Analogy Making and the Puzzles of Index Option Returns and Implied Volatility Skew: Theory and Empirical Evidence
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Constantinides et al (2013) put forward a number of empirical findings regarding leverage adjusted S&P 500 index option returns. Their findings are puzzling in the context of the Black-Scholes-Merton Option Pricing Model and the Capital Asset Pricing Model. Experimental evidence as well as the opinions of experienced market professionals indicate that call options are valued in analogy with the underlying stock. In this article, the implications of such analogy making for option pricing are explored, and the resulting analogy based option pricing model is put forward. In a one period binomial setting, I show the conditions under which arbitrage profits cannot be made against the analogy makers ensuring their survival. I show that the analogy model is consistent with the empirical findings in Constantinides et al (2013). Furthermore, the analogy model generates the implied volatility skew. Two predictions of the analogy model are also empirically tested and are found to be strongly supported in the data.