We empirically estimate the option implied coefficient of risk aversion of the market maker for European S&P 500 index options (SPX), involving asset allocation and option market making problems in the presence of proportional transaction costs in trading the underlying asset. We assume that the market maker has constant relative risk aversion utility and holds a two-asset portfolio consisting of the underlying and the riskless asset for a fixed, finite investment horizon which exceeds the option maturity, and she enters a position in the option market with an optimized portfolio. We follow the discrete time approach of Czerwonko and Perrakis (2016a, 2016b) to derive the market maker's simple investment policy and value functions, and apply a value matching condition to find option upper and lower bounds. Data on the S&P 500 index and the SPX options is collected over the period 1996-2016, 244 months in total, and the major variable, volatility, is re-estimated under the physical distribution. By matching observed SPX prices with numerically derived reservation prices, we estimate the level of implied risk aversion. Results show that in general, the market maker has lower risk aversion compared to investors who she trades with in order to accomplish a trade. A pattern that high risk aversion precedes rare market events is also exhibited, suggesting that a market maker may adopt a waiting policy if market events can be anticipated due to the information asymmetry.

A relationship exists between aggregate risk-neutral and subjective probability distributions and risk aversion functions. We empirically derive risk aversion functions implied by option prices and realized returns on the Samp;P500 index simultaneously. These risk aversion functions dramatically change shapes around the 1987 crash: Precrash, they are positive and decreasing in wealth and largely consistent with standard assumptions made in economic theory. Postcrash, they are partially negative and partially increasing and irreconcilable with those assumptions. Mispricing in the option market is the most likely cause. Simulated trading strategies exploiting this mispricing shows excess returns even after accounting for the possibility of further crashes, transaction costs, and hedges against the downside risk.

Cross-sections of option prices embed the risk-neutral probability densities functions (PDFs) for the future values of the underlying asset. Theory suggests that risk-neutral PDFs differ from market expectations due to risk premia. Using a utility function to adjust the risk-neutral PDF to produce subjective PDFs, we can obtain measures of the risk aversion implied in option prices. Using FTSE 100 and Samp;P 500 options, and both power and exponential utility functions, we show that subjective PDFs accurately forecast the distribution of realizations, while risk-neutral PDFs do not. The estimated coefficients of relative risk aversion are all reasonable. The relative risk aversion estimates are remarkably consistent across utility functions and across markets for given horizons. The degree of relative risk aversion declines with the forecast horizon and is lower during periods of high market volatility.

An anchoring-adjusted option pricing model is developed in which the volatility of the underlying stock return is used as a starting point that gets adjusted upwards to form expectations about call option volatility. I show that the anchoring price lies within the bounds implied by risk-averse expected utility maximization when there are proportional transaction costs. The anchoring model provides a unified explanation for key option pricing puzzles. Two predictions of the anchoring model are empirically tested and found to be strongly supported with nearly 26 years of options data.