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.

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.

A COMPLETE YIELD CURVE DESCRIPTION OF A MARKOV INTEREST RATE MODEL

2003 ◽  
Vol 06 (04) ◽  
pp. 317-326 ◽  
Author(s):  
ROBERT J. ELLIOTT ◽  
ROGEMAR S. MAMON
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Yield Curve ◽  
Forward Rate ◽  
Rate Model ◽  
Bond Price ◽  
Forward Measure ◽  
Expectation Hypothesis ◽  
Complete Set ◽  
Interest Rate Model

This paper aims to present a complete term structure characterisation of a Markov interest rate model. To attain this objective, we first give a proof that establishes the Unbiased Expectation Hypothesis (UEH) via the forward measure. The UEH result is then employed, which considerably facilitates the calculation of an explicit analytic expression for the forward rate f(t, T). The specification of the bond price P(t, T), yield rate Y(t, T) and f(t, T) gives a complete set of yield curve descriptions for an interest rate market where the short rate r is a function of a continuous time Markov chain.

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.

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