Funding Value Adjustment and Incomplete Markets

TL;DR

This paper explores how incomplete markets affect the valuation adjustments of uncollateralized trades, proposing a framework where such trades are treated as primary assets, with valuation depending on market completion choices.

Contribution

It introduces a novel approach to valuing uncollateralized trades as primary assets, accounting for market incompleteness and investor risk appetite in the valuation process.

Findings

Different market completions lead to varying valuation adjustments.

In limiting cases, the approach aligns with established literature.

Market incompleteness impacts the uniqueness of pricing measures.

Abstract

Value adjustment of uncollateralized trades is determined within a risk-neutral pricing framework. When hedging such trades, investors cannot freely trade protection on their own name, thus facing an incomplete market. This fact is reflected in the non-uniqueness of the pricing measure, which is only constrained by the values of the hedging instruments tradable by the investor. Uncollateralized trades should then be considered not as derivatives but as new primary assets in the investor's economy. Different choices of the risk-neutral measure correspond to different completions of the market, based on the risk appetite of the investor, leading to different levels of value adjustments. We recover, in limiting cases, results well known in the literature.