SMU SOE Seminar (November 18, 2022): Optimal Measure Preserving Derivatives Revisited

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OPTIMAL MEASURE PRESERVING DERIVATIVES REVISITED

ABSTRACT Paper 1: Optimal Measure Preserving Derivatives Revisited This article clarifies the relationship between pricing kernel monotonicity and the existence of opportunities for stochastic arbitrage in a complete and frictionless market of derivative securities written on a market portfolio. The relationship depends on whether the payoff distribution of the market portfolio satisfies a technical condition called adequacy, meaning that it is atomless or is comprised of finitely many equally probable atoms. Under adequacy, pricing kernel nonmonotonicity is equivalent to the existence of a strong form of stochastic arbitrage involving distributional replication of the market portfolio at a lower price. If the adequacy condition is dropped then this equivalence no longer holds, but pricing kernel nonmonotonicity remains equivalent to the existence of a weaker form of stochastic arbitrage involving second-order stochastic dominance of the market portfolio at a lower price. A generalization of the optimal measure preserving derivative is obtained which achieves distributional replication at the minimum cost of all second-order stochastically dominant securities under adequacy. Paper 2: Stochastic Arbitrage with Market Index Options Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset, generates a payoff which stochastically dominates the payoff from the direct investment in the underlying asset. We provide linear and mixed integer-linear programs for computing the stochastic arbitrage opportunity providing the maximum option premium to an investor. We apply our programs to 18 years of data on monthly put and call options on the Standard & Poors 500 index, confining attention to options with moderate moneyness, and using two specifications of the underlying asset return distribution, one symmetric and one skewed. The pricing of market index options with moderate moneyness appears to be broadly consistent with our skewed specification of market returns. Click here to view the CV.
		PRESENTER Brendan K. Beare University of Sydney
		RESEARCH FIELDS Econometrics Finance
		DATE: 18 November 2022 (Friday)
		TIME: 1pm - 2.30pm
		VENUE: Interactive Learning Room School of Economics Level 5 Singapore Management University 90 Stamford Road Singapore 178903

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