scholarly journals Term structure modeling under volatility uncertainty

2021 ◽  
Author(s):  
Julian Hölzermann
Keyword(s):  
Brownian Motion ◽  
Term Structure ◽  
Market Price ◽  
Forward Rate ◽  
Traditional Model ◽  
Diffusion Term ◽  
Market Prices ◽  
Term Structure Models ◽  
Drift Condition ◽  
Term Structure Modeling

AbstractIn this paper, we study term structure movements in the spirit of Heath et al. (Econometrica 60(1):77–105, 1992) under volatility uncertainty. We model the instantaneous forward rate as a diffusion process driven by a G-Brownian motion. The G-Brownian motion represents the uncertainty about the volatility. Within this framework, we derive a sufficient condition for the absence of arbitrage, known as the drift condition. In contrast to the traditional model, the drift condition consists of several equations and several market prices, termed market price of risk and market prices of uncertainty, respectively. The drift condition is still consistent with the classical one if there is no volatility uncertainty. Similar to the traditional model, the risk-neutral dynamics of the forward rate are completely determined by its diffusion term. The drift condition allows to construct arbitrage-free term structure models that are completely robust with respect to the volatility. In particular, we obtain robust versions of classical term structure models.

On filtering in Markovian term structure models: an approximation approach

2001 ◽  
Vol 33 (04) ◽  
pp. 794-809 ◽  
Author(s):  
Carl Chiarella ◽  
Sara Pasquali ◽  
Wolfgang J. Runggaldier
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Nonlinear Filtering ◽  
Stochastic Dynamics ◽  
Market Price ◽  
Time Discretization ◽  
Interest Rate Risk ◽  
Forward Rate ◽  
Interest Rate Models ◽  
Volatility Function

We consider a parametrization of the Heath-Jarrow-Morton (HJM) family of term structure of interest rate models that allows a finite-dimensional Markovian representation of the stochastic dynamics. This parametrization results from letting the volatility function depend on time to maturity and on two factors: the instantaneous spot rate and one fixed-maturity forward rate. Our main purpose is an estimation methodology for which we have to model the observations under the historical probability measure. This leads us to consider as an additional third factor the market price of interest rate risk, that connects the historical and the HJM martingale measures. Assuming that the information comes from noisy observations of the fixed-maturity forward rate, the purpose is to estimate recursively, on the basis of this information, the three Markovian factors as well as the parameters in the model, in particular those in the volatility function. This leads to a nonlinear filtering problem, for the solution of which we describe an approximation methodology, based on time discretization and quantization. We prove the convergence of the approximate filters for each of the observed trajectories.

WEIGHTED MONTE CARLO: A NEW TECHNIQUE FOR CALIBRATING ASSET-PRICING MODELS

2001 ◽  
Vol 04 (01) ◽  
pp. 91-119 ◽  
Author(s):  
MARCO AVELLANEDA ◽  
ROBERT BUFF ◽  
CRAIG FRIEDMAN ◽  
NICOLAS GRANDECHAMP ◽  
LUKASZ KRUK ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Term Structure ◽  
Implied Volatility ◽  
Empirical Measure ◽  
Forward Rate ◽  
Exotic Options ◽  
Finite Sample ◽  
Market Prices ◽  
A New Technique ◽  
Implied Volatility Surfaces

A general approach for calibrating Monte Carlo models to the market prices of benchmark securities is presented. Starting from a given model for market dynamics (price diffusion, rate diffusion, etc.), the algorithm corrects price-misspecifications and finite-sample effects in the simulation by assigning "probability weights" to the simulated paths. The choice of weights is done by minimizing the Kullback–Leibler relative entropy distance of the posterior measure to the empirical measure. The resulting ensemble prices the given set of benchmark instruments exactly or in the sense of least-squares. We discuss pricing and hedging in the context of these weighted Monte Carlo models. A significant reduction of variance is demonstrated theoretically as well as numerically. Concrete applications to the calibration of stochastic volatility models and term-structure models with up to 40 benchmark instruments are presented. The construction of implied volatility surfaces and forward-rate curves and the pricing and hedging of exotic options are investigated through several examples.

Real-world jump-diffusion term structure models

2010 ◽  
Vol 10 (1) ◽  
pp. 23-37 ◽  
Author(s):  
Nicola Bruti-Liberati§ ◽  
Christina Nikitopoulos-Sklibosios ◽  
Eckhard Platen
Keyword(s):  
Term Structure ◽  
Real World ◽  
Jump Diffusion ◽  
Diffusion Term ◽  
Term Structure Models

AN ALTERNATIVE INTEREST RATE TERM STRUCTURE MODEL

2005 ◽  
Vol 08 (06) ◽  
pp. 717-735 ◽  
Author(s):  
ECKHARD PLATEN
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Market Price ◽  
Forward Rate ◽  
Term Structure Model ◽  
Forward Rates ◽  
Consistent Price System ◽  
Interest Rate Term Structure ◽  
The Interest Rate ◽  
Total Market

This paper proposes an alternative approach to the modeling of the interest rate term structure. It suggests that the total market price for risk is an important factor that has to be modeled carefully. The growth optimal portfolio, which is characterized by this factor, is used as reference unit or benchmark for obtaining a consistent price system. Benchmarked derivative prices are taken as conditional expectations of future benchmarked prices under the real world probability measure. The inverse of the squared total market price for risk is modeled as a square root process and shown to influence the medium and long term forward rates. With constant parameters and constant short rate the model already generates a hump shaped mean for the forward rate curve and other empirical features typically observed.

On filtering in Markovian term structure models: an approximation approach

2001 ◽  
Vol 33 (4) ◽  
pp. 794-809 ◽  
Author(s):  
Carl Chiarella ◽  
Sara Pasquali ◽  
Wolfgang J. Runggaldier
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Nonlinear Filtering ◽  
Stochastic Dynamics ◽  
Market Price ◽  
Time Discretization ◽  
Interest Rate Risk ◽  
Forward Rate ◽  
Interest Rate Models ◽  
Volatility Function

We consider a parametrization of the Heath-Jarrow-Morton (HJM) family of term structure of interest rate models that allows a finite-dimensional Markovian representation of the stochastic dynamics. This parametrization results from letting the volatility function depend on time to maturity and on two factors: the instantaneous spot rate and one fixed-maturity forward rate. Our main purpose is an estimation methodology for which we have to model the observations under the historical probability measure. This leads us to consider as an additional third factor the market price of interest rate risk, that connects the historical and the HJM martingale measures. Assuming that the information comes from noisy observations of the fixed-maturity forward rate, the purpose is to estimate recursively, on the basis of this information, the three Markovian factors as well as the parameters in the model, in particular those in the volatility function. This leads to a nonlinear filtering problem, for the solution of which we describe an approximation methodology, based on time discretization and quantization. We prove the convergence of the approximate filters for each of the observed trajectories.

Models of the Yield Curve and Term Structure

2019 ◽  
pp. 229-246
Author(s):  
Tom P. Davis ◽  
Dmitri Mossessian
Keyword(s):  
Term Structure ◽  
Yield Curve ◽  
Market Price ◽  
Analytical Framework ◽  
Point Of View ◽  
Relative Value ◽  
Classic Approach ◽  
Term Structure Modeling ◽  
Value Pricing ◽  
Short Rate Models

This chapter presents an overview of the modern state of term structure modeling techniques. It provides an analytical framework that is applicable to all short rate models and considers them from the point of view of the classic approach of pricing by replication. The market price of risk and its relation to the drift of a short rate model are important considerations in modeling the term structure. The notable short rate models used in the industry for relative value pricing are introduced with a brief description of the class of affine short rate models employed for forecasting the real-world dynamics of bond prices. The chapter also includes a description of the Heath-Jarrow-Morton derivative pricing framework and an analysis of the LIBOR market model.

scholarly journals Default Ambiguity

Risks ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 64
Author(s):  
Tolulope Fadina ◽  
Thorsten Schmidt
Keyword(s):  
Credit Risk ◽  
Term Structure ◽  
Market Value ◽  
Forward Rate ◽  
Term Structure Models ◽  
Default Intensity ◽  
Drift Conditions

This paper discusses ambiguity in the context of single-name credit risk. We focus on uncertainty in the default intensity but also discuss uncertainty in the recovery in a fractional recovery of the market value. This approach is a first step towards integrating uncertainty in credit-risky term structure models and can profit from its simplicity. We derive drift conditions in a Heath–Jarrow–Morton forward rate setting in the case of ambiguous default intensity in combination with zero recovery, and in the case of ambiguous fractional recovery of the market value.

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