for sigma > 0.03, but the closed form starts working for virtually all beta for sigma > 0.1. Although for beta close to the BS case, it is also unreliable for much higher values of sigma. It would be really great if I could take a look at your code! EDIT: I just s...

I initially did use a combined approach. However, there is a small range where the closed form doesn't work and the perturbation expansion already starts to look convex (i.e. wrong). I have to implement it in C++ and don't have access to Mathematica. Do they really precisely document online their ap...

Sorry, 'blows up' wasn't the right term. The bisection doesn't converge because the prices start violating no-arbitrage. Can you point me to any literature about the specifics of your or any other high-precision approach? I tried several methods, but all suffered from this caveat. Thanks again for y...

Thanks a lot for the quick reply, Alan! That's what I feared, so I guess I'll have to use the closed form then. Do you also get problems with the CEV closed form solution for small sigma/beta? For sigma less than 0.1, it blows up for a wide range of values for beta. If not: Which algorithm do you us...

Hi, I am currently trying to implement the Bergomi model to price forward skew sensitive options. In order to calibrate the stock price process, I need to compute the model implied spot skew ( difference between 95 and 105 moneyness implied vols). Since the stock SDE corresponds to a standard CEV mo...

The way I would intuitively replicate a Turbo is via buying/selling (and rolling) the corresponding futures contract. If the spot price hits the barrier, the position simply will be closed.

<t>QuoteOriginally posted by: acastaldoQuoteyou need capital to hold a long short position.Or if you have a Prime Broker who will let me hold $498 of stock long and short $502 of stock without my putting up any capital please let me know the name and phone number.You might be pleased to hear that my...

<t>QuoteOriginally posted by: daveangelyou can't have $4 of cash all the time - your capital is growing or shrinking depending on the the returns from your l/s position.If the P&L of the portfolio positions is realized every day you are right. If, as I assumed, interest rates are zero and I do n...

QuoteOriginally posted by: acastaldoOK, but how much Cash do you have ? It seems the least arbitrary to start with zero cash. If the investment is set up at [$]t_1[$] (and not changed over time) and interest rates are zero, I have 4$ cash all the time.

I have trouble turning your last sentence into math. Can you give me the weights for the following simple example:[$]Asset_1(t_1)[$]: 498[$]Asset_2(t_1)[$]: -502[$]P(t_1) = Asset_1(t_1)+Asset_2(t_1) = -4[$]Thanks!