The Supply And Demand Of S&P 500 Put Options

H/T AbnomalReturns

George M. Constantinides

University of Chicago – Booth School of Business; National Bureau of Economic Research (NBER)

Lei Lian

University of Massachusetts Amherst – Isenberg School of Management

July 11, 2015

Fama-Miller Working Paper

Chicago Booth Research Paper No. 15-38

Abstract:

We document that the skew of S&P500 index puts is non-decreasing in the disaster index and risk-neutral variance, contrary to the implications of no-arbitrage models. Our model resolves the puzzle by recognizing that, as the disaster risk increases, customers demand more puts as insurance while market makers become more credit constrained in writing puts. The skew steepens because the credit constraint is more sensitive to out-of-the-money puts. Consistent with the data, the model also predicts that the skew is increasing in the broker-dealers’ liability-to-asset ratio; and the net buy of puts is decreasing in the disaster index, variance, put price, and liability-to-asset ratio.

The Supply And Demand Of S&P 500 Put Options – Introduction

We document that the implied volatility (IV) skew of S&P 500 index puts, defined as the IV of out-of-the money (OTM) puts minus the IV of at-the-money (ATM) puts is non-decreasing in the disaster index and risk-neutral (RN) variance. We dub this the “skew response puzzle” because, as we demonstrate, a broad class of widely used no-arbitrage models for pricing options that allow for stochastic volatility and price jumps implies that the skew is a decreasing function of the disaster index and RN variance.

We address the skew response puzzle by departing from the class of no-arbitrage models of pricing options and endogenizing the supply and demand of index puts. The key departure lies in recognizing that the principal writers of index puts are market makers who face credit constraints which we model here as an exogenously imposed Value-at-Risk (VaR) constraint. The model captures the scenario where risk neutral market makers write “overpriced” index puts to maximize their expected profit, subject to their credit constraint, while risk averse customers buy the index to maximize their expected utility and hedge their exposure to downside risk by buying index puts. The key to the puzzle lies in recognizing that, as the disaster risk and variance increase, customers demand more puts as insurance while market makers become more credit-constrained in writing puts. The resulting increase in the equilibrium price is more pronounced in OTM than in ATM puts because the credit constraint is more sensitive to OTM than ATM puts. The IV skew becomes steeper, thereby resolving the puzzle. Consistent with the data, the model also predicts that the skew is increasing in the broker-dealers liability-to-asset (L/A) ratio.

We define the “net buy” by public customers of index options of given moneyness and maturity in a month as the average of the daily executed total buy orders by public customers (to open new positions or close existing ones) during the month minus their daily executed total sell orders. The net buy is the equilibrium quantity determined at the intersection of the supply and demand curves, unlike some earlier literature that treats the net buy as a proxy for demand.

The shift in the supply and demand for S&P 500 put options not only explains the IV skew puzzle but also explains a novel set of observations about the net buy of puts which challenge earlier models. In particular, these observations suggest that the demand pressure hypothesis alone is insufficient to explain the net buy of puts. The supply shift by credit-constrained market makers plays an important role in explaining the net buy of puts. Our model provides implications regarding the net buy that are born out in the data.

The model and the data consistently imply that the net buy of puts by public customers is decreasing in the RN variance and disaster index. The intuition is that, when the RN variance and/or disaster index increase, public customers like to buy more puts as insurance but market makers become more credit-constrained. That is, the supply curve shifts to the left and the demand curve shifts to the right. The supply shift turns out to be the driving factor in the decrease in the equilibrium net buy of puts.

We also address the model implications regarding the relationship between the net buy of puts and their price. The model implies that the net buy of OTM and ATM puts is decreasing in their price. The intuition is the same as above. Both the supply and demand curves shift. The supply shift turns out to be the driving factor in the decrease in the equilibrium net buy and the price increase of OTM puts. These implications are born out in the data.

S&P 500 Put Options

S&P 500 Put Options

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