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Author: Ling Chen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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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: Ling Chen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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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: 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: Valeriy Zakamulin
Publisher:
ISBN:
Category :
Languages : en
Pages : 27
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Book Description
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.
Author: Carley Garner
Publisher: FT Press
ISBN: 0137154224
Category : Business & Economics
Languages : en
Pages : 288
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Book Description
Don’t Miss out on Today’s Hottest Trading Arena: Commodity Options! “The authors have written the definitive work on trading commodity options. Their in-depth knowledge of this subject is legendary among industry professionals and expert traders alike, and their ability to relay their knowledge through text, pictures, and the spoken word is unparalleled in our industry.” –Lan Turner, CEO, Gecko Software, Inc. “This book captures the realities of commodity option trading in a simple and easy- to-read presentation that will be beneficial for traders of all sizes and skill levels.” –Chris Jarvis, CFA, CMT, Caprock Risk Management, LLC “Even the most experienced investors often overlook the fact that options on futures are fundamentally different from options on stocks. This book fills that gap and sets the record straight with clear and concise descriptions that are easy to understand. Guaranteed to become a true source of value creation for anyone interested in trading commodity options.” –Jeff Augen, author, The Volatility Edge in Options Trading “Commodity Options arms readers with the strategies and tactics needed to take a more active approach to managing risk in today’s turbulent markets. The authors exhaustively break down every component of a commodity option to its lowest common denominator, making this book an essential piece of information for those looking to expand their trading tool box or further build on existing option strategies.” –John Netto, Chief Investment Strategist, NetBlack Capital and author, One Shot–One Kill Trading Investors worldwide are discovering the enormous opportunities available through commodity options trading. However, because commodities have differing underlying characteristics from equities, commodity options behave differently as well. In this book, two of the field’s most respected analysts present strategies built from the ground up for commodity options. Carley Garner and Paul Brittain begin with a quick primer on how commodity options work, how they evolved, and why conventional options strategies often fail in the commodity options markets. Next, using detailed examples based on their own extensive research, they show how to leverage the unique characteristics of commodity options in your own trades. You’ll walk through trades from “top to bottom,” master both long- and short-option approaches, and learn powerful strategies usually ignored in options books. For example, the authors introduce synthetic swing trading strategies that systematically reduce volatility from the market. This book’s easy-to-use trading strategies are strategically employed by the author’s clients every day: With Commodity Options, you can work to put the odds in your favor, too! • Why commodity options are different—and what it means to you Understand key differences in the underlying assets and the logistics of market execution • Systematically rewrite the odds in your favor Four ways to make winning trades more likely—and losing trades less common • When to trade short options—and how to manage the risk Why careful option selling may improve your odds of success • Master strategies designed for diverse market conditions Combine long and short options to create the right strategy for any market opportunity • Exploit short-lived trends through “synthetic” swing trading Get the advantages of futures contracts without the volatility
Author: Yonggan Zhao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Valeriy Zakamulin
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
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.
Author: Lihui Zheng
Publisher:
ISBN:
Category : Investment analysis
Languages : en
Pages : 52
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Book Description
Author: Ilya German
Publisher:
ISBN:
Category :
Languages : en
Pages : 118
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Author: Alet Roux
Publisher: VDM Publishing
ISBN: 9783836492393
Category : Algorithms
Languages : en
Pages : 0
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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: Valeriy Zakamulin
Publisher:
ISBN:
Category :
Languages : en
Pages : 28
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Book Description
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.
