A Note on the Utility Based Option Pricing with Proportional Transaction Costs Under Large Risk Aversion PDF Download
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Author: Bruno Bouchard
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
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Author: Bruno Bouchard
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
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Author: Erling Dalgaard Andersen
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Category :
Languages : en
Pages :
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The purpose of the present work is to examine the financial problem of finding the reservation purchase price of a European call option written on a risky security when there is proportional transaction costs in the market. Existing papers within this area have all simplified the analysis by considering only one risky security and assumed exponential utility functions. The goal of the present paper is to suggest an approach to compute the reservation price of an option in an economy with more than one risky security and where trade involves transaction costs. Furthermore, the new approach enables us to investigate to what extent the above mentioned simplifications affect the reservation prices. We consider an economy with a riskless security, two risky securities, and agents with HARA utility functions. We suggest an approach to compute reservation prices using convex optimization. Unfortunately, the proposed optimization models become large in terms of the number of constraints and variables. However, using a newly developed interior-point algorithm, we manage to solve problems of an interesting size. The major findings are: (i) the investor's reservation purchase price of a European call option is almost insensitive to the functional form of the utility function, but sensitive (only slightly) to the initial level of absolute risk aversion, and (ii) the presence of diversification opportunities does not affect the reservation price in any unique way.interior-point optimization, reservation prices of options, optimal portfolio choice, diversification.
Author: Erling D. Andersen
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
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Author: Stylianos Perrakis
Publisher: Springer
ISBN: 3030115909
Category : Business & Economics
Languages : en
Pages : 277
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This book illustrates the application of the economic concept of stochastic dominance to option markets and presents an alternative option pricing paradigm to the prevailing no arbitrage simultaneous equilibrium in the frictionless underlying and option markets. This new methodology was developed primarily by the author, working independently or jointly with other co-authors, over the course of more than thirty years. Among others, it yields the fundamental Black-Scholes-Merton option value when markets are complete, presents a new approach to the pricing of rare event risk, and uncovers option mispricing that leads to tradeable strategies in the presence of transaction costs. In the latter case it shows how a utility-maximizing investor trading in the market and a riskless bond, subject to proportional transaction costs, can increase his/her expected utility by overlaying a zero-net-cost portfolio of options bought at their ask price and written at their bid price, irrespective of the specific form of the utility function. The book contains a unified presentation of these methods and results, making it a highly readable supplement for educators and sophisticated professionals working in the popular field of option pricing. It also features a foreword by George Constantinides, the Leo Melamed Professor of Finance at the Booth School of Business, University of Chicago, USA, who was a co-author in several parts of the book.
Author: Kamlesh Mathur
Publisher:
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Category :
Languages : en
Pages :
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This article establishes bounds on option prices in an economy where the representative investor has non increasing absolute risk aversion. The bounds do not require knowledge of any specific utility parameters, nor do they require specific joint distribution assumptions between the marginal utility of aggregate consumption and the underlying stock price. To drive our results we only require that the expected marginal utility of consumption conditional on the stock price is monotone non increasing in the stock price, and that the marginal distribution of the stock price is given. With this assumption, the lower bound on option prices is given by the solution to a non-linear mathematical program. We identify the general solution of this program. If the underlying process is multinomial, we show that the lower bound is set up as if the representative investor had constant proportional risk aversion. For this case, a risk neutral valuation relationship exists. As a result, the lower bound does not depend on the drift term, nor is it affected by the number of permissible trading periods prior to expiration. Moreover, if the underlying distribution is lognormal, the lower bound is the Black Scholes price. The upper bound on option prices is also identified and its behavior as multiple portfolio opportunities exist is examined.
Author: Guy Barles
Publisher:
ISBN:
Category :
Languages : en
Pages :
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In a market with transaction costs, generally, there is no nontrivial portfolio that dominates a contingent claim. Therefore, in such a market, preferences have to be introduced in order to evaluate the prices of options. The main goal of this article is to quantify this dependence on preferences in the specific example of a European call option. This is achieved by using the utility function approach of Hodges and Neuberger together with an asymptotic analysis of partial differential equations. We are led to a nonlinear Black-Scholes equation with an adjusted volatility which is a function of the second derivative of the price itself. In this model, our attitude towards risk is summarized in one free parameter a which appears in the nonlinear Black-Scholes equation : we provide an upper bound for the probability of missing the hedge in terms of a and the magnitude of the proportional transaction cost which shows the connections between this parameter a and the risk.
Author: Nicolae Garleanu
Publisher:
ISBN:
Category : Hedging (Finance)
Languages : en
Pages : 68
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We model the demand-pressure effect on prices when options cannot be perfectly hedged. The model shows that demand pressure in one option contract increases its price by an amount proportional to the variance of the unhedgeable part of the option. Similarly, the demand pressure increases the price of any other option by an amount proportional to the covariance of their unhedgeable parts. Empirically, we identify aggregate positions of dealers and end users using a unique dataset, and show that demand-pressure effects help explain well-known option-pricing puzzles. First, end users are net long index options, especially out-of-money puts, which helps explain their apparent expensiveness and the smirk. Second, demand patterns help explain the prices of single-stock options.
Author: Ajay Subramanian
Publisher:
ISBN:
Category :
Languages : en
Pages : 63
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In this paper, we study the problem of European Option Pricing in a market with short-selling constraints and transaction costs having a very general form. We consider two types of proportional costs and a strictly positive fixed cost. We study the problem within the framework of the theory of stochastic impulse control. We show that determining the price of a European option involves calculating the value functions of two stochastic impulse control problems. We obtain explicit expressions for the quasi-variational inequalities satisfied by the value functions and derive the solution in the case where the parameters of the price processes are constants and the investor's utility function is linear. We use this result to obtain a price for a call option on the stock and prove that this price is a nontrivial lower bound on the hedging price of the call option in the presence of general transaction costs and short-selling constraints. We then consider the situation where the investor's utility function has a general form and characterize the value function as the pointwise limit of an increasing sequence of solutions to associated optimal stopping problems. We thereby devise a numerical procedure to calculate the option price in this general setting and implement the procedure to calculate the option price for the class of exponential utility functions. Finally, we carry out a qualitative investigation of the option prices for exponential and linear-power utility functions.
Author: Lukasz Stettner
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Various aspects of pricing of contingent claims in discrete time for incomplete market models are studied. Formulas for prices with proportional transaction costs are obtained. Some results concerning pricing with concave transaction costs are shown. Pricing by the expected utility of terminal wealth isalso considered.
Author: Jens Carsten Jackwerth
Publisher:
ISBN:
Category :
Languages : en
Pages :
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