The pricing of contingent claims and optimal positions in asymptotically complete markets

Michail Anthropelos, Scott Robertson and Konstantinos Spiliopoulos

Papers from arXiv.org

Abstract: We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken positions become large in absolute value at a specific rate. We draw motivation from and make connections to Large Deviations theory, and in particular, the celebrated G\"{a}rtner-Ellis theorem. We analyze a series of well studied examples where this limiting behavior occurs, such as fixed markets with vanishing risk aversion, the basis risk model with high correlation, models of large markets with vanishing trading restrictions and the Black-Scholes-Merton model with either vanishing default probabilities or vanishing transaction costs. Lastly, we show that the large claim regime could naturally arise in partial equilibrium models.

Date: 2015-09, Revised 2016-09
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1509.06210

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