scholarly journals How Firms Can Hedge Against Market Risk

2014 ◽  
Vol 37 (1) ◽  
pp. 39-49
Author(s):  
Krzysztof Echaust
Keyword(s):  
Absolute Risk ◽  
Future Price ◽  
Utility Model ◽  
Forward Contracts ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Absolute Risk Aversion ◽  
Black Scholes ◽  
Expected Utility Model ◽  
Constant Absolute Risk Aversion

Abstract The article presents a problem of proper hedging strategy in expected utility model when forward contracts and options strategies are available. We consider a case of hedging when an investor formulates his own expectation on future price of underlying asset. In this paper we propose the way to measure effectiveness of hedging strategy, based on optimal forward hedge ratio. All results are derived assuming a constant absolute risk aversion utility function and a Black-Scholes framework.

Constant Absolute Risk Aversion, Bankruptcy, and Wealth-Dependent Decisions

1980 ◽  
Vol 53 (3) ◽  
pp. 285 ◽  
Author(s):  
Steven A. Lippman ◽  
John J. McCall ◽  
Wayne L. Winston
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Absolute Risk Aversion ◽  
Constant Absolute Risk Aversion

DE FINETTI ON RISK AVERSION

2009 ◽  
Vol 25 (2) ◽  
pp. 153-159
Author(s):  
Joseph B. Kadane ◽  
Gaia Bellone
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Risk Premia ◽  
Absolute Risk Aversion ◽  
Kenneth Arrow ◽  
De Finetti ◽  
Constant Absolute Risk Aversion ◽  
Special Case

According to Mark Rubinstein (2006) ‘In 1952, anticipating Kenneth Arrow and John Pratt by over a decade, he [de Finetti] formulated the notion of absolute risk aversion, used it in connection with risk premia for small bets, and discussed the special case of constant absolute risk aversion.’ The purpose of this note is to ascertain the extent to which this is true, and at the same time, to correct certain minor errors that appear in de Finetti's work.

scholarly journals The Extended Black-Scholes Model with-LAGS-and “Hedging Errors”

2003 ◽  
Author(s):  
Mondher Bellalah
Keyword(s):  
Stock Price ◽  
Standard Form ◽  
Small Time ◽  
Market Model ◽  
Short Term ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Elapsed Time ◽  
Black Scholes Model ◽  
Black Scholes

The Black-Scholes model is derived under the assumption that heding is done instantaneously. In practice, there is a “small” time that elapses between buying or selling the option and hedging using the underlying asset. Under the following assumptions used in the standard Black-Scholes analysis, the value of the option will depend only on the price of the underlying asset S, time t and on other Variables assumed constants. These assumptions or “ideal conditions” as expressed by Black-Scholes are the following. The option us European, The short term interest rate is known, The underlying asset follows a random walk with a variance rate proportional to the stock price. It pays no dividends or other distributions. There is no transaction costs and short selling is allowed, i.e. an investment can sell a security that he does not own. Trading takes place continuously and the standard form of the capital market model holds at each instant. The last assumption can be modified because in practice, trading does not take place in-stantaneouly and simultaneously in the option and the underlying asset when implementing the hedging strategy. We will modify this assumption to account for the “lag”. The lag corresponds to the elapsed time between buying or selling the option and buying or selling - delta units of the underlying assets. The main attractions of the Black-Scholes model are that their formula is a function of “observable” variables and that the model can be extended to the pricing of any type of option. All the assumptions are conserved except the last one.

Bifractional Black-Scholes Model for Pricing European Options and Compound Options

2020 ◽  
Vol 8 (4) ◽  
pp. 346-355
Author(s):  
Feng Xu
Keyword(s):  
Empirical Studies ◽  
Asset Price ◽  
European Options ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Bifractional Brownian Motion ◽  
Compound Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Delta Hedging

AbstractRecent empirical studies show that an underlying asset price process may have the property of long memory. In this paper, it is introduced the bifractional Brownian motion to capture the underlying asset of European options. Moreover, a bifractional Black-Scholes partial differential equation formulation for valuing European options based on Delta hedging strategy is proposed. Using the final condition and the method of variable substitution, the pricing formulas for the European options are derived. Furthermore, applying to risk-neutral principle, we obtain the pricing formulas for the compound options. Finally, the numerical experiments show that the parameter HK has a significant impact on the option value.

scholarly journals TAIL BEHAVIOR OF STOPPED LÉVY PROCESSES WITH MARKOV MODULATION

2021 ◽  
pp. 1-28
Author(s):  
Brendan K. Beare ◽  
Won-Ki Seo ◽  
Alexis Akira Toda
Keyword(s):  
Economic Model ◽  
Absolute Risk ◽  
Tail Behavior ◽  
Tail Probabilities ◽  
Absolute Risk Aversion ◽  
Distribution Of Wealth ◽  
State Dependent ◽  
Markov Modulated ◽  
Constant Absolute Risk Aversion ◽  
Simple Economic

This article concerns the tail probabilities of a light-tailed Markov-modulated Lévy process stopped at a state-dependent Poisson rate. The tails are shown to decay exponentially at rates given by the unique positive and negative roots of the spectral abscissa of a certain matrix-valued function. We illustrate the use of our results with an application to the stationary distribution of wealth in a simple economic model in which agents with constant absolute risk aversion are subject to random mortality and income fluctuation.

scholarly journals Incentives, ability and disutility of effort

SERIEs ◽  
2021 ◽  
Author(s):  
Silvia Martinez-Gorricho ◽  
Miguel Sanchez Villalba
Keyword(s):  
Absolute Risk ◽  
Assortative Matching ◽  
Marginal Rate ◽  
Absolute Risk Aversion ◽  
Marginal Rate Of Substitution ◽  
New Novel ◽  
Effort Function ◽  
Parameter Values ◽  
Constant Absolute Risk Aversion ◽  
Rate Of Substitution

AbstractWe generalize the disutility of effort function in the linear-Constant Absolute Risk Aversion (CARA) pure moral hazard model. We assume that agents are heterogeneous in ability. Each agent’s ability is observable and treated as a parameter that indexes the disutility of effort associated with the task performed. In opposition to the literature (the “traditional” scenario), we find a new, “novel” scenario, in which a high-ability agent may be offered a weaker incentive contract than a low-ability one, but works harder. We characterize the conditions for the existence of these two scenarios: formally, the “traditional” (“novel”) scenario occurs if and only if the marginal rate of substitution of the marginal disutility of effort function is increasing (decreasing) in effort when evaluated at the second-best effort. If, further, this condition holds for all parameter values and matching is endogenous, less (more) talented agents work for principals with riskier projects in equilibrium. This implies that the indirect and total effects of risk on incentives are negative under monotone assortative matching.

Portfolio Choice

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Risk Aversion ◽  
Portfolio Choice ◽  
Choice Model ◽  
Absolute Risk ◽  
Risk Tolerance ◽  
Absolute Risk Aversion ◽  
Initial Wealth ◽  
Optimal Investments ◽  
Mean Variance ◽  
Constant Absolute Risk Aversion

The portfolio choice model is introduced, and the first‐order condition is derived. Properties of the demand for a single risky asset are derived from second‐order risk aversion and decreasing absolute risk aversion. Optimal investments are independent of initial wealth for investors with constant absolute risk aversion. Optimal investments are affine functions of initial wealth for investors iwth linear risk tolerance. The optimal portfolio for an investor with constant absolute risk aversion is derived when asset returns are normally distributed. Investors with quadratic utility have mean‐variance preferences, and investors have mean‐variance preferences when returns are elliptically distributed.

scholarly journals Short‐term investments and indices of risk

2020 ◽  
Vol 15 (3) ◽  
pp. 891-921
Author(s):  
Yuval Heller ◽  
Amnon Schreiber
Keyword(s):  
Risk Aversion ◽  
Absolute Risk ◽  
Risk Index ◽  
Decision Makers ◽  
Decision Problems ◽  
Risk Averse ◽  
Short Term ◽  
Risky Assets ◽  
Absolute Risk Aversion ◽  
Constant Absolute Risk Aversion

We study various decision problems regarding short‐term investments in risky assets whose returns evolve continuously in time. We show that in each problem, all risk‐averse decision makers have the same (problem‐dependent) ranking over short‐term risky assets. Moreover, in each problem, the ranking is represented by the same risk index as in the case of constant absolute risk aversion utility agents and normally distributed risky assets.

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