A Bond Consistent Derivative Fair Value

TL;DR

This paper introduces a new, bond-consistent pricing equation for derivatives that aligns with market bond prices and addresses recent challenges posed by Funding Valuation Adjustments, ensuring symmetry and practical applicability.

Contribution

It proposes a rigorously derived pricing equation for derivatives that is consistent with bonds and market quotes, incorporating funding considerations and practical proxies.

Findings

The new pricing equation is consistent with bond prices and market quotes.

It provides practical proxies like bond-based CVA and DVA calculations.

The approach ensures symmetry and a well-defined exit price.

Abstract

In this paper we present a rigorously motivated pricing equation for derivatives, including general cash collateralization schemes, which is consistent with quoted market bond prices. Traditionally, there have been differences in how instruments with similar cash flow structures have been priced if their definition falls under that of a financial derivative versus if they correspond to bonds, leading to possibilities such as funding through derivatives transactions. Furthermore, the problem has not been solved with the recent introduction of Funding Valuation Adjustments in derivatives pricing, and in some cases has even been made worse. In contrast, our proposed equation is not only consistent with fixed income assets and liabilities, but is also symmetric, implying a well-defined exit price, independent of the entity performing the valuation. Also, we provide some practical proxies, such as first-order approximations or basing calculations of CVA and DVA on bond curves, rather than Credit Default Swaps.