Consistent Valuation Across Curves Using Pricing Kernels

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.Comment: 56 page

An intertemporally-consistent and arbitrage-free version of the Nelson and Siegel class of yield curve models

This article derives a generic, intertemporally-consistent, and arbitrage-free version of the popular class of yield curve models originally introduced by Nelson and Siegel (1987). The derived model has a theoretical foundation (conferred via the Heath, Jarrow and Morton (1992) framework) that allows it to be used in applications that involve an implicit or explicit time-series context. As an example of the potentialapplication of the model, the intertemporal consistency is exploited to derive a theoretical time-series process that may be used to forecast the yield curve. The empirical application of the forecasting framework to United States data results in out-of-sample forecasts that outperform the random walk over a sample period of almost 50 years, for forecast horizons ranging from six months to three years

Modelling the fair value of annuities contracts: the impact of interest rate risk and mortality risk

The purpose of this paper is to analyze the problem of the fair valuation of annuities contracts. The market consistent valuation of these products requires a pricing framework which includes the two main sources of risk affecting the value of the annuity, i.e. interest rate risk and mortality risk. As the IASB has not set any specific guidelines as to which models are the most appropriate for these risks, in this note we consider a range of different models calibrated with historical data. We calculate the fair value of the annuity as a portfolio of zero coupon bonds, each with maturity set equal to the date of the annuity payments; the weights in the portfolio are given by the survival probabilities. Moreover, we focus on the additional information provided by stochastic simulations in order to define a suitable risk margin. The nature of the risk margin is one of the main key issues concerning the IASB and Solvency project

Markov Functional Market Model nd Standard Market Model

The introduction of so called Market Models (BGM) in 1990s has developed the world of interest rate modelling into a fresh period. The obvious advantages of the market model have generated a vast amount of research on the market model and recently a new model, called Markov functional market model, has been developed and is becoming increasingly popular. To be clearer between them, the former is called standard market model in this paper. Both standard market models and Markov functional market models are practically popular and the aim here is to explain theoretically how each of them works in practice. Particularly, implementation of the standard market model has to rely on advanced numerical techniques since Monte Carlo simulation does not work well on path-dependent derivatives. This is where the strength of the Longstaff-Schwartz algorithm comes in. The successful application of the Longstaff-Schwartz algorithm with the standard market model, more or less, adds another weight to the fact that the Longstaff-Schwartz algorithm is extensively applied in practice