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Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In the first essay American call and put options on the S & P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (CP, 2007) over 1983-2006 are identified as potentially profitable investment opportunities. Call bid prices more frequently violate their upper bound than put bid prices do, while evidence of underpriced calls and puts over this period is scant. In out-of-sample tests, the inclusion of short positions in such overpriced calls, puts, and, particularly, straddles in the market portfolio is shown to increase the expected utility of any risk averse investor and also increase the Sharpe ratio, net of transaction costs and bid-ask spreads. The results are strongly supportive of mispricing and also strongly supportive of the CP bounds as screening mechanisms for mispriced options. The second essay introduces a result for call lower bound more powerful that the one applied in the first part of this thesis. The Proposition 5 call lower bound in Constantinides and Perrakis (2002) is shown to have a non-trivial limit as the time interval tends to zero. This establishes the bound as the first call lower bound known in the literature on derivative pricing in the presence of transaction costs with a non-trivial limit. The bound is shown to be tight even for a low number of time subdivisions. Novel numerical methods to derive recursive expectations under a Markovian but non-identically distributed stochastic process are presented. The third essay relaxes an assumption in the first part of this thesis on the optimal trading policy in the presence of transaction costs. We derive the boundaries of the region of no transaction when the risky asset follows a mixed jump-diffusion instead of a simple diffusion process. These boundaries are shown to differ from their diffusion counterparts in relation to the jump intensity for lognormally distributed jump size. A general numerical approach is presented for iid risky asset returns in discrete time. An error in an earlier published work on the region of no transaction for discretized diffusions is demonstrated and corrected results are presented. Comparative results with a recent study on the same topic are presented and it is shown that the numerical algorithm has equally attractive approximation properties to the unknown continuous time limit.
Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In the first essay American call and put options on the S & P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (CP, 2007) over 1983-2006 are identified as potentially profitable investment opportunities. Call bid prices more frequently violate their upper bound than put bid prices do, while evidence of underpriced calls and puts over this period is scant. In out-of-sample tests, the inclusion of short positions in such overpriced calls, puts, and, particularly, straddles in the market portfolio is shown to increase the expected utility of any risk averse investor and also increase the Sharpe ratio, net of transaction costs and bid-ask spreads. The results are strongly supportive of mispricing and also strongly supportive of the CP bounds as screening mechanisms for mispriced options. The second essay introduces a result for call lower bound more powerful that the one applied in the first part of this thesis. The Proposition 5 call lower bound in Constantinides and Perrakis (2002) is shown to have a non-trivial limit as the time interval tends to zero. This establishes the bound as the first call lower bound known in the literature on derivative pricing in the presence of transaction costs with a non-trivial limit. The bound is shown to be tight even for a low number of time subdivisions. Novel numerical methods to derive recursive expectations under a Markovian but non-identically distributed stochastic process are presented. The third essay relaxes an assumption in the first part of this thesis on the optimal trading policy in the presence of transaction costs. We derive the boundaries of the region of no transaction when the risky asset follows a mixed jump-diffusion instead of a simple diffusion process. These boundaries are shown to differ from their diffusion counterparts in relation to the jump intensity for lognormally distributed jump size. A general numerical approach is presented for iid risky asset returns in discrete time. An error in an earlier published work on the region of no transaction for discretized diffusions is demonstrated and corrected results are presented. Comparative results with a recent study on the same topic are presented and it is shown that the numerical algorithm has equally attractive approximation properties to the unknown continuous time limit.
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: Michal Czerwonko
Publisher:
ISBN:
Category : Stock options
Languages : en
Pages : 0
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Book Description
This paper investigates the multi-period upper bound on the European call price in the presence of transaction costs derived by Constantinides-Perrakis (2002). Numerical results verifying an assumption of the monotonictity of wealth of the call writer in the underlying asset on which the Constantinides-Perrakis (2002) model relies are derived, and it is shown that the assumption is satisfied for relatively small ratios of stock to option account. The classic second order stochastic dominance argument is applied to the dynamic trading in discrete time in the S & P 500 options under the portfolio selection criteria in the presence of transaction costs. It is shown that the improvement in expected utility does occur under the prescribed investment policy in the S & P 500 calls whose prices exceed the bound. Under the lognormality of the S & P 500 price process, the quantitative improvement in expected utility is derived.
Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
This paper examines the stochastic dominance efficiency in the presence of transaction costs for Samp;P 500 index futures call and put options by estimating bounds on reservation write and reservation purchase prices and then verifying whether the observed option prices satisfy them. The bounds are estimated from data on past realizations of the underlying asset and under various data-based assumptions about the investor-assumed distribution of that asset. The bounds are then compared to observed market prices and several violations are identified under all distributional assumptions, although these violations are relatively few under forward-looking distributions. The paper then derives trading strategies that exploit these violations and increase expected utility for any risk averse investor. It develops a metric that evaluates the increase in expected utility for any given investor within a certain utility class and links it with the traditional second degree stochastic dominance criterion. Last, it demonstrates by out-of-sample tests with realized underlying asset prices that these strategies to exploit the mispricing of index futures options do indeed improve risk-adjusted returns for risk averse investors.
Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
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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: Haim Levy
Publisher: Springer Science & Business Media
ISBN: 0387293116
Category : Business & Economics
Languages : en
Pages : 439
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Book Description
This book is devoted to investment decision-making under uncertainty. The book covers three basic approaches to this process: the stochastic dominance approach; the mean-variance approach; and the non-expected utility approach, focusing on prospect theory and its modified version, cumulative prospect theory. Each approach is discussed and compared. In addition, this volume examines cases in which stochastic dominance rules coincide with the mean-variance rule and considers how contradictions between these two approaches may occur.
Author: George M. Constantinides
Publisher:
ISBN:
Category : Derivative securities
Languages : en
Pages : 56
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Book Description
By applying stochastic dominance arguments, upper bounds on the reservation write price of European calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security. The primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option. A tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put. These results jointly impose tight upper and lower bounds on the implied volatility
Author: Ioan Mihai Oancea
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This thesis examines the pricing of options under several models with market incompleteness. The theoretical approach relies on the absence of stochastically dominating portfolios containing the underlying asset, the option and the riskless bond. The stochastic dominance approach provides two bounds on the equilibrium pricing of options by risk-averse investors. The two bounds are discounted conditional expectations of the option payoff under two probability measures. This research generalizes the previous stochastic dominance pricing results in discrete time to non-i.i.d. underlying asset return processes and to contingent claims with non-convex payoffs. The new results are then used to examine the stochastic dominance pricing bounds for several discrete and continuous time processes of the underlying asset. The continuous time bounds are obtained by constructing a sequence of discrete approximations that converge weakly to a given continuous time process. The weak convergence property provides the convergence of the two option bounds, which are discounted expectations of the option payoff. In the case of a univariate diffusion process, the two option bounds converge to a common limit. The two bounds converge to distinct limits when the underlying asset follows a jump-diffusion mixture. The non-iid stochastic dominance pricing results are then applied to the pricing of options for a LARCH specification of the underlying asset returns. The two stochastic dominance bounds are obtained both for conditional normal and non-normal returns. The impact of the model estimation error is examined by generating a return sample from a known model and computing the stochastic dominance bounds implied by several estimated models.
Author: Stylianos Perrakis
Publisher:
ISBN:
Category :
Languages : en
Pages : 28
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Book Description
Author: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 9780521573542
Category : Business & Economics
Languages : en
Pages : 348
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Book Description
Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.
