Current Status

3rd Year, Ph.D. program in Economics

Research Papers

An Empirical Test of Pricing Kernel Monotonicity

with Brendan Beare, Working Paper

A recent literature in finance concerns a curious recurring feature of estimated pricing kernels. Classical theory dictates that the pricing kernel -- defined loosely as the ratio of Arrow security prices to an objective probability measure -- should be a decreasing function of aggregate resources. Yet a large number of recent empirical studies appear to contradict this prediction. The nonmonotonicity of empirical pricing kernel estimates has become known as the pricing kernel puzzle. In this paper we propose and apply a formal statistical test of pricing kernel monotonicity. The test involves assessing the concavity of the ordinal dominance curve associated with the risk neutral and physical return distributions. We apply the test using thirteen years of data from the market for European put and call options written on the S\&P 500 index. Statistically significant violations of pricing kernel monotonicity occur in a substantial proportion of months.

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on The Dimensionality of Bounds Generated by the Shapley-Folkman Theorem

Accepted, Journal of Mathematical Economics

The Shapley-Folkman Theorem places a scalar upper bound on the distance between a sum of non-convex sets and its convex hull. We observe that some information is lost when a vector is converted to a scalar to generate this bound and propose a simple normalization of the underlying space which removes this loss of information. As an example, we apply this result to the Anderson (1978) core convergence theorem, and demonstrate how our normalization leads to an intuitive, unitless upper bound on the discrepancy between an arbitrary core allocation and the corresponding competitive equilibrium allocation.

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One Solution to the Option Pricing Overvaluation Problem: Using Down and Out Call Options

with Ronald Schmidt, Business Valuation Update, May 2011

Recent articles have pointed to concerns about the validity of using option pricing models (OPM) to determine the value of common stock in 409(a) valuations. At issue is the question of whether OPMs provide appropriate methodologies to establish the appropriate fair market value of common stock. Specifically, use of standard Black-Scholes algorithms will overstate the value of common stock by not properly modeling the impact of failure scenarios. We argue that claims to equity of early-stage companies may be more appropriately modeled as “down and out” call options, rather than traditional European call options (as required by the Black-Scholes formula). Like Black-Scholes, these options still have the benefit of a simple, closed-form solution, but they better account for the path dependence of enterprise value and allow for a higher probability of failure. We demonstrate that these alternative option pricing models can be used to either estimate enterprise value (back-solving) or to allocate value, and that their use can result in more reasonable estimates of common stock when compared with Black-Scholes.

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