Pricing for Large Positions in Contingent Claims

TL;DR

This paper analyzes the asymptotic behavior of utility indifference prices for large positions in contingent claims, revealing how utility decay rates influence pricing and providing explicit limits in diffusion models.

Contribution

It introduces general approximations for large position sizes, linking utility decay to pricing, and explicitly computes limiting prices in diffusion models for exponential investors.

Findings

Prices depend on utility decay rates for large negative wealths.

Explicit limiting prices are derived for exponential investors in diffusion models.

Large claim limits relate to vanishing hedging errors.

Abstract

Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches infinity, the utility function's decay rate for large negative wealths is the primary driver of prices. For utilities with exponential decay, one may price like an exponential investor. For utilities with a power decay, one may price like a power investor after a suitable adjustment to the rate at which the position size becomes large. In a sizable class of diffusion models, limiting indifference prices are explicitly computed for an exponential investor. Furthermore, the large claim limit is seen to endogenously arise as the hedging error for the claim vanishes.