Equilibrium Pricing Bounds on Option Prices PDF Download
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Author: Marie Chazal
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
We consider the problem of valuing European options in a complete market but with incomplete data. Typically, when the underlying asset dynamics is not specified, the martingale probability measure is unknown. Given a consensus on the actual distribution of the underlying price at maturity, we derive an upper bound on the call option price by putting two kind of restrictions on the pricing probability measure.First, we put a restriction on the second risk-neutral moment of the underlying asset terminal value. Second, from equilibrium pricing arguments one can put a monotonicity restriction on the Radon-Nikodym density of the pricing probability with respect to the true probability measure. This density is restricted to be a nonincreasing function of the underlying price at maturity. The bound appears then as the solution of a constrained optimization problem and we adopt a duality approach to solve it.We obtain a weak sufficient condition for strong duality and existence for the dual problem to hold, for options defined by general payoff functions. Explicit bounds are provided for the call option. Finally, we provide a numerical example.
Author: Marie Chazal
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
We consider the problem of valuing European options in a complete market but with incomplete data. Typically, when the underlying asset dynamics is not specified, the martingale probability measure is unknown. Given a consensus on the actual distribution of the underlying price at maturity, we derive an upper bound on the call option price by putting two kind of restrictions on the pricing probability measure.First, we put a restriction on the second risk-neutral moment of the underlying asset terminal value. Second, from equilibrium pricing arguments one can put a monotonicity restriction on the Radon-Nikodym density of the pricing probability with respect to the true probability measure. This density is restricted to be a nonincreasing function of the underlying price at maturity. The bound appears then as the solution of a constrained optimization problem and we adopt a duality approach to solve it.We obtain a weak sufficient condition for strong duality and existence for the dual problem to hold, for options defined by general payoff functions. Explicit bounds are provided for the call option. Finally, we provide a numerical example.
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: Kyriakos Chourdakis
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
This paper derives a general equilibrium option-pricing model for a European call assuming that the economy is exogenously driven by a dividend process following Hamilton's (1989) Markov regime switching model. The derived formula is used to investigate if the European call option prices are consistently priced with the stock market prices. This is done by obtaining the implied risk aversion preferences, based on traded option prices data.
Author: Heber Farnsworth
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
In an equilibrium framework the dynamics of the aggregate dividend are taken as given and the volatility of the wealth portfolio is determined by the prices of risk in the model. Since option prices depend strongly on volatility they are very informative about these risk prices. We use this observation to compare the pricing of S&P 500 options to a model in which preferences are recursive and aggregate consumption has stochastic growth and volatility. We find that the pricing of the risk of shocks to the growth rate of consumption is inconsistent with a model in which the representative agent has isoelastic recursive utility.
Author: Leonid Kogan
Publisher: Forgotten Books
ISBN: 9780666532459
Category : Mathematics
Languages : en
Pages : 82
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Book Description
Excerpt from Pricing American Options: A Duality Approach The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. In addition, we explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is obtained by simulating a different stochastic process that is determined by choosing an appropriate supermartingale. We justify this procedure by representing the American option price as a solution of a dual minimization problem, which is the main theoretical result of this paper. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Paul McCloud
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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Book Description
Option pricing is the most elemental challenge of mathematical finance. Knowledge of the prices of options at every strike is equivalent to knowing the entire pricing distribution for a security, as derivatives contingent on the security can be replicated using options. The available data may be insufficient to determine this distribution precisely, however, and the question arises: What are the bounds for the option price at a specified strike, given the market-implied constraints?Positivity of the price map imposed by the principle of no-arbitrage is here utilised, via the Gelfand-Naimark-Segal construction, to transform the problem into the domain of operator algebras. Optimisation in this larger context is essentially geometric, and the outcome is simultaneously super-optimal for all commutative subalgebras.This generates an upper bound for the price of a basket option. With innovative decomposition of the assets in the basket, the result is used to create converging families of price bounds for vanilla options, interpolate the volatility smile, price options on cross FX rates, and analyse the relationships between swaption and caplet prices.
Author: Steven Manaster
Publisher:
ISBN:
Category : Stock price forecasting
Languages : en
Pages : 50
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Book Description
Author: Cheng Few Lee
Publisher: World Scientific
ISBN: 9811202400
Category : Business & Economics
Languages : en
Pages : 5053
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Book Description
This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.
Author: George M. Constantinides
Publisher:
ISBN:
Category :
Languages : en
Pages : 70
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Book Description
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.
