scholarly journals Interest rate model with humped volatility under the real-world measure

2018 ◽  
Vol 7 (1) ◽  
Author(s):  
Takashi Yasuoka
Keyword(s):  
Interest Rate ◽  
Term Structure ◽  
Real World ◽  
Model Comparison ◽  
Market Price ◽  
Yield Data ◽  
Market Price Of Risk ◽  
The Real ◽  
Volatility Model ◽  
Price Of Risk

The purpose of this paper is to develop real-world modeling for interest rate volatility with a humped term structure. We consider humped volatility that can be parametrically characterized such that the Hull–White model is a special case. First, we analytically show estimation of the market price of risk with humped volatility. Then, using U.S. treasury yield data, we examine volatility fitting and estimate the market price of risk using the Heath–Jarrow–Morton model, Hull–White model, and humped volatility model. Comparison of the numerical results shows that the real-world humped volatility model is adequately developed.

LIBOR MARKET MODEL UNDER THE REAL-WORLD MEASURE

2013 ◽  
Vol 16 (04) ◽  
pp. 1350024 ◽  
Author(s):  
TAKASHI YASUOKA
Keyword(s):  
Real World ◽  
Market Price ◽  
Market Model ◽  
Market Price Of Risk ◽  
The Real ◽  
Libor Market Model ◽  
State Price ◽  
Number Of Factors ◽  
Price Of Risk ◽  
State Price Deflator

This paper consists of two parts. The first part aims to construct a LIBOR market model under the real-world measure (LMRW) according to the Jamshidian framework. Then, LIBOR rates, bond prices and a state price deflator are explicitly described under the LMRW. The second part aims to estimate the market price of risk, as well as to investigate the fundamental properties of real-world simulations. Then, the following subjects are theoretically investigated: (1) a method for determining the number of factors for real-world simulations, (2) the properties of real-world simulations, and (3) the value of the market price of risk in connection with sample data. Numerical examples demonstrate our results.

scholarly journals The Market Price of Risk in Interest Rate Swaps: The Roles of Default and Liquidity Risks*

2006 ◽  
Vol 79 (5) ◽  
pp. 2337-2359 ◽  
Author(s):  
Jun Liu ◽  
Francis A. Longstaff ◽  
Ravit E. Mandell
Keyword(s):  
Interest Rate ◽  
Market Price ◽  
Market Price Of Risk ◽  
Interest Rate Swaps ◽  
Price Of Risk

Theoretical Identifications of the Market Price of Risk under the Affine Interest Rate Model with Jumps

2005 ◽  
Vol 13 (2) ◽  
pp. 133-143
Author(s):  
Joon Hee Rhee
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Empirical Studies ◽  
Market Price ◽  
Rate Theory ◽  
Rate Model ◽  
Change Of Measure ◽  
Market Price Of Risk ◽  
Price Of Risk ◽  
Interest Rate Model

Any finance models must specify the market prices of risk that determines the relationship between the two probability measures. Although the general form of the change of measure is well known, few papers have investigated the change of measure for interest rate models and their implications for the way a model can fit to empirical facts about the behaviour of interest rates. This paper demonstrates that arbitrary specifications of market price of risk in empirical studies under the two factor affine interest rate model with jumps are not compatible with the theory of original interest rate model. Particularly, the empirical models of Duffee (2002) and Duarte (2003) may be wrong specifications in some parts under a rigorous theoretical interest rate theory.

scholarly journals Maximum likelihood estimator of the volatility of forward rates driven by geometric spatial AR sheet

2004 ◽  
Vol 2004 (4) ◽  
pp. 293-309 ◽  
Author(s):  
József Gáll ◽  
Gyula Pap ◽  
Martien C. A. van Zuijlen
Keyword(s):  
Maximum Likelihood ◽  
Interest Rate ◽  
Maximum Likelihood Estimator ◽  
Discrete Time ◽  
Market Price ◽  
Likelihood Estimator ◽  
Market Price Of Risk ◽  
Forward Rates ◽  
No Arbitrage ◽  
Price Of Risk

Discrete-time forward interest rate curve models are studied, where the curves are driven by a random field. Under the assumption of no-arbitrage, the maximum likelihood estimator of the volatility parameter is given and its asymptotic behaviour is studied. First, the so-called martingale models are examined, but we will also deal with the general case, where we include the market price of risk in the discount factor.

Defined contribution pension planning with a stochastic interest rate and mean-reverting returns under the hyperbolic absolute risk aversion preference

2019 ◽  
Author(s):  
Hao Chang ◽  
Chunfeng Wang ◽  
Zhenming Fang ◽  
Dan Ma
Keyword(s):  
Interest Rate ◽  
Absolute Risk ◽  
Market Price ◽  
Optimal Strategies ◽  
Stochastic Interest Rate ◽  
Market Price Of Risk ◽  
Absolute Risk Aversion ◽  
Stochastic Interest ◽  
Price Of Risk ◽  
The Interest Rate

Abstract The interest rate and the market price of risk may be stochastic in a real-world financial market. In this paper, the interest rate is assumed to be driven by a stochastic affine interest rate model and the market price of risk from the stock market is a mean-reverting process. In addition, the dynamics of the stock are simultaneously driven by random sources of interest rate and the stock market itself. In pension fund management, different fund managers may have different risk preferences. We suppose risk preference is described by the hyperbolic absolute risk aversion utility, which is a general utility function describing different risk preferences. Legendre transform-dual theory is presented to successfully obtain explicit expressions for optimal strategies. A numerical example illustrates the sensitivity of optimal strategies to market parameters. Theoretical results imply that the risks from stochastic interest rate and stochastic return may be completely hedged by adopting specific portfolios.

AFFINE MODELS WITH STOCHASTIC MARKET PRICE OF RISK

2017 ◽  
Vol 20 (04) ◽  
pp. 1750027 ◽  
Author(s):  
RICCARDO REBONATO
Keyword(s):  
Term Structure ◽  
Yield Curve ◽  
Market Price ◽  
Model Specification ◽  
Reduced Form ◽  
State Variables ◽  
Market Price Of Risk ◽  
Affine Models ◽  
Price Of Risk ◽  
Stochastic Market

In this paper we discuss the common shortcomings of a large class of essentially-affine models in the current monetary environment of repressed rates, and we present a class of reduced-form stochastic-market-risk affine models that can overcome these problems. In particular, we look at the extension of a popular doubly-mean-reverting Vasicek model, but the idea can be applied to all essentially-affine models. The model straddles the [Formula: see text]- and [Formula: see text]-measures. By allowing for a market price of risk whose stochasticity is not fully spanned by the yield-curve state variables that enter the model specification, we break the deterministic link between the yield-curve-based return-predicting factors and the market price of risk, but we retain, on average, the observed statistical regularities reported in the literature. We discuss in detail how this approach relates to the recent work by Joslin et al. (2014) [S. Joslin, M. Priebsch & K. J. Singleton (2014) Risk premiums in dynamic term structure models with unspanned macro risk, Journal of Finance LXIX (3), 1197–1233]. We show that the parameters of the model can be estimated in a simple and robust manner using survey-like information; and that the model we propose affords a more plausible decomposition of observed market yields into expectations and risk premia during an important recent market event than the one produced by mainstream essentially-affine models.

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