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Author: A. Basso
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
For a theoretical valuation of a financial option, various models have been proposed that require specific hypotheses regarding both the stochastic process driving the price behaviour of the underlying security and market efficiency. When some of these assumptions are removed, we obtain an uncertainty interval for the option price. Up to now, the most restrictive intervals for option prices have been obtained using the DARA rule in a state preference approach.Precautionary saving entails the concept of prudence; in particular, decreasing absolute prudence is a necessary and sufficient condition that guarantees that the saving of wealthier people is less sensitive to the risk associated to future incomes. If this condition is coupled with the decreasing absolute risk aversion assumption we obtain standard risk aversion, which guarantees on the one hand that introducing a zero-mean background risk to wealth makes people less willing to accept another independent risk and on the other hand that an increase in the risk of the returns distribution of an asset reduces the demand for this asset.The main idea of this contribution is to apply decreasing absolute prudence and standard risk aversion rules in a state preference context in order to obtain efficient bounds for the value of European-style options portfolio strategies.Lower and upper bounds for the options portfolio value are obtained by solving non linear optimization problems. The numerical experiments carried out show the efficiency of the technique proposed.
Author: A. Basso
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
For a theoretical valuation of a financial option, various models have been proposed that require specific hypotheses regarding both the stochastic process driving the price behaviour of the underlying security and market efficiency. When some of these assumptions are removed, we obtain an uncertainty interval for the option price. Up to now, the most restrictive intervals for option prices have been obtained using the DARA rule in a state preference approach.Precautionary saving entails the concept of prudence; in particular, decreasing absolute prudence is a necessary and sufficient condition that guarantees that the saving of wealthier people is less sensitive to the risk associated to future incomes. If this condition is coupled with the decreasing absolute risk aversion assumption we obtain standard risk aversion, which guarantees on the one hand that introducing a zero-mean background risk to wealth makes people less willing to accept another independent risk and on the other hand that an increase in the risk of the returns distribution of an asset reduces the demand for this asset.The main idea of this contribution is to apply decreasing absolute prudence and standard risk aversion rules in a state preference context in order to obtain efficient bounds for the value of European-style options portfolio strategies.Lower and upper bounds for the options portfolio value are obtained by solving non linear optimization problems. The numerical experiments carried out show the efficiency of the technique proposed.
Author: Kamlesh Mathur
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This article establishes bounds on option prices in an economy where the representative investor has non increasing absolute risk aversion. The bounds do not require knowledge of any specific utility parameters, nor do they require specific joint distribution assumptions between the marginal utility of aggregate consumption and the underlying stock price. To drive our results we only require that the expected marginal utility of consumption conditional on the stock price is monotone non increasing in the stock price, and that the marginal distribution of the stock price is given. With this assumption, the lower bound on option prices is given by the solution to a non-linear mathematical program. We identify the general solution of this program. If the underlying process is multinomial, we show that the lower bound is set up as if the representative investor had constant proportional risk aversion. For this case, a risk neutral valuation relationship exists. As a result, the lower bound does not depend on the drift term, nor is it affected by the number of permissible trading periods prior to expiration. Moreover, if the underlying distribution is lognormal, the lower bound is the Black Scholes price. The upper bound on option prices is also identified and its behavior as multiple portfolio opportunities exist is examined.
Author: Jens Carsten Jackwerth
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: James Huang
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
In this paper, we derive option bounds from concurrently expiring option prices assuming the (pricing) representative investor's relative risk aversion is bounded. We show that given n concurrently expiring options, the option bounds are given by pricing kernels that have (n+2)- segmented piecewise constant elasticity. Closed form formulas are presented for the case where the distribution of the stock price is log-normal.
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: 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: Unyong Pyo
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
This paper constructs narrow bounds around the value of real options embedded in capital budgeting decisions by applying the minimax deviations approach to real options in incomplete markets. While it is straightforward to obtain the unique value of a real option with HARA utility functions, the parameters of risk-aversion are often subject to misspecification and raise concerns for practical uses. Recognizing that investors allow deviation from parameter values related to a benchmark pricing kernel, we derive narrow bounds on a real option price. Comparison with the approaches in the literature clarifies advantages of the minimax bounds: simple, consistent, and efficient.
Author: Ruediger Kiesel
Publisher:
ISBN:
Category :
Languages : en
Pages : 54
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Book Description
We present a new option-pricing model, which explicitly captures the difference in the persistence of volatility under historical and risk-neutral probabilities. The model also allows to capture the empirical properties of pricing kernels, such as time-variation and the typical S-shape. We apply our model for two purposes. First, we analyze the risk preferences of market participants invested in S&P 500 index options during 2001-2009. We find that risk-aversion strongly increases during stressed market conditions and relaxes during normal market conditions. Second, we extract forward-looking information from S&P 500 index options and perform out-of-sample Value-at-Risk (VaR) forecasts during the period of the subprime mortgage crises. We compare the VaR forecasting performance of our model with four alternative VaR models and find that 2-Factor Stochastic Volatility models have the best forecasting performance.
Author: Cheng Few Lee
Publisher: World Scientific
ISBN: 9811280282
Category : Business & Economics
Languages : en
Pages : 1001
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Book Description
Futures and Options are concerned with the valuation of derivatives and their application to hedging and speculating investments. This book contains 22 chapters and is divided into five parts. Part I contains an overview including a general introduction as well as an introduction to futures, options, swaps, and valuation theories. Part II: Forwards and Futures discusses futures valuation, the futures market, hedging strategies, and various types of futures. Part III: Option Theories and Applications includes both the basic and advanced valuation of options and option strategies in addition to index and currency options. Part IV: Advanced Analyses of Options takes a look at higher level strategies used to quantitatively approach the analysis of options. Part V: Special Topics of Options and Futures covers the applications of more obscure and alternative methods in derivatives as well as the derivation of the Black-Scholes Option Pricing Model.This book applies an active interdisciplinary approach to presenting the material; in other words, three projects involving the use of real-world financial data on derivative, in addition to homework assignments, are made available for students in this book.
Author: Alessandro Beber
Publisher:
ISBN:
Category : Bonds
Languages : en
Pages : 60
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Book Description
We examine the effect of regularly scheduled macroeconomic announcements on the beliefs and preferences of participants in the U.S. Treasury market by comparing the option-implied state-price density (SPD) of bond prices shortly before and after the announcements. We find that the announcements reduce the uncertainty implicit in the second moment of the SPD regardless of the content of the news. The changes in the higher-order moments, in contrast, depend on whether the news is good or bad for economic prospects. Using a standard model for interest rates to disentangle changes in beliefs and changes in preferences, we demonstrate that our results are consistent with time-varying risk aversion in the spirit of habit formation.
