Conditional Davis Pricing

35 Pages Posted: 9 May 2018 Last revised: 21 Aug 2018

See all articles by Kasper Larsen

Kasper Larsen

Rutgers, The State University of New Jersey

Halil Mete Soner

ETH Zürich; Swiss Finance Institute

Gordan Zitkovic

University of Texas at Austin

Date Written: February 7, 2017

Abstract

We study the set of marginal utility-based prices of a financial derivative in the case where the investor has a non-replicable random endowment. We provide an example showing that even in the simplest of settings - such as Samuelson's geometric Brownian motion model - the interval of marginal utility-based prices can be a non-trivial strict subinterval of the set of all no-arbitrage prices. This is in stark contrast to the case with a replicable endowment where non- uniqueness is exceptional. We provide formulas for the end points for these prices and illustrate the theory with several examples.

Keywords: Incomplete markets, utility-maximization, unspanned endowment, local martingales, linearization, directional derivative

JEL Classification: C61, G11

Suggested Citation

Larsen, Kasper and Soner, Halil Mete and Zitkovic, Gordan, Conditional Davis Pricing (February 7, 2017). Swiss Finance Institute Research Paper No. 18-39, Available at SSRN: https://ssrn.com/abstract=3175364 or http://dx.doi.org/10.2139/ssrn.3175364

Kasper Larsen

Rutgers, The State University of New Jersey ( email )

311 North 5th Street
New Brunswick, NJ 08854
United States

Halil Mete Soner (Contact Author)

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Gordan Zitkovic

University of Texas at Austin ( email )

2317 Speedway
Austin, TX 78712
United States

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