Lévy–vasicek Models and the Long-Bond Return Process

Brody, Dorje C.; Hughston, Lane P.; Meier, David M.

doi:10.1142/s0219024918500267

Cited by 4 publications

(4 citation statements)

References 25 publications

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“…Thus, by use of a pricing kernel technique we have obtained an expression for the price of a unit discount bond of maturity T in the Lévy-Ito Vasicek model, generalizing results of Vasicek [40], Cairns [41], Norberg [15], and Brody, Hughston & Meier [42]. The extra freedom provided by the functions {λ(x)} and {σ(x)} gives the model flexibility when it comes to fitting it to market data.…”

Section: Vasicek Model Of the L éVy-ito Typementioning

confidence: 82%

Lévy-Ito Models in Finance

Bouzianis,

Hughston,

Jaimungal

et al. 2019

Preprint

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We propose a class of financial models in which the prices of assets are Lévy-Ito processes driven by Brownian motion and a dynamic Poisson random measure. Each such model consists of a pricing kernel, a money market account, and one or more risky assets. The Poisson random measure is associated with an n-dimensional Lévy process. We show that the excess rate of return of a risky asset in a pure-jump model is given by an integral of the product of a term representing the riskiness of the asset and a term representing the level of market risk aversion. The integral is over the state space of the Poisson random measure and is taken with respect to the Lévy measure associated with the n-dimensional Lévy process. The resulting framework is applied to the theory of interest rates and foreign exchange, allowing one to construct new models as well as various generalizations of familiar models.

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Section: Vasicek Model Of the L éVy-ito Typementioning

confidence: 82%

Lévy-Ito Models in Finance

Bouzianis,

Hughston,

Jaimungal

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Thus, by use of a pricing kernel we have obtained the price of a unit discount bond in the Lévy-Ito Vasicek model, generalizing results of [67,17,79,18]. The extra freedom provided by λ(x, t) and σ(x, t) gives the model extra flexibility for fitting it to market data.…”

Section: S) ν(Dx) Dsmentioning

confidence: 84%

“…Such behavioral characteristics can be accommodated into Lévy-Ito models. The so-called Lévy-Vasicek models [67,17,31], obtained by setting n = 1 with λ(x, t) = λx and σ(x, t) = σx for λ, σ ∈ R, constitute a more specialized class, and do not allow for the possibility of showing different levels of risk aversion or volatility for different jump sizes and time frames. In a Lévy-Vasicek model, once we reinstate the Brownian term, the dynamical equation satisfied by the short rate takes the form…”

Section: S) ν(Dx) Dsmentioning

confidence: 99%

“…The resulting theory is more general than the well-known interest rate models driven by Brownian motion and pure-jump Lévy processes, yet remains tractable and suitable for implementation. As an example of a Lévy-Ito interest rate model, in Section 5 we present an extension of the Vasicek model to the Lévy-Ito category, summarized in Proposition 4, generalizing results of [79,18,67,17,31] and others.…”

Section: Introductionmentioning

confidence: 99%

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Lévy-Ito models in finance

et al. 2021

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We present an overview of the broad class of financial models in which the prices of assets are Lévy-Ito processes driven by an n-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is associated with an n-dimensional Lévy process. Each model consists of a pricing kernel, a money market account, and one or more risky assets. We show how the excess rate of return above the interest rate can be calculated for risky assets in such models, thus showing the relationship between risk and return when asset prices have jumps. The framework is applied to a variety of asset classes, allowing one to construct new models as well as interesting generalizations of familiar models.

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State Space Decomposition and Classification of Term Structure Shapes in the Two-Factor Vasicek Model

KELLER-RESSEL,

SACHSE

2023

Int. J. Theor. Appl. Finan.

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In this paper, we analyze the shapes of forward curves and yield curves that can be attained in the two-factor Vasicek model. We show how to partition the state space of the model, such that each partition is associated to a particular shape (normal, inverse, humped, etc.). The partitions and the corresponding shapes are determined by the winding number of a single curve with possible singularities and self-intersections, which can be constructed as the envelope of a family of lines. Building on these results, we classify possible transitions between term structure shapes, give results on attainability of shapes conditional on the level of the short rate, and propose a simple method to determine the relative frequency of different shapes of the forward curve and the yield curve.

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Lévy–vasicek Models and the Long-Bond Return Process

Cited by 4 publications

References 25 publications

Lévy-Ito Models in Finance

Lévy-Ito Models in Finance

Lévy-Ito models in finance

State Space Decomposition and Classification of Term Structure Shapes in the Two-Factor Vasicek Model

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