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Consistent Valuation Across Curves Using Pricing Kernels

Andrea Macrina () and Obeid Mahomed ()
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Andrea Macrina: Department of Mathematics, University College London, London WC1E 6BT, UK
Obeid Mahomed: African Institute of Financial Markets and Risk Management, University of Cape Town, Rondebosch 7701, South Africa

Risks, 2018, vol. 6, issue 1, 1-39

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.

Keywords: pricing kernel approach; rational pricing models; multi-curve term structures; OIS and LIBOR; spread models; HJM; multi-curve potential model; linear-rational term structure models; inflation-linked and foreign-exchanged securities; valuation in emerging markets (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 M2 M4 K2 (search for similar items in EconPapers)
Date: 2018
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