Abstract
The inclusion of funding costs in the valuation of derivatives resulting in the so-called funding valuation adjustment (FVA) is a topic of intense debate, model development, and research. One issue with standard formulations of FVA is that it is the same for liquid and illiquid assets. Even if assets can be liquidated in a matter of days without discount, FVA implies that funding costs for the full term are included in the valuation. This paper studies the effect of liquidity risk on the valuation of assets through a simple model. This model assumes a Poisson process for liquidity stress events (LSEs) of random duration. In an LSE, a bank needs to liquidate an asset if the funding term is not sufficient to keep the asset funded throughout the LSE. We show that this model generates an FVA and liquidity spread. Both vanish when the asset is perfectly liquid. It is also possible to determine an optimal funding term in this model.
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