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The ticker symbol SKF is an ultra short ETF that is designed so that it's daily return will be approximately -2 * daily return on the XLF (a financial industry ETF).I'm not exactly sure how it is composed, but I believe it is implemented via some sort of exotic swap.My question is what is the correct way to value options on this ETF. Because the drift component of the stock price process is (I believe) -2 * risk free rate, it seems like some sort of equivalent Martingale measure is called for. Am I thinking about this in the right way or do I treat the stock price process as I would for any other stock. Thanks in advance.

Nah, you just have twice the notional on.

Exuse me for butting in, but I don't think this is the case.Let's take the ultra long, as its easier to illustrate. The ultra trades such that it has a DAILY return that is double the index value, in any given, lengthy time period, the "expected value" will not be 2X the index (this is due to volatility drag). This little nuance makes it more than just having twice the notional exposure. Maybe I am looking at this wrong, but I don't think the valuation is that straight forward.

Exuse me for butting in, but I don't think this is the case.Let's take the ultra long, as its easier to illustrate. The ultra trades such that it has a DAILY return that is double the index value, in any given, lengthy time period, the "expected value" will not be 2X the index (this is due to volatility drag). This little nuance makes it more than just having twice the notional exposure. Maybe I am looking at this wrong, but I don't think the valuation is that straight forward.

QuoteOriginally posted by: PaperCutNah, you just have twice the notional on.Nah. Dunno how to do it but it's not that simple. The Ultra 2x - ETF compounds at twice the daily return in the underlying. It's not the same if you have 2x the notional due to volatility and compounding.

No, the drift of any tradeable asset is always r.Consider a call... we want to price the payoff Where K' is S_0 - K/2Therefore, call on this payoff is twice the price of the Black-Scholes put with the modified strike. Of course this is wrong in the context of the problem given as it is an ETF, and you want an option on a basket of underlying financial stocks (rather a slight variation of the return on the basket). Assuming that the ETF is log-normally distributed would be wrong I guess. The problem is interesting, I'm currently stuck with some assignments, will try to come back to it soon.

Guys these ETFs are DAILY rebalance. No exotic swaps involved. They just rebalance at end of day probably put MOC orders to keep a constant daily exposure to the underlying that's either double long or double short. (they probably screw investors by putting massive moc imbalances regardless of market impact)Pricing this is NOT 2 times (S_T-S_0). Vol is twice yes (obviously since daily return is twice magnified), but the forward is basically same so there is a large negative convexity term. You can work it out directly using Ito's lemma it's pretty simple multiplication. In flat vol world (assume 0 rates, no dividends, no borrow) Ultra long = exp( -convex term + 2 vol sqrt(T) normal) now to make this so that E(ultra long) = 1 => 2 vol^2 - convex = 0 => convex term = -2vol^2 T Ultra long = exp(-2vol^2 T + 2 vol sqrt(T) normal)now just integrate this with call payoff to price call option. Same thing for ultra short. So with skew it gets slightly more interesting but skew stays the same more or less. The reason for E(ultra) = 1 is that there is no optionality for anyone, ETF guys are just doing execution for you so hence this is a expected value 0 strategy.

I am convinced it is how the ETF operators are supposed to administer the Leveraged long/short ETF for S&P, FTSE, STOXX products.... They would probably use futures contracts to achieve the 2x daily return. Rebalancing is easy and they could do that frequently at minimal cost. The cash hold in the account is more than sufficient to cover the margin requirement. I can't see any point for them to use more exotic instruments or strategies. In the past, I don't aware there are futures contracts that covers individual equity sector, FTSE/Xinhua China 25, MSCI EM index .... But check the CME page. They seem to have quite everything. http://www.cme.com/trading/prd/equity/index.htmlEven futures on ETF.... I don't know how this circular logic could work out...

I agree - implemented using futures, and rolling. Simple. However, since the strategy must adjust its futures positions daily to ensure the x2 leverage, the long-term performance is not simply x2 .... see the article below.http://seekingalpha.com/article/123123- ... ource=feed