Option pricing in the large risk aversion, small transaction cost limit

TL;DR

This paper analyzes the pricing of European options for highly risk-averse sellers in markets with small transaction costs, using asymptotic analysis of nonlinear PDEs and extending prior single-asset results to multiple assets.

Contribution

It generalizes previous single-asset models to multi-asset options, introducing a nonlinear PDE eigenvalue problem in the context of small transaction costs and high risk aversion.

Findings

Characterization of option prices via nonlinear diffusion equations

Extension of single-asset results to multi-asset scenarios

Identification of a nonlinear PDE eigenvalue problem in the pricing model

Abstract

We characterize the price of a European option on several assets for a very risk averse seller, in a market with small transaction costs as a solution of a nonlinear diffusion equation. This problem turns out to be one of asymptotic analysis of parabolic PDE, and the interesting feature is the role of a nonlinear PDE eigenvalue problem. In particular, we generalize previous work of Guy Barles and H. Mete Soner who studied this problem for a European option on a single asset.