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Author: Roberto Baviera
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Book Description
We provide closed formulas for European call option ask and bid prices in presence of transaction costs. Underlying prices have the same dynamics of Black-Scholes model and a bid-ask spread proportional to bid price. We suppose that a market maker has to quote a bid and ask price for an option in a perfect competition market. Under these conditions derivative prices are obtained imposing the No Almost Sure Arbitrage Principle: the market maker fixes bid (ask) price as the highest buying (lowest selling) price that can accepted by an investor who maximizes the growth rate of his portfolio.
Author: Roberto Baviera
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Book Description
We provide closed formulas for European call option ask and bid prices in presence of transaction costs. Underlying prices have the same dynamics of Black-Scholes model and a bid-ask spread proportional to bid price. We suppose that a market maker has to quote a bid and ask price for an option in a perfect competition market. Under these conditions derivative prices are obtained imposing the No Almost Sure Arbitrage Principle: the market maker fixes bid (ask) price as the highest buying (lowest selling) price that can accepted by an investor who maximizes the growth rate of his portfolio.
Author: Valeriy Zakamulin
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
In the presence of transaction costs the perfect option replication is impossible which invalidates the celebrated Black and Scholes (1973) model. In this chapter we consider some approaches to option pricing and hedging in the presence of transaction costs. The distinguishing feature of all these approaches is that the solution for the option price and hedging strategy is given by a nonlinear partial differential equation (PDE). We start with a review of the Leland (1985) approach which yields a nonlinear parabolic PDE for the option price, one of the first such in finance. Since the Leland's approach to option pricing has been criticized on different grounds, we present a justification of this approach and show how the performance of the Leland's hedging strategy can be improved. We extend the Leland's approach to cover the pricing and hedging of options on commodity futures contracts, as well as path-dependent and basket options. We also present examples of finite-difference schemes to solve some nonlinear PDEs. Then we proceed to the review of the most successful approach to option hedging with transaction costs, the utility-based approach pioneered by Hodges and Neuberger (1989). Judging against the best possible tradeoff between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. The asymptotic analysis of the option pricing and hedging in this approach reveals that the solution is also given by a nonlinear PDE. However, this approach has one major drawback that prevents the broad application of this approach in practice, namely, the lack of a closed-form solution. The numerical computations are cumbersome to implement and the calculations of the optimal hedging strategy are time consuming. Using the results of asymptotic analysis we suggest a simplified parameterized functional form of the optimal hedging strategy for either a single option or a portfolio of options and a method for finding the optimal parameters.
Author: Christopher John Danielian
Publisher:
ISBN:
Category :
Languages : en
Pages : 104
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Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Stylianos Perrakis
Publisher: Springer
ISBN: 3030115909
Category : Business & Economics
Languages : en
Pages : 277
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Book Description
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: Valeriy Zakamulin
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
In this paper we examine the problem of finding the reservation option prices and corresponding exercise policies of American options in a market with proportional transaction costs using the utility based approach proposed by Davis and Zariphopoulou (1995). We present a model where the option holder has a constant absolute risk aversion. We discuss the numerical algorithm and propose a new characterization of the option holder's value function. We suggest original discretization schemes for computing reservation prices and exercise policies of American options. The discretization schemes are implemented for the cases of American put and call options. We present the study of the optimal transaction policy of the option holder. We examine the effects on the reservation option prices and the corresponding exercise policies of varying the levels of absolute risk aversion and transaction costs.
Author: Ajay Subramanian
Publisher:
ISBN:
Category :
Languages : en
Pages : 63
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Book Description
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: Lihui Zheng
Publisher:
ISBN:
Category : Investment analysis
Languages : en
Pages : 52
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Author: Anthony Neuberger
Publisher:
ISBN:
Category :
Languages : en
Pages :
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In the presence of proportional transactions costs, the tightest bounds that can be imposed on the price of a call option when the asset price follows a geometric diffusion are those imposed by static portfolio strategies. The price of a call is bounded above by the value of the asset and below by its intrinsic value. However, with a pure jump process it is possible to obtain much tighter arbitrage bounds on the value of a contingent claim, which converge to the no-transaction-cost valuation as transaction costs become small.
Author: George M. Constantinides
Publisher:
ISBN:
Category :
Languages : en
Pages : 70
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Book Description
