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Author: Haim Reisman Publisher: ISBN: Category : Languages : en Pages : 6
Book Description
The paper shows that in the presence of transaction costs, there exists a viable price system in which the price of a call option is arbitrarily close to the price of the stock (minus the bid-ask spread on the stock and the option). The construction of such an example is possible no matter how small is the volatility of the stock or how small are the transaction costs.
Author: Haim Reisman Publisher: ISBN: Category : Languages : en Pages : 6
Book Description
The paper shows that in the presence of transaction costs, there exists a viable price system in which the price of a call option is arbitrarily close to the price of the stock (minus the bid-ask spread on the stock and the option). The construction of such an example is possible no matter how small is the volatility of the stock or how small are the transaction costs.
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: Timothy Falcon Crack Publisher: Timothy Crack ISBN: 9781991155436 Category : Business & Economics Languages : en Pages : 0
Book Description
[Note: eBook now available; see Amazon author page for details.] Dr. Crack studied PhD-level option pricing at MIT and Harvard Business School, taught undergrad and MBA option pricing at Indiana University (winning many teaching awards), was an independent consultant to the New York Stock Exchange, worked as an asset management practitioner in London, and has traded options for 20+ years. This unique mix of learning, teaching, consulting, practice, and trading is reflected in every page. This revised 6th edition gives clear explanations of Black-Scholes option pricing theory, and discusses direct applications of the theory to trading. The presentation does not go far beyond basic Black-Scholes for three reasons: First, a novice need not go far beyond Black-Scholes to make money in the options markets; Second, all high-level option pricing theory is simply an extension of Black-Scholes; and Third, there already exist many books that look far beyond Black-Scholes without first laying the firm foundation given here. The trading advice does not go far beyond elementary call and put positions because more complex trades are simply combinations of these. UNIQUE SELLING POINTS -The basic intuition you need to trade options for the first time, or interview for an options job. -Honest advice about trading: there is no simple way to beat the markets, but if you have skill this advice can help make you money, and if you have no skill but still choose to trade, this advice can reduce your losses. -Full immersion treatment of transactions costs (T-costs). -Lessons from trading stated in simple terms. -Stylized facts about the markets (e.g., how to profit from reversals, when are T-costs highest/lowest during the trading day, implications of the market for corporate control, etc.). -How to apply European-style Black-Scholes pricing to the trading of American-style options. -Leverage through margin trading compared to leverage through options, including worked spreadsheet examples. -Black-Scholes pricing code for HP17B, HP19B, and HP12C. -Five accompanying Excel sheets: forecast T-costs for options using simple models; explore option sensitivities including the Greeks; compare stock trading to option trading; GameStop example; and, explore P(ever ITM). -Practitioner Bloomberg Terminal screenshots to aid learning. -Simple discussion of continuously-compounded returns. -Introduction to "paratrading" (trading stocks side-by-side with options). -Unique "regrets" treatment of early exercise decisions and trade-offs for American-style calls and puts. -Unique discussion of put-call parity and option pricing. -How to calculate Black-Scholes in your head in 10 seconds (also in Heard on The Street: Quantitative Questions from Wall Street Job Interviews). -Special attention to arithmetic Brownian motion with general pricing formulae and comparisons of Bachelier (1900) with Black-Scholes. -Careful attention to the impact of dividends in analytical American option pricing. -Dimensional analysis and the adequation formula (relating FX call and FX put prices through transformed Black-Scholes formulae). -Intuitive review of risk-neutral pricing/probabilities and how and why these are related to physical pricing/probabilities. -Careful distinction between the early Merton (non-risk-neutral) hedging-type argument and later Cox-Ross/Harrison-Kreps risk-neutral pricing -Simple discussion of Monte-Carlo methods in science and option pricing. -Simple interpretations of the Black-Scholes formula and PDE and implications for trading. -Careful discussion of conditional probabilities as they relate to Black-Scholes. -Intuitive treatment of high-level topics e.g., bond-numeraire interpretation of Black-Scholes (where N(d2) is P(ITM)) versus the stock-numeraire interpretation (where N(d1) is P(ITM)). -Introduction and discussion of the risk-neutral probability that a European-style call or put option is ever in the money during its life.
Author: Timothy Falcon Crack Publisher: ISBN: 9780995117396 Category : Languages : en Pages : 284
Book Description
[Note: eBook now available; see Amazon author page for details.] THE AUTHOR: Dr. Crack studied PhD-level option pricing at MIT and Harvard Business School, taught undergrad and MBA option pricing at Indiana University (winning many teaching awards), was an independent consultant to the New York Stock Exchange, worked as an asset management practitioner in London, and has traded options for over 20 years. This unique mix of learning, teaching, consulting, practice, and trading is reflected in every page. This revised 5th edition gives clear explanations of Black-Scholes option pricing theory, and discusses direct applications of the theory to trading. The presentation does not go far beyond basic Black-Scholes for three reasons: First, a novice need not go far beyond Black-Scholes to make money in the options markets; Second, all high-level option pricing theory is simply an extension of Black-Scholes; and Third, there already exist many books that look far beyond Black-Scholes without first laying the firm foundation given here. The trading advice does not go far beyond elementary call and put positions because more complex trades are simply combinations of these. UNIQUE SELLING POINTS -The basic intuition you need to trade options for the first time, or interview for an options job. -Honest advice about trading: there is no simple way to beat the markets, but if you have skill this advice can help make you money, and if you have no skill but still choose to trade, this advice can reduce your losses. -Full immersion treatment of transactions costs (T-costs). -Lessons from trading stated in simple terms. -Stylized facts about the markets (e.g., how to profit from reversals, when are T-costs highest/lowest during the trading day, implications of the market for corporate control, etc.). -How to apply European-style Black-Scholes pricing to the trading of American-style options. -Leverage through margin trading compared to leverage through options, including worked spreadsheet example. -Black-Scholes pricing code for the HP17B, HP19B, and HP12C. -Three downloadable spreadsheets. One allows the user to forecast T-costs for option positions using simple models. Another allows the user to explore option sensitivities including the Greeks. -Practitioner Bloomberg Terminal screenshots to aid learning. -Simple discussion of continuously-compounded returns. -Introduction to "paratrading" (trading stocks side-by-side with options to generate additional profit). -Unique "regrets" treatment of early exercise decisions and trade-offs for American-style calls and puts. -Unique discussion of put-call parity and option pricing. -How to calculate Black-Scholes in your head in 10 seconds (also in Heard on The Street: Quantitative Questions from Wall Street Job Interviews). -Special attention to arithmetic Brownian motion with general pricing formulae and comparisons to Bachelier (1900) and Black-Scholes. -Careful attention to the impact of dividends in analytical American option pricing. -Dimensional analysis and the adequation formula (relating FX call and FX put prices through transformed Black-Scholes formulae). -Intuitive review of risk-neutral pricing/probabilities and how and why these are related to physical pricing/probabilities. -Careful distinction between the early Merton (non-risk-neutral) hedging-type argument and later Cox-Ross/Harrison-Kreps risk-neutral pricing -Simple discussion of Monte-Carlo methods in science and option pricing. -Simple interpretations of the Black-Scholes formula and PDE and implications for trading. -Careful discussion of conditional probabilities as they relate to Black-Scholes. -Intuitive treatment of high-level topics e.g., bond-numeraire interpretation of Black-Scholes (where N(d2) is P(ITM)) versus the stock-numeraire interpretation (where N(d1) is P(ITM)). -Introduction and discussion of the risk-neutral probability that a European-style call or put option is ever in the money during its life.
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: Michal Czerwonko Publisher: ISBN: Category : Languages : en Pages : 37
Book Description
We examine the stochastic dominance bounds for call options in the presence of proportional transaction costs, developed in a discrete time and for a discrete or continuous state model of the returns of the underlying asset by Constantinides and Perrakis (CP, 2002, 2007). We consider a lognormal diffusion model of these returns and we formulate a discrete time trading version that converges to diffusion as the time partition becomes progressively more dense. Given the existence of a partition-independent and tight upper bound already derived in CP (2002), we focus on the lower bound, for which the results of that study were not available in a useful formulation. We then show that the CP lower bound for European call options converges to a non-trivial and tight limit that is a function of the transaction cost parameter. This limit defines a reservation purchase price under realistic trading conditions for the call options. The limit is a Black-Scholes type expression that becomes equal to the exact Black-Scholes value if the transaction cost parameter is set equal to zero, thus providing the only known generalization of the Black-Scholes model that produces useful results under transaction costs. We also develop a novel numerical algorithm that computes the CP lower bound for any discrete time partition and converges to the theoretical continuous time limit in a relatively small number of iterations. Last, we extend the lower bound results to American index options.
Author: Stylianos Perrakis Publisher: ISBN: Category : Languages : en Pages : 48
Book Description
We derive a reservation purchase price for a call option price under proportional transaction costs. The price is derived in discrete time for a general distribution of the returns of the underlying asset, as in Constantinides and Perrakis (CP, 2002, 2007). We then consider a lognormal diffusion model of these returns, and we formulate a discrete time trading version that converges to diffusion as the time partition becomes progressively more dense. Given the existence of a partition-independent and tight upper bound already derived in CP (2002), we focus on the lower bound. We show that the CP approach results in a lower bound for European call options that converges to a non-trivial and tight limit that is a function of the transaction cost parameter. This limit defines a reservation purchase price under realistic trading conditions for the call options and becomes equal to the exact Black-Scholes-Merton value if the transaction cost parameter is set equal to zero. We also develop a novel numerical algorithm that computes the CP lower bound for any discrete time partition and converges to the theoretical continuous time limit in a relatively small number of iterations. Last, we extend the lower bound results to American index and index futures options.
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: Haim Reisman
Author: Haim Reisman
Author: Guy Barles
Author: Timothy Falcon Crack
Author: Timothy Falcon Crack
Author: Ling Chen
Author: Michal Czerwonko
Author: Yuri Kabanov
Author: Stylianos Perrakis
Author: Stepan Sahakyan
Author: George M. Constantinides