HETEROGENEITY IN RISK PREFERENCES LEADS TO STOCHASTIC VOLATILITY

2018 ◽  
Vol 21 (06) ◽  
pp. 1850035 ◽  
Author(s):  
DIETMAR P. J. LEISEN
Keyword(s):  
Risk Preferences ◽  
Price Volatility ◽  
Relative Risk Aversion ◽  
Book Value ◽  
Price Process ◽  
State Price ◽  
State Dependent ◽  
Crra Preferences ◽  
Pure Exchange ◽  
Pure Exchange Economy

This paper studies the price processes of a claim on terminal endowment and of a claim on firm book value when the underlying variables follow a bivariate geometric Brownian motion. If the state-price process is multiplicatively separable into time and endowment functions, our main result shows that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, the endowment function is not a power function. In a pure exchange economy populated by two agents with constant relative risk aversion (CRRA) preferences we confirm the separability, and we show furthermore that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, both agents are heterogeneous in risk-preferences.

A NOTE ON THE RISK-PREMIUM PROCESS IN AN EQUILIBRIUM

2008 ◽  
Vol 11 (07) ◽  
pp. 705-716
Author(s):  
JUN SEKINE
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Risk Premium ◽  
Jacobian Matrix ◽  
Marginal Utility ◽  
Relative Risk Aversion ◽  
State Variables ◽  
Pure Exchange ◽  
Pure Exchange Economy ◽  
Risk Aversion Coefficient

Results in He–Leland (1993) are extended and properties of the risk-premium process in an equilibrium are examined in a pure exchange economy with a representative agent: for example, (i) the risk-premium process is characterized by using a martingale representation of the reciprocal of a terminal marginal utility, (ii) it is expressed as a (conditional) expected value including the relative risk aversion coefficient of a terminal utility and the Jacobian matrix process of the state variables, and, (iii) a "mean-reverting" property relates to the monotonic decreasing property of the relative risk aversion coefficient.

scholarly journals Equilibrium Pricing in Incomplete Markets

2005 ◽  
Vol 40 (4) ◽  
pp. 833-848 ◽  
Author(s):  
Abdelhamid Bizid ◽  
Elyès Jouini
Keyword(s):  
Stochastic Volatility ◽  
Incomplete Markets ◽  
Stochastic Volatility Model ◽  
Time Model ◽  
Equilibrium Pricing ◽  
Discrete Time Model ◽  
Price Process ◽  
State Price ◽  
Volatility Model ◽  
Market Framework

AbstractGiven the exogenous price process of some assets, we constrain the price process of other assets that are characterized by their final payoffs. We deal with an incomplete market framework in a discrete-time model and assume the existence of the equilibrium. In this setup, we derive restrictions on the state-price deflators. These restrictions do not depend on a particular choice of utility function. We investigate numerically a stochastic volatility model as an example. Our approach leads to an interval of admissible prices that is more robust than the arbitrage pricing interval.

A RECOMBINING TREE METHOD FOR OPTION PRICING WITH STATE-DEPENDENT SWITCHING RATES

2016 ◽  
Vol 19 (02) ◽  
pp. 1650012 ◽  
Author(s):  
J. X. JIANG ◽  
R. H. LIU ◽  
D. NGUYEN
Keyword(s):  
Option Pricing ◽  
Regime Switching ◽  
Asset Price ◽  
Numerical Results ◽  
Price Process ◽  
State Dependent ◽  
Switching Models ◽  
Markovian Regime Switching ◽  
Tree Method ◽  
Markovian Regime

This paper develops simple and efficient tree approaches for option pricing in switching jump diffusion models where the rates of switching are assumed to depend on the underlying asset price process. The models generalize many existing models in the literature and in particular, the Markovian regime-switching models with jumps. The proposed trees grow linearly as the number of tree steps increases. Conditions on the choices of key parameters for the tree design are provided that guarantee the positivity of branch probabilities. Numerical results are provided and compared with results reported in the literature for the Markovian regime-switching cases. The reported numerical results for the state-dependent switching models are new and can be used for comparison in the future.

Design and pricing of derivative contracts in a spectrum market

2015 ◽  
Vol 02 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Aparna Gupta ◽  
Koushik Kar ◽  
Praveen K. Muthuswamy
Keyword(s):  
Wireless Channels ◽  
Numerical Study ◽  
Price Volatility ◽  
Spot Price ◽  
Spectrum Access ◽  
Self Similarity ◽  
Price Process ◽  
Management Objectives ◽  
Price Increases ◽  
Spectrum Market

We propose a secondary spectrum market that allows wireless providers to purchase spectrum access licenses of short duration in the form of spot contracts and derivative contracts on spectrum. A spot contract provides immediate access to one or more wireless channels and cannot be further traded. On the other hand, derivative contracts on spectrum typically involve purchase of spectrum licenses in the future for predefined terms, and they can play an important role in risk management objectives of wireless providers. In this paper, we utilize a model for the spot price of spectrum licenses in which the price increases with increasing congestion in spectrum usage caused by the primary demand for spectrum. The spot price process, modeled as driven by a fractional Brownian motion (fBm) process to capture the self-similarity properties of wireless traffic, is utilized in fractional stochastic calculus to obtain the value of derivative contracts. We design a variety of derivative contracts considering the risk profile of both the buyers and sellers of spectrum. Through a detailed numerical study, we examine the value of these derivative contracts for changes in spot price volatility and the parameters that define the contracts.

AN ECONOMIC PREMIUM PRINCIPLE UNDER THE DUAL THEORY OF THE SMOOTH AMBIGUITY MODEL

2017 ◽  
Vol 47 (3) ◽  
pp. 787-801 ◽  
Author(s):  
Yoichiro Fujii ◽  
Hideki Iwaki ◽  
Yusuke Osaki
Keyword(s):  
Ambiguity Aversion ◽  
Sufficient Conditions ◽  
Exchange Economy ◽  
Comparative Statics ◽  
Ambiguous Loss ◽  
Dual Theory ◽  
Demand For Insurance ◽  
Smooth Ambiguity Model ◽  
Pure Exchange ◽  
Pure Exchange Economy

AbstractThis study considers a pure exchange economy with insurance against ambiguous loss. Ambiguity preferences are represented by the dual theory of the smooth ambiguity model from Iwaki and Osaki (2014). The economic premium principle of Bühlmann (1980, 1984) is extended to ambiguity. We also perform some comparative statics and present sufficient conditions under which an increase in ambiguity aversion increases insurance demand and insurance premiums. Contrary to the result in Tsanakas and Christofides (2006), the optimal demand for insurance is not always comonotonic, because our model permits an economy comprising both ambiguity averse and ambiguity loving agents.

Power Law with Exponential Cut‐off Utility

Metamorphosis ◽  
2014 ◽  
Vol 13 (1) ◽  
pp. 26-32
Author(s):  
Afreen Arif H. ◽  
T.P.M. Pakkala
Keyword(s):  
Risk Aversion ◽  
Utility Function ◽  
Power Law ◽  
Risk Preferences ◽  
Portfolio Allocation ◽  
Utility Functions ◽  
Relative Risk Aversion ◽  
Optimal Solutions ◽  
New Class ◽  
Exponential Power

Most of the utility functions studied earlier concentrated on properties of risk aversion. In this article, the authors have introduced a new class of utility function called the Power Law with Exponential Cut-off (PLEC) utility function, which exhibits all the absolute and relative risk aversion and risk loving preferences of individuals, under various conditions. It generalises and encompasses other systems of utility functions like that of exponential power. Certain properties of this utility function are discussed. Sensitivity analysis exhibits different portfolio allocations for various risk preferences. The analysis also shows that arbitrary risk preferences may lead to biased risk response estimates. Performance of PLEC utility function in portfolio allocation problem is demonstrated through numerical examples. This is evaluated through optimal solutions.

scholarly journals Asset Returns and State-Dependent Risk Preferences

2004 ◽  
Vol 22 (3) ◽  
pp. 241-252 ◽  
Author(s):  
Stephen Gordon ◽  
Pascal St-Amour
Keyword(s):  
Risk Preferences ◽  
Asset Returns ◽  
State Dependent
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