2/ First up, some definitions. Assuming you know how perps work, here are the three flavors. A linear perp is most common, e.g. BTCUSDT on Binance. Pnl is linear in the trade price, denominated in the collateral (e.g. USDT): pnl = side * size * (exit_price - entry_price)

3/ Inverse perps used to be popular on Bitmex. Easiest way to think about it is you're trading a linear perp USD/BTC but everything is quoted in USD terms so that normies can think in terms of the price of BTC.

4/ The last and most interesting are quanto perps. The quote asset of the spot index is different from the margin asset. E.g. BTC margined ETH/USD on Bitmex used to be big. Rules are similar to linear perps, and pnl formula is the same, just denominated in a third asset

5/ Why are quanto contracts interesting? If the perp margin asset is correlated with the spot quote asset, your collateral is worth more when the price goes up. The perp is not actually linear, it's a much better deal to buy because you make more when you're correct

6/ Of course, perps have the funding mechanism to equilibrate the demand imbalance. When the quote and margin assets are positively correlated like BTC-margined ETH/USD perps, the funding will be consistently positive. That is longs continuously pay shorts for the convexity.

7/ There's probably a good strategy to be made pricing and trading this funding rate. As a starter, you can model returns over a funding period BTC_return ~ N(0, s^2) ETH_return = beta * BTC_return + Z Z ~ N(0, t^2) is independent noise

8/ Now compute the return distribution return_in_USD = (1 + ETH_return) * (1 + BTC_return) - 1 ~ beta * s^2 * chi_squared_2 + Z' where Z' is zero mean (cross terms normal and Z is independent noise) Here chi_squared_2 is the distribution of a standard normal variable squared

9/ Now the expected return over this funding interval is the mean of this distribution, which gives a model value for the funding rate predicted funding = E(return) = beta * s^2 * 2

10/ The important thing is chi-squared is not zero mean, so the funding rate is dominated by first order effects of market conditions and not more subtle things like cost to borrow, interest rates etc. Got good correlation or volatility alpha? Now you can price funding rates.

11/ It's pretty cool that normal delta-one alpha can apply to a funding trade. This is reminiscent of this thread I wrote which is using the alpha you understand to break into strategy classes that you don't current trade https://x.com/chameleon_jeff/s...

12/ Obviously the example model I gave is just a toy. The joint distribution of volatile assets might itself be quite volatile, and there is probably edge in modeling it more precisely. This is just back of the envelope stuff, but hopefully interesting for some of you.

@chameleon_jeff Is deribit perps considered quanto? Since it's margin ccy is same as base ccy. And then modeling will be slightly easier with beta 1

@23timmyy93 That is a special case indeed, though I'm surprised any exchange would do that over inverse perps

@chameleon_jeff don’t understand, but jeff says hft i like