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Author: Kamlesh Mathur
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Languages : en
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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: Kamlesh Mathur
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Languages : en
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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: A. Basso
Publisher:
ISBN:
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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: Jens Carsten Jackwerth
Publisher:
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Category :
Languages : en
Pages :
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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: Florentin Rahe
Publisher:
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Languages : en
Pages :
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Author: Jens Carsten Jackwerth
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Languages : en
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A relationship exists between aggregate risk-neutral and subjective probability distributions and risk aversion functions. We empirically derive risk aversion functions implied by option prices and realized returns on the Samp;P500 index simultaneously. These risk aversion functions dramatically change shapes around the 1987 crash: Precrash, they are positive and decreasing in wealth and largely consistent with standard assumptions made in economic theory. Postcrash, they are partially negative and partially increasing and irreconcilable with those assumptions. Mispricing in the option market is the most likely cause. Simulated trading strategies exploiting this mispricing shows excess returns even after accounting for the possibility of further crashes, transaction costs, and hedges against the downside risk.
Author: Louis Eeckhoudt
Publisher: Princeton University Press
ISBN: 1400829216
Category : Business & Economics
Languages : en
Pages : 245
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Book Description
An understanding of risk and how to deal with it is an essential part of modern economics. Whether liability litigation for pharmaceutical firms or an individual's having insufficient wealth to retire, risk is something that can be recognized, quantified, analyzed, treated--and incorporated into our decision-making processes. This book represents a concise summary of basic multiperiod decision-making under risk. Its detailed coverage of a broad range of topics is ideally suited for use in advanced undergraduate and introductory graduate courses either as a self-contained text, or the introductory chapters combined with a selection of later chapters can represent core reading in courses on macroeconomics, insurance, portfolio choice, or asset pricing. The authors start with the fundamentals of risk measurement and risk aversion. They then apply these concepts to insurance decisions and portfolio choice in a one-period model. After examining these decisions in their one-period setting, they devote most of the book to a multiperiod context, which adds the long-term perspective most risk management analyses require. Each chapter concludes with a discussion of the relevant literature and a set of problems. The book presents a thoroughly accessible introduction to risk, bridging the gap between the traditionally separate economics and finance literatures.
Author: Antonio Camara
Publisher:
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Languages : en
Pages :
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This article develops a discrete-time, risk-neutral valuation relation (RNVR) for the pricing of contingent claims when preferences in the economy are characterized by decreasing absolute risk aversion and the marginal distribution of the underlying is an inverse coshnormal. The RNVR is applied to obtain closed-form expressions for calls and puts written on nondividend-paying stocks, futures contracts, foreign currencies, and dividend-paying stocks. Such pricing equations contain two parameters, the threshold and rescale parameters, not contained in the Black-Scholes valuation equation. Inverse-coshnormal option values make the approach look interesting.
Author: Bruno Bouchard
Publisher:
ISBN:
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Languages : en
Pages : 16
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Author: Qian Han
Publisher:
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Category :
Languages : en
Pages : 0
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Considering a pure exchange economy with habit formation utility, the theoretical part of this dissertation explores the equilibrium relationships between the market pricing kernel, the market prices of risks and the market risk aversion under a continuous time stochastic volatility model completed by liquidly traded put options. We demonstrate with these equilibrium relations that the risk neutral pricing partial differential equation is a restricted version of the fundamental pricing equation provided in Garman (1976). We also show that in this completed market stochastic volatility cannot explain the documented empirical pricing kernel puzzle (Jackwerth (2000)). Instead, a habit formation utility offers a possible explanation of the puzzle. The derived quantitative relation between the market prices of risks and the market risk aversion also provides a new way to extract empirical market risk aversion. Based upon this theoretical relation between market prices of risks and the market risk aversion in a Heston model, we empirically extract the market prices of risks and risk aversion from the options market using cross-sectional fitting. Specifically we consider a restricted model where only the volatility risk is allowed to freely change and an unrestricted model where all model parameters are allowed to freely change. For the restricted model, we determine other parameters by Efficient Method of Moments (EMM). Using European call options data, we find an implied risk aversion smile, indicating that individual groups of investors trading options with different strike prices have different risk aversions. We also extracted an average or aggregated market risk aversion by minimizing the mean squared pricing error across all strikes. This represents the risk aversion level for the whole market in the sense of "averaging". None of these risk aversions are negative across moneyness, hence indicating that adding stochastic volatility to the model will not reproduce the documented pricing kernel puzzle. In addition, the market price of volatility risk is small in values compared with the market price of asset risk, implying that the major driving factor of market risk aversion and pricing kernel is the asset risk. This is consistent with the sensitivity analysis conducted on the option prices with respect to the market prices of risks. For the unrestricted model, we observe similar behavior for the two market prices of risks using a different data set, S&P500 index futures options. We find that the asset risk and volatility risk premium generally move opposite across the strikes. The variation of volatility risk decreases and the absolute values converge to zero with longer time to maturity. So the asset risk dominates the pricing more for options with longer maturities.
