Research

Quantifying Ambiguity in the Stock Market Using Option Data 

 Abstract: I quantify the level of ambiguity in the US stock market using option data. Firstly, I set up a representative agent asset pricing model where ambiguity is modelled using the framework of recursive multiple-priors utility. This model serves as an economic foundation for a reduced-form model which keeps its main characteristics and is easy to estimate. Then, I derive a closed-form option pricing formula based on this reduced-form model of the market index. I also provide an asymptotic expansion for the corresponding short-maturity at-the-money implied volatility. I use these results to quantify the level of ambiguity with option data from 1996 to 2020. I find that the role of ambiguity is more pronounced for the recent stock market crash due to COVID-19 than for the 2008 Financial Crisis. Furthermore, the level of ambiguity spikes during crises and decreases to its normal level rapidly than risk.

Comment on A Theoretical Foundation of Ambiguity Measurement

(with Bertrand Melenberg and Nikolaus Schweizer), Accepted at Journal of Economic Theory

Abstract: In this paper, we study asymptotic expansions for distorted probabilities under ambiguity, revisiting the framework and analysis of Izhakian (2020). We argue that the first order terms in these expansions need to be corrected and provide alternatives. We also revisit later results in this paper on the separation of ambiguity and ambiguity attitudes.  We argue that a crucial lemma is flawed implying that Izhakian's ambiguity measure is not an equivalent way of representing preferences it is supposed to represent.

Market Incompleteness and Option Returns

Abstract: In this paper, I empirically quantify the degree of market incompleteness for the U.S. market in a model-free way. The basic idea comes from Fundamental Theorem of Asset Pricing, where the existence of multiple risk-neutral measures indicates the market is incomplete. To construct the metric, I apply statistical distances to measure the differences among risk-neutral distributions extracted from options on the S\&P 500 Index. It turns out that this metric has a close link with the option hedging error, which is traditionally viewed as an approximate measure for the degree of market incompleteness. I further explore its effect on the index option return and find a robust negative relation, which adds to the growing literature about the determinants of option returns.