Inferring ETF Funding Costs from Short-Dated Option Parity

Summary

The document describes a method for estimating an ETF’s implied funding or borrowing spread from option prices. It first adjusts American option prices toward European equivalents using the American–European price difference from a fitted volatility model. It then applies put-call parity, using a market dividend schedule and a constructed interest-rate curve, and regresses the parity relationship against strike to infer a spread over the rate curve.

The author reports implausibly large positive and negative estimates for short maturities, while longer-maturity estimates align more closely with expected index funding costs. The document poses possible explanations, including errors in the American-to-European adjustment and hedging or market-microstructure effects, but does not resolve the issue. Its results are an observed anomaly rather than evidence that the proposed estimator works reliably; short-dated option pricing, dividend assumptions, curve construction, and liquidity effects may all affect the estimate.

Key ideas

• The proposed estimator adjusts American ETF option prices using a volatility model’s American–European price difference.
• It applies put-call parity with expected dividends and a market-derived interest-rate curve.
• A strike regression is used to infer a funding or borrowing spread.
• The reported short-maturity estimates are extreme, while longer-maturity estimates appear more plausible.
• The document leaves the source of the short-dated anomaly unresolved.

Tags

# Implied Funding/Borrow Costs in Short-Dated ETF Option Prices


# Implied Funding/Borrow Costs in Short-Dated ETF Option Prices












I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say SPY options) using put-call parity. My method is as follows:

1.) "Europeanize" the options by taking a reasonable parameterization of an implied/local vol model (say SVI), using this model to price Euros and Americans at the same tenor/strike/etc as my market data and subtracting the difference between the modeled American and modeled European from the market American prices.

2) Using these pseudo-european prices, regress put call parity, importantly using the current market expected fixed dividend schedule for the underlying and a multi-stripped rate curve from a number of market rates, swaps, and derivative contracts.

3) From here, it is straightforward to use the regression results to rip out the implied funding/borrowing/some-other-spread-to-the-bank-rate part of the equation. For clarity, I am regressing against strike, leading to

$$X = -e^{(r+\delta) T}[C-P] + e^{(r + \delta)T}[S_0 - \Sigma e^{-r_t t}D_t]$$

and attempting to infer $e^{\delta T}$. The resulting numbers are nonsense for short maturities (+/- 10%, 20%, even 30% I'm seeing), however the long-maturity asymptotic behavior is very much in line with, say, SPX funding costs. Could this be step 1 modeling error in "europeanizing" of short-term options, some operational/microstructure effect of hedging short-dated ETF options, or something else?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.