scholarly journals Lévy Interest Rate Models with a Long Memory

Risks ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2
Author(s):  
Donatien Hainaut
Keyword(s):  
Interest Rate ◽  
Long Memory ◽  
Sample Path ◽  
Rate Model ◽  
Short Term ◽  
Uhlenbeck Process ◽  
Interest Rate Models ◽  
Infinite Dimensional ◽  
Bond Options ◽  
Interest Rate Model

This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein–Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag–Leffler function. Based on a representation in term of an infinite dimensional Markov processes, we present the main characteristics of bonds and short-term rates in this setting. Their dynamics under risk neutral and forward measures are studied. Finally, bond options are valued with a discretization scheme and a discrete Fourier’s transform.

scholarly journals COHERENT CHAOS INTEREST-RATE MODELS

2015 ◽  
Vol 18 (03) ◽  
pp. 1550016
Author(s):  
DORJE C. BRODY ◽  
STALA HADJIPETRI
Keyword(s):  
Interest Rate ◽  
General Context ◽  
Rate Model ◽  
Bond Price ◽  
Linear Superposition ◽  
Pricing Kernel ◽  
Interest Rate Models ◽  
Multiple Copies ◽  
Rate Processes ◽  
Interest Rate Model

The Wiener chaos approach to interest-rate modeling arises from the observation that in the general context of an arbitrage-free model with a Brownian filtration, the pricing kernel admits a representation in terms of the conditional variance of a square-integrable generator, which in turn admits a chaos expansion. When the expansion coefficients of the random generator factorize into multiple copies of a single function, the resulting interest-rate model is called "coherent", whereas a generic interest-rate model is necessarily "incoherent". Coherent representations are of fundamental importance because an incoherent generator can always be expressed as a linear superposition of coherent elements. This property is exploited to derive general expressions for the pricing kernel and the associated bond price and short rate processes in the case of a generic nth order chaos model, for each n ∈ ℕ. Pricing formulae for bond options and swaptions are obtained in closed form for a number of examples. An explicit representation for the pricing kernel of a generic incoherent model is then obtained by use of the underlying coherent elements. Finally, finite-dimensional realizations of coherent chaos models are investigated and we show that a class of highly tractable models can be constructed having the characteristic feature that the discount bond price is given by a piecewise-flat (simple) process.

Pricing for options in a mixed fractional Hull–White interest rate model

2017 ◽  
Vol 04 (01) ◽  
pp. 1750011 ◽  
Author(s):  
Jian Pan ◽  
Xiangying Zhou
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Long Memory ◽  
Option Price ◽  
Mathematical Physics ◽  
Rate Model ◽  
Pricing Model ◽  
European Options ◽  
Numerical Examples ◽  
Interest Rate Model

In this paper, we present a pricing model for European options in a mixed fractional Hull–White interest rate model. By using the variable transform techniques and mathematical physics methods, we derive closed-form pricing formulas for this pricing problem, which are the main contribution of this paper and expand the relevant literature’s conclusions. Moreover, we provide numerical examples to illustrate the effects of main parameters of the mixed fractional interest rate model on the option price. Numerical results show that the long memory property of interest rates plays an important role in determining the option price and cannot be neglected in option pricing.

A general lower bound of parameter estimation for reflected Ornstein–Uhlenbeck processes

2016 ◽  
Vol 53 (1) ◽  
pp. 22-32 ◽  
Author(s):  
Qing-Pei Zang ◽  
Li-Xin Zhang
Keyword(s):  
Parameter Estimation ◽  
Lower Bound ◽  
Unknown Parameter ◽  
Extended Model ◽  
Rate Model ◽  
Short Term ◽  
Uhlenbeck Process ◽  
Mild Conditions ◽  
Ornstein Uhlenbeck Process ◽  
Interest Rate Model

AbstractA reflected Ornstein–Uhlenbeck process is a process that returns continuously and immediately to the interior of the state space when it attains a certain boundary. It is an extended model of the traditional Ornstein–Uhlenbeck process being extensively used in finance as a one-factor short-term interest rate model. Under some mild conditions, this paper is devoted to the study of the analogue of the Cramer–Rao lower bound of a general class of parameter estimation of the unknown parameter in reflected Ornstein–Uhlenbeck processes.

scholarly journals A General Gaussian Interest Rate Model Consistent with the Current Term Structure

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Marco Di Francesco
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Goodness Of Fit ◽  
Rate Model ◽  
Credit Crisis ◽  
Interest Rate Models ◽  
Deterministic Function ◽  
Current Term ◽  
Critical Issues ◽  
Interest Rate Model

We describe an extension of Gaussian interest rate models studied in literature. In our model, the instantaneous spot rate is the sum of several correlated stochastic processes plus a deterministic function. We assume that each of these processes has a Gaussian distribution with time-dependent volatility. The deterministic function is given by an exact fitting to observed term structure. We test the model through various numeric experiments about the goodness of fit to European swaptions prices quoted in the market. We also show some critical issues on calibration of the model to the market data after the credit crisis of 2007.

A simple long-memory equilibrium interest rate model

1996 ◽  
Vol 53 (3) ◽  
pp. 317-321 ◽  
Author(s):  
Jin-Chuan Duan ◽  
Kris Jacobs
Keyword(s):  
Interest Rate ◽  
Long Memory ◽  
Rate Model ◽  
Interest Rate Model

A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model

1997 ◽  
Vol 13 (5) ◽  
pp. 615-645 ◽  
Author(s):  
George J. Jiang ◽  
John L. Knight
Keyword(s):  
Interest Rate ◽  
Diffusion Processes ◽  
Kernel Estimator ◽  
Estimation Procedure ◽  
Regularity Conditions ◽  
Rate Model ◽  
Normal Mixture ◽  
Short Term ◽  
Interest Rate Model ◽  
Diffusion Function

In this paper, we propose a nonparametric identification and estimation procedure for an ltd diffusion process based on discrete sampling observations. The nonparametric kernel estimator for the diffusion function developed in this paper deals with general ltd diffusion processes and avoids any functional form specification for either the drift function or the diffusion function. It is shown that under certain regularity conditions the nonparametric diffusion function estimator is pointwise consistent and asymptotically follows a normal mixture distribution. Under stronger conditions, a consistent nonparametric estimator of the drift function is also derived based on the diffusion function estimator and the marginal density of the process. An application of the nonparametric technique to a short-term interest rate model involving Canadian daily 3-month treasury bill rates is also undertaken. The estimation results provide evidence for rejecting the common parametric or semiparametric specifications for both the drift and diffusion functions.

A short term interest rate model

1999 ◽  
Vol 3 (2) ◽  
pp. 215-225 ◽  
Author(s):  
Eckhard Platen
Keyword(s):  
Interest Rate ◽  
Rate Model ◽  
Short Term ◽  
Interest Rate Model
Sign in / Sign up

Export Citation Format

Share Document