SMU SOE Seminar Series (December 12, 2024): Do Equity and Options Markets Agree about Volatility?

TOPIC:

ABSTRACT

We address this question by deriving tight pricing kernel restrictions from zero-date options, which are options that expire on the same day they are traded. These restrictions concern the volatility of small and frequent asset price moves that the equity and options markets must agree on in a frictionless economy where the two markets are integrated. We show that violations of such restrictions lead to local arbitrage opportunities that can be exploited using a static portfolio of zero-date options and a dynamic position in the underlying asset. These local arbitrage opportunities are characterized by arbitrarily high reward-to-risk ratios and cause local explosion of conditional moments of the aggregate pricing kernel. Empirically, we find no evidence of such local arbitrage opportunities. Thus, in spite of the nontrivial risk premium embedded in zero-date options, their prices correctly reflect the time-varying volatility of the underlying asset.

Keywords: Arbitrage, Market Segmentation, Options, Pricing kernel, Risk-neutral Probability, Stochastic Discount Factor, Stochastic Volatility.

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