The Market Price of Risk of the Variance Term Structure

2011 ◽  
Author(s):  
George Dotsis
Keyword(s):  
Term Structure ◽  
Market Price ◽  
Market Price Of Risk ◽  
Price Of Risk

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.

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.

scholarly journals Implicit incentives for fund managers with partial information

2021 ◽  
Author(s):  
Flavio Angelini ◽  
Katia Colaneri ◽  
Stefano Herzel ◽  
Marco Nicolosi
Keyword(s):  
Asset Allocation ◽  
Partial Information ◽  
Market Price ◽  
Investment Strategy ◽  
Expected Returns ◽  
Martingale Method ◽  
Fund Manager ◽  
Market Price Of Risk ◽  
Fund Managers ◽  
Price Of Risk

AbstractWe study the optimal asset allocation problem for a fund manager whose compensation depends on the performance of her portfolio with respect to a benchmark. The objective of the manager is to maximise the expected utility of her final wealth. The manager observes the prices but not the values of the market price of risk that drives the expected returns. Estimates of the market price of risk get more precise as more observations are available. We formulate the problem as an optimization under partial information. The particular structure of the incentives makes the objective function not concave. Therefore, we solve the problem by combining the martingale method and a concavification procedure and we obtain the optimal wealth and the investment strategy. A numerical example shows the effect of learning on the optimal strategy.

Multidimensional Models: Martingale Approach

2019 ◽  
pp. 191-201
Author(s):  
Tomas Björk
Keyword(s):  
Market Price ◽  
Representation Formula ◽  
Explicit Representation ◽  
Martingale Measure ◽  
Market Price Of Risk ◽  
Martingale Approach ◽  
Price Of Risk ◽  
Equivalent Martingale ◽  
Absence Of Arbitrage ◽  
Multidimensional Models

In this chapter we study a very general multidimensional Wiener-driven model using the martingale approach. Using the Girsanov Theorem we derive the martingale equation which is used to find an equivalent martingale measure. We provide conditions for absence of arbitrage and completeness of the model, and we discuss hedging and pricing. For Markovian models we derive the relevant pricing PDE and we also provide an explicit representation formula for the stochastic discount factor. We discuss the relation between the market price of risk and the Girsanov kernel and finally we derive the Hansen–Jagannathan bounds for the Sharpe ratio.

A Primer on Incomplete Markets

2019 ◽  
pp. 128-137
Author(s):  
Tomas Björk
Keyword(s):  
Incomplete Markets ◽  
Factor Model ◽  
Market Price ◽  
Market Price Of Risk ◽  
Market Incompleteness ◽  
Price Of Risk

We discuss market incompleteness within the relatively simple framework of a factor model. The corresponding pricing PDE is derived and we relate it to the market price of risk.

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