2018/01/15 by Andrea Macrina, Macrina, Andrea, Obeid Mahomed +1
Economics, Econometrics and Finance · #FOS: Economics and business #Mathematical Finance (q-fin.MF) #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1801.04994
56 pages
arxiv created 2018/02/16 · arxiv updated 2018/02/19
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.