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.

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.

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

Adaptive control of time-varying non-linear plants by speed-gradient algorithms

2019 ◽  
pp. 37-44 ◽  
Author(s):  
O. P. Tomchina ◽  
D. N. Polyakhov ◽  
O. I. Tokareva ◽  
A. L. Fradkov
Keyword(s):  
Adaptive Control ◽  
Adaptive Systems ◽  
Reference Model ◽  
Maximum Deviation ◽  
Model Parameters ◽  
Time Varying ◽  
System Solution ◽  
Non Linear ◽  
Initial Uncertainty ◽  
Speed Gradient

Introduction: The motion of many real world systems is described by essentially non-linear and non-stationary models. A number of approaches to the control of such plants are based on constructing an internal model of non-stationarity. However, the non-stationarity model parameters can vary widely, leading to more errors. It is only assumed in this paper that the change rate of the object parameters is limited, while the initial uncertainty can be quite large.Purpose: Analysis of adaptive control algorithms for non-linear and time-varying systems with an explicit reference model, synthesized by the speed gradient method.Results: An estimate was obtained for the maximum deviation of a closed-loop system solution from the reference model solution. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limit error in the system can be made arbitrarily small. Systems designed by the direct approach and systems based on the identification approach are both considered. The procedures for the synthesis of an adaptive regulator and analysis of the synthesized system are illustrated by an example.Practical relevance: The obtained results allow us to build and analyze a broad class of adaptive systems with reference models under non-stationary conditions.

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