Optimal Hedging Of Option Portfolios With Transaction Costs

Download Optimal Hedging Of Option Portfolios With Transaction Costs full books in PDF, epub, and Kindle. Read online Optimal Hedging Of Option Portfolios With Transaction Costs ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Optimal Hedging of Option Portfolios with Transaction Costs

Author : Valeriy Zakamulin
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis Optimal Hedging of Option Portfolios with Transaction Costs by : Valeriy Zakamulin

Download or read book Optimal Hedging of Option Portfolios with Transaction Costs written by Valeriy Zakamulin and published by . This book was released on 2006 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most successful approaches to option hedging with transaction costs is the utility based approach pioneered by Hodges and Neuberger (1989). However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. The direct numerical computations of the utility based hedging strategy are cumbersome in a practical implementation. Despite some recent advances in finding an explicit description of the utility based hedging strategy by using either asymptotic, approximation, or other methods, so far they were concerned primarily with hedging a single plain-vanilla option. However, in practice one often faces the problem of hedging a portfolio of options on the same underlying asset. Since the knowledge of the optimal hedging strategy for a portfolio of options is of great practical significance, in this paper we suggest a simplified parameterized description of the utility based hedging strategy for a portfolio of options and a simple method for finding the optimal parameters. We provide an empirical testing of our optimized hedging strategies against some alternative strategies and show that our strategies outperform all the others.

Optimal Partial Hedging of Options with Small Transaction Costs

Author : A. Elizabeth Whalley
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis Optimal Partial Hedging of Options with Small Transaction Costs by : A. Elizabeth Whalley

Download or read book Optimal Partial Hedging of Options with Small Transaction Costs written by A. Elizabeth Whalley and published by . This book was released on 2019 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper uses asymptotic analysis to derive optimal hedging strategies for option portfolios hedged using an imperfectly correlated hedging asset with small fixed and/or proportional transaction costs, obtaining explicit formulae in special cases. This is of use when it is impractical to hedge using the underlying asset itself. The hedging strategy holds a position in the hedging asset whose value lies between two bounds, which are independent of the hedging asset's current value. For low absolute correlation between hedging and hedged assets, highly risk-averse investors and large portfolios, hedging strategies and option values differ significantly from their perfect market equivalents.

Optimal Hedging Portfolios for Derivative Securities in the Presence of Large Transaction Costs

Author : Marco Avellaneda
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis Optimal Hedging Portfolios for Derivative Securities in the Presence of Large Transaction Costs by : Marco Avellaneda

Download or read book Optimal Hedging Portfolios for Derivative Securities in the Presence of Large Transaction Costs written by Marco Avellaneda and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a new class of strategies for hedging derivative securities taking into account transaction costs, assuming lognormal continuous-time prices for the underlying asset. We do not assume that the payoff is convex as in Leland (J of Finance, 1985), or that the transaction costs are small compared to the price changes between portfolio adjustments, as in Hoggard, Whalley and Wilmott (Adv. in Futures and Options Res., 1993). The Leland number, A, which is proportional to the ratio of the round-trip tansaction cost over the typical price movement during the period between transactions, is a measure of the importance of transaction costs versus hedging risk. If A is greater than or equal to one, standard delta-hedging methods fail unless the payoff of the derivative security is a convex function of the price of the underlying asset. In contrast, our new strategies can be used effectively in the presence of large transaction costs to control simultaneously hedge-slippage as well as hedging costs. These strategies are associated with the solution an quot;obstacle problemquot; for a Black-Scholes diffusion equation with Leland's quot;augmentedquot; volatility, a parameter which depends on the volatility of the underlying asset as well as on A. The new strategies are such that the frequency for rebalancing the portfolio is variable. There are periods in which rehedging takes place often to control gamma-risk and other periods, which can be relatively long, when no transactions are needed. Moreover, instead of replicating exactly the final payoff, the strategies can yield a positive cash flow at expiration, according to the price history of the underlying security. The solution to the quot;obstacle problemquot; is often simple to calculate. There exist closed-form solutions for various securities of practical interest, such as digital options.

Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations

Author : Valeriy Zakamulin
Publisher :
ISBN 13 :
Total Pages : 45 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations by : Valeriy Zakamulin

Download or read book Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations written by Valeriy Zakamulin and published by . This book was released on 2008 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Hedging Option Portfolios in the Presence of Transaction Costs

Author : Paul Wilmott
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis Hedging Option Portfolios in the Presence of Transaction Costs by : Paul Wilmott

Download or read book Hedging Option Portfolios in the Presence of Transaction Costs written by Paul Wilmott and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a nonlinear parabolic partial differential equation for the value of portfolios of options in the presence of proportional transaction costs. This assumes a Leland world of transacting after each time interval, which is of fixed length. The equation reduces to the modified variance case described by Leland in the case of a single option. We demonstrate the nonlinear nature of option portfolios and give results for several simple combinations of options.

The Best Hedging Strategy in the Presence of Transaction Costs

Author : Valeriy Zakamulin
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis The Best Hedging Strategy in the Presence of Transaction Costs by : Valeriy Zakamulin

Download or read book The Best Hedging Strategy in the Presence of Transaction Costs written by Valeriy Zakamulin and published by . This book was released on 2008 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considerable theoretical work has been devoted to the problem of option pricing and hedging with transaction costs. A variety of methods have been suggested and are currently being used for dynamic hedging of options in the presence of transaction costs. However, very little was done on the subject of an empirical comparison of different methods for option hedging with transaction costs. In a few existing studies the different methods are compared by studying their empirical performances in hedging only a plain-vanilla short call option. The reader is tempted to assume that the ranking of the different methods for hedging any kind of option remains the same as that for a vanilla call. The main goal of this paper is to show that the ranking of the alternative hedging strategies depends crucially on the type of the option position being hedged and the risk preferences of the hedger. In addition, we present and implement a simple optimization method that, in some cases, improves considerably the performance of some hedging strategies.

Optimal Hedging of Derivatives with Transaction Costs

Author : Erik Aurell
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis Optimal Hedging of Derivatives with Transaction Costs by : Erik Aurell

Download or read book Optimal Hedging of Derivatives with Transaction Costs written by Erik Aurell and published by . This book was released on 2005 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at hand, these conditions simply imply arbitrage-free (Black-Scholes) pricing of the derivative. While pricing is hence not changed by friction allow a portfolio to fluctuate around a delta hedge. In the limit of weak friction, we determine the optimal control to essentially be of two parts: a strong control, which tries to bring the stock-and-derivative portfolio towards a Black-Scholes delta hedge; and a weak control, which moves the portfolio by adding or subtracting a Black-Scholes hedge. For simplicity we assume growth-optimal investment criteria and quadratic friction.

Yet Another Note on the Leland's Option Hedging Strategy with Transaction Costs

Author : Valeriy Zakamulin
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis Yet Another Note on the Leland's Option Hedging Strategy with Transaction Costs by : Valeriy Zakamulin

Download or read book Yet Another Note on the Leland's Option Hedging Strategy with Transaction Costs written by Valeriy Zakamulin and published by . This book was released on 2016 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a market with transaction costs the option hedging is costly. The idea presented by Leland (1985) was to include the expected transaction costs in the cost of a replicating portfolio. The resulting Leland's pricing and hedging method is an adjusted Black-Scholes method where one uses a modified volatility in the Black-Scholes formulas for the option price and delta. The Leland's method has been criticized on different grounds. Despite the critique, the risk-return tradeoff of the Leland's strategy is often better than that of the Black-Scholes strategy even in the case when a hedger starts with the same initial value of a replicating portfolio. This implies that the Leland's modification of volatility does optimize somehow the Black-Scholes hedging strategy in the presence of transaction costs. In this paper we explain how the Leland's modified volatility works and show how the performance of the Leland's hedging strategy can be improved by finding the optimal modified volatility. It is not claimed that the Leland's hedging strategy is optimal. Rather, the optimization mechanism of the modified hedging volatility can be exploited to improve the risk-return tradeoffs of other well-known option hedging strategies in the presence of transaction costs.

On Leland's Option Hedging Strategy with Transaction Costs

Author : Yonggan Zhao
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (118 download)

DOWNLOAD NOW!

Book Synopsis On Leland's Option Hedging Strategy with Transaction Costs by : Yonggan Zhao

Download or read book On Leland's Option Hedging Strategy with Transaction Costs written by Yonggan Zhao and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Optimal Dynamic Hedging of Equity Options

Author : Andrea Petrelli
Publisher :
ISBN 13 :
Total Pages : 85 pages
Book Rating : 4.:/5 (13 download)

DOWNLOAD NOW!

Book Synopsis Optimal Dynamic Hedging of Equity Options by : Andrea Petrelli

Download or read book Optimal Dynamic Hedging of Equity Options written by Andrea Petrelli and published by . This book was released on 2019 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: Attempted dynamic replication based valuation of equity options is analyzed using the Optimal Hedge Monte-Carlo (OHMC) method. Detailed here are (1) the option hedging strategy and its costs; (2) irreducible hedging errors associated with realistically fat-tailed & asymmetric return distributions; (3) impact of transaction costs on hedging costs and hedge-performance; (4) impact of conditioning hedging strategy on realized volatility. The asset returns are addressed by the General Auto-Regressive Asset Model (GARAM, Wang et al [2009]) that employs two stochastic processes to model the return magnitude and sign and results in a realistic term-structure of the fat-tails, dynamic-asymmetry, and clustering of volatility. The relationship between the option price and ensuing return versus risk characteristics of the option seller-hedger & buyer-hedger are described for different conditioning regimes in GARAM. A hurdle return is employed to assess bounding values of options that reflect hedging costs, the inevitable hedge slippage, & transaction costs. The hurdle return can also be used to make relative-value inferences (e.g., by comparing to the return-risk profile of a delta-1 position in the underlying) or even fit option values to market while still informing the trader about residual risk and its asymmetry between option buyer-hedger and seller-hedger. Tail-risk measures are shown to diminish by conditioning the hedging strategy and valuation on realized volatility. The role of fat-tails and uncertainty of realized volatility and its temporal persistence in controlling the optimal hedge ratios, irreducible hedging errors, and option-trading risk premiums are delineated.

Options Under Transaction Costs

Author : Alet Roux
Publisher : VDM Publishing
ISBN 13 : 9783836492393
Total Pages : 0 pages
Book Rating : 4.4/5 (923 download)

DOWNLOAD NOW!

Book Synopsis Options Under Transaction Costs by : Alet Roux

Download or read book Options Under Transaction Costs written by Alet Roux and published by VDM Publishing. This book was released on 2008-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Option Hedging

Author :
Publisher :
ISBN 13 :
Total Pages : 62 pages
Book Rating : 4.:/5 (936 download)

DOWNLOAD NOW!

Book Synopsis Option Hedging by :

Download or read book Option Hedging written by and published by . This book was released on 2002 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs

Author : Valeriy Zakamulin
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs by : Valeriy Zakamulin

Download or read book European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs written by Valeriy Zakamulin and published by . This book was released on 2010 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

American Options Under Proportional Transaction Costs

Author : Tomasz Zastawniak
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis American Options Under Proportional Transaction Costs by : Tomasz Zastawniak

Download or read book American Options Under Proportional Transaction Costs written by Tomasz Zastawniak and published by . This book was released on 2007 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: American options are priced and hedged in a general discrete market in the presence of arbitrary proportional transaction costs inherent in trading the underlying asset, modelled as bid-ask spreads. Pricing, hedging and optimal stopping algorithms are established for a short position (seller's position) in an American option with an arbitrary payoff settled by physical delivery. The seller's price representation as the expectation of the stopped payoff under an approximate martingale measure is also considered. The algorithms cover and extend the various special cases considered in the literature to-date. Any specific restrictions that were imposed on the form of the payoff, the magnitude of transaction costs or the discrete market model itself are relaxed. The pricing algorithm under transaction costs can be viewed as a natural generalisation of the iterative Snell envelope construction.

Optimal Hedging of Options with Small But Arbitrary Transaction Cost Structure

Author : A. E. Whalley
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (93 download)

DOWNLOAD NOW!

Book Synopsis Optimal Hedging of Options with Small But Arbitrary Transaction Cost Structure by : A. E. Whalley

Download or read book Optimal Hedging of Options with Small But Arbitrary Transaction Cost Structure written by A. E. Whalley and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hedging Market Exposures

Author : Oleg V. Bychuk
Publisher : John Wiley & Sons
ISBN 13 : 111808537X
Total Pages : 322 pages
Book Rating : 4.1/5 (18 download)

DOWNLOAD NOW!

Book Synopsis Hedging Market Exposures by : Oleg V. Bychuk

Download or read book Hedging Market Exposures written by Oleg V. Bychuk and published by John Wiley & Sons. This book was released on 2011-06-28 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Identify and understand the risks facing your portfolio, how to quantify them, and the best tools to hedge them This book scrutinizes the various risks confronting a portfolio, equips the reader with the tools necessary to identify and understand these risks, and discusses the best ways to hedge them. The book does not require a specialized mathematical foundation, and so will appeal to both the generalist and specialist alike. For the generalist, who may not have a deep knowledge of mathematics, the book illustrates, through the copious use of examples, how to identify risks that can sometimes be hidden, and provides practical examples of quantifying and hedging exposures. For the specialist, the authors provide a detailed discussion of the mathematical foundations of risk management, and draw on their experience of hedging complex multi-asset class portfolios, providing practical advice and insights. Provides a clear description of the risks faced by managers with equity, fixed income, commodity, credit and foreign exchange exposures Elaborates methods of quantifying these risks Discusses the various tools available for hedging, and how to choose optimal hedging instruments Illuminates hidden risks such as counterparty, operational, human behavior and model risks, and expounds the importance and instability of model assumptions, such as market correlations, and their attendant dangers Explains in clear yet effective terms the language of quantitative finance and enables a non-quantitative investment professional to communicate effectively with professional risk managers, "quants", clients and others Providing thorough coverage of asset modeling, hedging principles, hedging instruments, and practical portfolio management, Hedging Market Exposures helps portfolio managers, bankers, transactors and finance and accounting executives understand the risks their business faces and the ways to quantify and control them.

Option Pricing and Hedging with Transaction Costs

Author : Ling Chen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (665 download)

DOWNLOAD NOW!

Book Synopsis Option Pricing and Hedging with Transaction Costs by : Ling Chen

Download or read book Option Pricing and Hedging with Transaction Costs written by Ling Chen and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.