scholarly journals Estimation of risk-neutral processes in single-factor jump-diffusion interest rate models

2016 ◽  
Vol 291 ◽  
pp. 48-57 ◽  
Author(s):  
L. Gómez-Valle ◽  
J. Martínez-Rodríguez
Keyword(s):  
Interest Rate ◽  
Jump Diffusion ◽  
Single Factor ◽  
Interest Rate Models ◽  
Neutral Processes ◽  
Risk Neutral ◽  
Estimation Of Risk

scholarly journals Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Interest Rate ◽  
Algebraic Approach ◽  
Dynamical Symmetry ◽  
Bond Pricing ◽  
Model Parameters ◽  
Time Varying ◽  
Single Factor ◽  
Bond Price ◽  
Interest Rate Models ◽  
Root Model

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

Valuation of derivatives based on single-factor interest rate models

2007 ◽  
Vol 18 (2) ◽  
pp. 251-269 ◽  
Author(s):  
Ghulam Sorwar ◽  
Giovanni Barone-Adesi ◽  
Walter Allegretto
Keyword(s):  
Interest Rate ◽  
Single Factor ◽  
Interest Rate Models

scholarly journals Modeling the Dynamics of Shanghai Interbank Offered Rate Based on Single-Factor Short Rate Processes

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xili Zhang
Keyword(s):  
Diffusion Model ◽  
Mean Reversion ◽  
Jump Diffusion ◽  
Single Factor ◽  
Interest Rate Models ◽  
Successful Model ◽  
Rate Processes ◽  
Jump Diffusion Model ◽  
The Mean ◽  
Selection Of

Using the Shanghai Interbank Offered Rate data of overnight, 1 week, 2 week and 1 month, this paper provides a comparative analysis of some popular one-factor short rate models, including the Merton model, the geometric Brownian model, the Vasicek model, the Cox-Ingersoll-Ross model, and the mean-reversion jump-diffusion model. The parameter estimation and the model selection of these single-factor short interest rate models are investigated. We document that the most successful model in capturing the Shanghai Interbank Offered Rate is the mean-reversion jump-diffusion model.

scholarly journals The Gauss2++ model: a comparison of different measure change specifications for a consistent risk neutral and real world calibration

2021 ◽  
Author(s):  
Christoph Berninger ◽  
Julian Pfeiffer
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Real World ◽  
Risk Premium ◽  
Risk Measures ◽  
Insurance Industry ◽  
Gaussian Model ◽  
Interest Rate Models ◽  
Risk Neutral

AbstractEspecially in the insurance industry interest rate models play a crucial role, e.g. to calculate the insurance company’s liabilities, performance scenarios or risk measures. A prominant candidate is the 2-Additive-Factor Gaussian Model (Gauss2++ model)—in a different representation also known as the 2-Factor Hull-White model. In this paper, we propose a framework to estimate the model such that it can be applied under the risk neutral and the real world measure in a consistent manner. We first show that any time-dependent function can be used to specify the change of measure without loosing the analytic tractability of, e.g. zero-coupon bond prices in both worlds. We further propose two candidates, which are easy to calibrate: a step and a linear function. They represent two variants of our framework and distinguish between a short and a long term risk premium, which allows to regularize the interest rates in the long horizon. We apply both variants to historical data and show that they indeed produce realistic and much more stable long term interest rate forecast than the usage of a constant function, which is a popular choice in the industry. This stability over time would translate to performance scenarios of, e.g. interest rate sensitive fonds and risk measures.

The Functional Stochastic Discount Factor

2019 ◽  
Vol 09 (04) ◽  
pp. 1950013 ◽  
Author(s):  
Ngoc-Khanh Tran
Keyword(s):  
Asset Pricing ◽  
Interest Rate ◽  
Term Structure ◽  
Discount Factor ◽  
Stochastic Discount Factor ◽  
State Variables ◽  
Interest Rate Models ◽  
Risk Neutral ◽  
Premium Puzzle ◽  
Linear Differential

By assuming that the stochastic discount factor (SDF) [Formula: see text] is a proper but unspecified function of state variables [Formula: see text], we show that this function [Formula: see text] must solve a simple second-order linear differential equation specified by state variables’ risk-neutral dynamics. Therefore, this assumption determines the most general possible SDFs and associated preferences, that are consistent with the given risk-neutral state dynamics and interest rate. A consistent SDF then implies the corresponding state dynamics in the data-generating measure. Our approach offers novel flexibilities to extend several popular asset pricing frameworks: affine and quadratic interest rate models, as well as models built on linearity-generating processes. We illustrate the approach with an international asset pricing model in which (i) interest rate has an affine dynamic term structure and (ii) the forward premium puzzle is consistent with consumption-risk rationales; the two asset pricing features previously deemed conceptually incompatible.

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