Modeling SPY Option Volatility with Early Exercise and Dividends

Summary

The document describes a difficulty matching implied volatilities for SPY calls and puts across strikes when using Black–Scholes with dividends. Matching the at-the-money vols by calibrating rates and dividends did not remove a discrepancy that widened toward the wings. The question raises American-style exercise as a possible missing factor.

The reported adjustment was to replace Black–Scholes with a binomial tree that accounts for early exercise and a known September dividend, then choose a drift rate to match at-the-money volatility. The author reports that call and put implied volatilities then matched more closely across the wings. This is an example rather than a controlled comparison: the document gives no market data, parameter details, or general accuracy assessment. Its practical lesson is that early exercise and discrete dividends may matter when modeling SPY options, so European-style pricing assumptions can leave strike-dependent discrepancies.

Key ideas

• Black–Scholes with dividends may not capture American-style SPY option values across strikes.
• A binomial tree can represent early exercise and a discrete dividend.
• The author reports closer call-put implied-volatility agreement after changing the pricer.
• The reported fit is anecdotal and does not establish general model performance.

Tags

# Put-call parity on SPY


# Put-call parity on SPY












I'm currently trying to model the IV curve for calls and puts on SPY using the Black-Scholes model with dividends. I'm able to calibrate the risk-free rate and dividends so that both ATM IVs match, but no matter what I do, there's always an IV discrepancy that gets bigger and bigger toward the wings. Is there an effect I'm not accounting for here? Could it be because options on SPY are American style?

## Answer by Alex (score 1)

https://quant.stackexchange.com/a/66693

Thanks to all for the input. After a bit of research, I replaced the Black-Scholes pricer with a binomial tree pricer that includes early exercise and the known dividend in September, using what's explained in van der Hoek (2006) I chose a drift rate such that ATM vols match and put-call vols now match pretty closely even toward the wings. I definitely underestimated the effect that early exercise has.

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