Publication

Unspanned stochastic volatility in the multifactor CIR model

Damir Filipovic, Martin Larsson, Francesco Statti
2019
Journal Articles

Résumé

Empirical evidence suggests that fixed-income markets exhibit unspanned stochastic volatility (USV), that is, that one cannot fully hedge volatility risk solely using a portfolio of bonds. While Collin-Dufresne and Goldstein (2002, Journal of Finance, 57, 1685–1730) showed that no two-factor Cox–Ingersoll–Ross (CIR) model can exhibit USV, it has been unknown to date whether CIR models with more than two factors can exhibit USV or not. We formally review USV and relate it to bond market incompleteness. We provide necessary and sufficient conditions for a multifactor CIR model to exhibit USV. We then construct a class of three-factor CIR models that exhibit USV. This answers in the affirmative the above previously open question. We also show that multifactor CIR models with diagonal drift matrix cannot exhibit USV.

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https://infoscience.epfl.ch/entities/publication/8ca08dfa-a938-4866-b818-75979f071b04

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Damir Filipovic, Martin Larsson, Francesco Statti
2019
Journal Articles

Résumé

Source officielle

https://infoscience.epfl.ch/entities/publication/8ca08dfa-a938-4866-b818-75979f071b04

À propos de ce résultat

Concepts associés (17)

Short-rate model

A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written . Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate. The short rate, , then, is the (continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time .

Lattice model (finance)

In finance, a lattice model is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date.

Incomplete markets

In economics, incomplete markets are markets in which there does not exist an Arrow–Debreu security for every possible state of nature. In contrast with complete markets, this shortage of securities will likely restrict individuals from transferring the desired level of wealth among states. An Arrow security purchased or sold at date t is a contract promising to deliver one unit of income in one of the possible contingencies which can occur at date t + 1.

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