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Author: Stepan Sahakyan Publisher: ISBN: Category : Languages : en Pages : 9
Book Description
In this paper we propose conceptually new approach to pricing European call options in markets with transaction costs. In contrast to the previous research, we introduce and model two - quote and gross (which includes transaction costs and fees) - price processes. Also using both price processes we introduce new portfolio replication concept, namely "quasi replication" strategy. The advantage of the proposed model is its simplicity, whereby the price of the European option is expressed in terms of the Black-Scholes type formulas.
Author: Stepan Sahakyan Publisher: ISBN: Category : Languages : en Pages : 9
Book Description
In this paper we propose conceptually new approach to pricing European call options in markets with transaction costs. In contrast to the previous research, we introduce and model two - quote and gross (which includes transaction costs and fees) - price processes. Also using both price processes we introduce new portfolio replication concept, namely "quasi replication" strategy. The advantage of the proposed model is its simplicity, whereby the price of the European option is expressed in terms of the Black-Scholes type formulas.
Author: Ajay Subramanian Publisher: ISBN: Category : Languages : en Pages : 63
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: Valeriy Zakamulin Publisher: ISBN: Category : Languages : en Pages : 27
Book Description
In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: We extend the framework developed by Davis, Panas and Zariphopoulou (1993) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whaley and Wilmott (1994). We provide a simulation analysis in order to compare the performance of the utility based hedging strategy against the asymptotic strategy and some other common strategies.
Author: Alet Roux Publisher: ISBN: Category : Languages : en Pages : 20
Book Description
The paper is devoted to optimal superreplication of European options in the discrete setting under proportional transaction costs on the underlying asset. In particular, general pricing and hedging algorithms are developed. This extends previous work by many authors, which has been focused on the binomial tree model and options with specific payoffs such as calls or puts, often under certain bounds on the magnitude of transaction costs. All such restrictions are hereby removed. The results apply to options with arbitrary payoffs in the general discrete market model with arbitrary proportional transaction costs. Numerical examples are presented to illustrate the results and their relationships to the earlier work on pricing options under transaction costs.
Author: Alet Roux Publisher: VDM Publishing ISBN: 9783836492393 Category : Algorithms Languages : en Pages : 0
Book Description
This book is aimed at researchers and PhD students in mathematical finance. It studies the pricing and hedging of options in financial markets with proportional transaction costs on trading in shares, modeled as bid-ask spreads, and different interest rates for borrowing and lending of cash. This is done by means of fair pricing and super-hedging. The fair price of an option is any market price for it that does not allow traders to make profit with no risk, and a super-hedging strategy allows the seller and buyer to remain in a solvent position after respectively delivering and receiving the option payoff. Efficient algo-rithms are presented for computing the bid and ask prices of European and American options; these prices serve as bounds on the fair prices. This unifies all existing algorithms for the calculation of such prices. As a by-product, a straightforward iterative method is found for determining the optimal super-hedging strategies (and stopping times) for both the buyer and seller of an option, and also optimal stopping strategies in the case of American options.
Author: Guy Barles Publisher: ISBN: Category : Languages : en Pages :
Book Description
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: Ling Chen Publisher: ISBN: Category : Languages : en Pages :
Book Description
The traditional Black-Scholes theory on pricing and hedging of European call options has long been criticized for its oversimplified and unrealistic model assumptions. This dissertation investigates several existing modifications and extensions of the Black-Scholes model and proposes new data-driven approaches to both option pricing and hedging for real data. The semiparametric pricing approach initially proposed by Lai and Wong (2004) provides a first attempt to bridge the gap between model and market option prices. However, its application to the S & P 500 futures options is not a success, when the original additive regression splines are used for the nonparametric part of the pricing formula. Having found a strong autocorrelation in the time-series of the Black-Scholes pricing residuals, we propose a lag-1 correction for the Black-Scholes price, which essentially is a time-series modeling of the nonparametric part in the semiparametric approach. This simple but efficient time-series approach gives an outstanding pricing performance for S & P 500 futures options, even compared with the commonly practiced and favored implied volatility approaches. A major type of approaches to option hedging with proportional transaction costs is based on singular stochastic control problems that seek an optimal balance between the cost and the risk of hedging an option. We propose a data-driven rule-based strategy to connect the theoretical approaches with real-world applications. Similar to the optimal strategies in theory, the rule-based strategy can be characterized by a pair of buy/sell boundaries and a no-transaction region in between. A two-stage iterative procedure is provided for tuning the boundaries to a long period of option data. Comparing the rule-based strategy with several other existing hedging strategies, we obtain favorable results in both the simulation studies and the empirical study using the S & P 500 futures and futures options. Making use of a reverting pattern of the S & P 500 futures price, we refine the rule-based strategy by allowing hedging suspension at large jumps in futures price.
Author: Stepan Sahakyan
Author: Stepan Sahakyan
Author: Asadullah Jawid
Author: Ajay Subramanian Aiyer
Author: Ajay Subramanian
Author: Yuri Kabanov
Author: Valeriy Zakamulin
Author: Alet Roux
Author: Alet Roux
Author: Guy Barles
Author: Ling Chen