Discounting Cleared Futures and Options Using Margin Funding

# Correct Discount Curve for Exchange Traded (Centrally Cleared) Products


# Correct Discount Curve for Exchange Traded (Centrally Cleared) Products












What's the correct discount curve to use for exchange traded products? Would these be discounted at the OIS rate (because of the central clearing house)?

E.g. the E-Mini S&P500 Future @ CME: I'm trying to model liquidity preferences and implied dividends based on listed futures and options- so I need an accurate curve for the index's discounting. Some back-of-the-envelope tricks (treasury curves + basis) don't show enough structure in longer durations.

The S&P500 future is a unique market with its own characteristics. What about an equity forward curve with uncertain liquidity and dividends? Should I compute the repo cost (could be hard-to-borrow) of the stock from box spreads in order to discount the single equity (vs discounting the index)? Is there a better method in practice?

Collateralized OTC products are discount at OIS because this is the rate paid on the collateral. What about exchange products? What about equities with interesting financing characteristics?

Edit: is it the case that the financing I am giving up is the secured overnight rate for centrally cleared products when trading the index, so I should use the risk-free rate? What about for stock options with more interesting borrowing markets?

## Answer by Jared (score 1, accepted)

https://quant.stackexchange.com/a/47445

This question Setting the r in put-call parity? shows the details are subtle and nuanced, but the answer is to use the rate paid on the collateral or margin.

## Answer by JoshK (score 1)

https://quant.stackexchange.com/a/47448

if you are asking how CME collateral is discounted, then you have two considerations:

- What does the CME give you on your USD cash? That's simple, it's OIS. You don't get the interest immediately, but instead I think once a month. I'm not sure if they compound it - but I would imagine they do as it references OIS.

- What's your funding situation. For example, your treasury might charge you a spread of OIS+20 on the collateral. So, when modeling the convexity factor of a future, you need to incorporate the spread if you want to be super accurate. But usually, for things like ESU9, it's less than 1/100 of a bp, so you can throw it away.

Now, if you are asking, how to compute funding cost for the underlying reference asset, that's different. Options with early exercise are more complicated - but European options and futures are simple. Front month dividends are fairly well telegraphed. On Bloomberg you can simply enter "ESU9 [Index] FAIR":

Just pay attention to section 14, in the middle, where it shows ESU9 in blue. That shows a four cent difference between spot and futures, $3.51 in divs, and an implied rate of 2.30.

For a base rate reference itself, pick your poison: OIS, Interpolated Libor, 1m libor, o/n libor, your personal credit card rate, etc...

Does that help with your question?