Consistent Valuation Across Curves Using Pricing Kernels

TL;DR

This paper introduces a pricing kernel framework for consistent asset valuation across multiple yield curves, ensuring arbitrage-free pricing in segmented markets with different risk characteristics.

Contribution

It develops a unified across-curve valuation formula and extends existing multi-curve models, enabling consistent pricing and hedging across diverse financial markets.

Findings

Derivation of an arbitrage-free across-curve pricing formula

Recovery and generalization of existing multi-curve models

Application to valuation of hybrid securities

Abstract

The general problem of asset pricing when the discount rate differs from the rate at which an asset's cash flows accrue is considered. A pricing kernel framework is used to model an economy that is segmented into distinct markets, each identified by a yield curve having its own market, credit and liquidity risk characteristics. The proposed framework precludes arbitrage within each market, while the definition of a curve-conversion factor process links all markets in a consistent arbitrage-free manner. A pricing formula is then derived, referred to as the across-curve pricing formula, which enables consistent valuation and hedging of financial instruments across curves (and markets). As a natural application, a consistent multi-curve framework is formulated for emerging and developed inter-bank swap markets, which highlights an important dual feature of the curve-conversion factor process. Given this multi-curve framework, existing multi-curve approaches based on HJM and rational pricing kernel models are recovered, reviewed and generalised, and single-curve models extended. In another application, inflation-linked, currency-based, and fixed-income hybrid securities are shown to be consistently valued using the across-curve valuation method.