<t>QuoteOriginally posted by: daveangel.I am just not sure why T crops up though ?These funds can be statically replicated (in continuous time) by a portfolio of options that has an S^a payoff. That payoff has the unique property of being shape-invariant over time under the usual Black-Scholes assum...

<t>Hmm, I seem to be having technical difficulties posting...With continuous rebalancing these funds would be producing an S^L payoff; an S^L payoff can be closely replicated with an appropriately weighted package of options of different strikes. So one way to understand these funds is just to think...

QuoteOriginally posted by: PaulAny further thoughts on valuation and management of these instruments? I have received several emails recently which suggest to me that they are not well understood.P

<t>QuoteThey seem to be quite different. Can you offer some more color on your statement?Consider a power payoff V = S^L. The instantaneous return dV/V on an investment in this is exactly L times the instantaneous return dS/S of the underlier. Change "instantaneous" to "daily" and you have the lever...

<t>The leveraged funds and ETFs are daily-balanced replications for derivatives with power payoffs like S^2, S^-2.With continuous replication the payoff over an interval T is (S(T)/S(0))^L exp(cT) where the carry c isL * q + (1-L) * r + L * (1-L) / 2 *sigma^2.Daily rebalancing just adds noise around...

<t>I think I need to expand on the calibration issue and how the historical variance swap data is used.The framework is a two factor model where the second factor is unobservable and controls instantaneous volatility, correlation, and potentially all the other process parameters. Since the second fa...

<t>> But I wonder how you will be able to calibrate it. <The calibration is a very interesting problem. The calibrations in the paper are based on simultaneously fitting currently observed option prices plus historical variance swap prices. The latter carry a lot of information about volatility-of-v...

<t>Popular SV models (e.g. Heston) all seem to assume a constant correlation between the underlier and vol/variance even though both underlier vol and vol vol move around dramatically. This seems odd on the face of it, and also considering that most people would expect equity-equity correlation to r...

<t>QuoteOriginally posted by: apineyes, you are correct that you should be quite sceptical especially on the close. however, the cboe provides delayed quotes throughout the day. so if you want, you can sample it as much as you wish. plus, you can always try to price the combos vs. the underlying quo...

<t>QuoteOriginally posted by: apinewhy not use qqq and get the data from yahoo? if you want the options, get them from quote.cboe.com. this won't give historical option data, but it will provide some solution. or try the futures. it should not be too expensive to get sp500 futures data. or just do a...

<t>There's a skew model I've wanted to look into for a long time but never had the time for before. The basic idea is that the instantaneous volatility should depend on S/A where A is a running average of S. You can throw in a stochastic contribution (independent of S) to A for good measure to lower...