# 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?

• Do your observed results look similar to those in this question? quant.stackexchange.com/questions/44722/… Whereby the funding/borrow costs represent a high proportional difference between pricing on short dated calls vs puts. – Daniel Sims Mar 27 '19 at 4:19