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1 – 10 of over 1000Don M. Chance and Tung-Hsiao Yang
In some contexts, this illiquidity of executive stock options is referred to as non-transferability. In others, the problem is cast in terms of the highly concentrated portfolios…
Abstract
In some contexts, this illiquidity of executive stock options is referred to as non-transferability. In others, the problem is cast in terms of the highly concentrated portfolios that managers hold, an implication of which is that managers could not trade the options to diversify. The notion of option liquidity usually conjures up images of trading pits at the Chicago Board Options Exchange or other exchanges. The existence of an active trading pit gives a powerful visual image of liquidity, but, as evidenced by the success of electronic options exchanges such as New York's International Securities Exchange and Frankfurt's EUREX, a trading pit is hardly a requirement for liquidity. The existence of a guaranteed market for standardized options as implied by options exchanges (whether pit-based or electronic) further gives a misleading appearance of high liquidity. There is also a very large market for customized over-the-counter options. It is a misconception to think that these options are not liquid when they are simply not standardized. If an investor can create a highly customized long position in an option, that investor should be able to create a highly customized short position in the same option at a later date before expiration. If both options are created through the same dealer, they will usually be treated as an offset, as they would if they were standardized options clearing through a clearinghouse. If the two transactions are not with the same dealer, they would both remain alive, but the market risks would offset. Only the credit risk, a factor we ignore in this paper, would remain. Hence, these seemingly illiquid options are, for all practical purposes, liquid.2
The development of standardized measures of institution‐wide volatility exposures has so far lagged that for measures of asset price and interest‐rate exposure—largely because it…
Abstract
The development of standardized measures of institution‐wide volatility exposures has so far lagged that for measures of asset price and interest‐rate exposure—largely because it is difficult to reconcile the various mathematical models used to value options. Recent mathematical results, however, can be used to construct standardized measures of volatility exposure. We consider here techniques for reconciling “vegas” for financial options valued using stochastic models that may be mathematically inconsistent with each other.
Jens Carsten Jackwerth and Mark Rubinstein
How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent…
Abstract
How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent stock market crash and the subsequent prices of U.S. index options. With the development of rich and deep markets in these options, it is now possible to use options prices to make inferences about the risk-neutral stochastic process governing the underlying index. We compare the ability of models including Black–Scholes, naïve volatility smile predictions of traders, constant elasticity of variance, displaced diffusion, jump diffusion, stochastic volatility, and implied binomial trees to explain otherwise identical observed option prices that differ by strike prices, times-to-expiration, or times. The latter amounts to examining predictions of future implied volatilities.
Certain naïve predictive models used by traders seem to perform best, although some academic models are not far behind. We find that the better-performing models all incorporate the negative correlation between index level and volatility. Further improvements to the models seem to require predicting the future at-the-money implied volatility. However, an “efficient markets result” makes these forecasts difficult, and improvements to the option-pricing models might then be limited.
The purpose of this paper is to explain the Black–Scholes model with minimal technical requirements and to illustrate its impact from a business perspective.
Abstract
Purpose
The purpose of this paper is to explain the Black–Scholes model with minimal technical requirements and to illustrate its impact from a business perspective.
Design/methodology/approach
The paper employs simple accounting concepts and an argument part based on business need.
Findings
The Black–Scholes partial differential equation can be derived in many ways, some easy to understand, some hard, some useful and others not. The two methods in this paper are extremely insightful.
Originality/value
The paper takes a big-picture view of derivatives valuation. As such, it is a simple accompaniment to more complex methods and aims to keep modelling grounded in reality.
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Keywords
Using volatility cones as the estimate of actual volatility instead of GARCH models, the purpose of this paper is to explore whether volatility arbitrage strategy can provide…
Abstract
Purpose
Using volatility cones as the estimate of actual volatility instead of GARCH models, the purpose of this paper is to explore whether volatility arbitrage strategy can provide positive profits and how the transaction costs existed in the real market affect the effectiveness of volatility arbitrage strategy.
Design/methodology/approach
A number of hedging approaches proposed to improve the hedging results and final returns of Black-Scholes model are analyzed and compared.
Findings
The general finding is that volatility arbitrage strategy can provide satisfactory returns based on the samples in Chinese market. Regarding transaction costs, the variable bandwidth delta and delta tolerance approach showed better results. Besides, choosing futures together with ETFs as hedging underlying can increase the VaR for better risk management.
Practical implications
This paper offers a new method for volatility arbitrage in Chinese financial market.
Originality/value
This paper researches the profitability of the volatility arbitrage strategy on ETF 50 options using volatility cones method for the first time. This method has advantage over the point-wise estimation such as GARCH model and stochastic volatility model.
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Dasheng Ji and B. Wade Brorsen
The purpose of this paper is to develop an option pricing model applicable to US options. The lognormality assumption that has typically been imposed with past binomial and…
Abstract
Purpose
The purpose of this paper is to develop an option pricing model applicable to US options. The lognormality assumption that has typically been imposed with past binomial and trinomial option pricing models is relaxed. The relaxed lattice model is then used to determine skewness and kurtosis of distributions of futures prices implied from option prices.
Design/methodology/approach
The relaxed lattice is based on Gaussian quadrature. The markets studied include corn, soybeans, and wheat. Skewness and kurtosis are implied by minimizing the squared deviations of actual option premia from predicted premia.
Findings
Positive skewness is the major source of nonnormality, but both skewness and kurtosis are important as the trinomial model that considers kurtosis has greater accuracy than the binomial model. The out‐of‐sample forecasting accuracy of the relaxed lattice models is better than the Black‐Scholes model in most, but not all cases.
Research limitations/implications
The model might benefit from using option prices from more than one day. The implied skewness and kurtosis were quite variable and using more data might reduce this variability.
Practical implications
Empirical results mostly show positive implied skewness, which suggests extreme price rises were more likely than extreme price decreases.
Originality/value
The relaxed lattice is a new model and the results about implied higher moments are new for these commodities. There are competing models available that should be able to get similar accuracy, so one key advantage of the new approach is its simplicity and ease of use.
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William R. Cron and Randall B. Hayes
Recent developments in accounting for stock options have increased interest in the analytical techniques used to value them. Techniques used to value the options of publicly…
Abstract
Recent developments in accounting for stock options have increased interest in the analytical techniques used to value them. Techniques used to value the options of publicly traded companies have been extensively discussed. In contrast, there has been almost no discussion of the valuation procedures of the options for non‐publicly traded companies. This paper addresses this gap. The paper suggests that a straightforward income capitalization model can be used to develop reasonable surrogates for the variables of the Black‐Scholes option pricing model. The paper also discusses how to adjust the income apitalization model for both lack of marketability and lack of control discounts.
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Hyeon‐Lo Lee, Jong Beom Moon, Wang Jin Yoo and Dong Myung Lee
The purpose of this paper is to apply the real option method with fuzzy logic to value the government‐sponsored projects of advanced technology development for strategic selection…
Abstract
Purpose
The purpose of this paper is to apply the real option method with fuzzy logic to value the government‐sponsored projects of advanced technology development for strategic selection in an uncertain competitive environment.
Design/methodology/approach
For strategic selection of government‐sponsored industrial R&D projects, in this paper, Carlsson and Fúller's model was adopted which employs fuzzy logic to estimate the benefits and costs calculated from various scenarios and utilizes Black‐Scholes‐Merton model. The model of strategic selection is suggested for government R&D with fuzzy real option valuation (FROV) and the portfolio planning model from GE‐Mckinsey matrix as well.
Findings
FROV was found to be more appropriate to measure the strategic value than the traditional financial method (net present value, NPV, etc.). When the NPV is ambiguous in deciding whether to go or not to go, for instance, just below zero NPV and high volatility of expected benefit, FROV can offer the additive value of the project reflecting volatility of benefit due to the volatility.
Research limitations/implications
Based on insufficient practical data, this methodology should be verified with various projects and measuring volatility of pay‐off requires precise analysis. In addition, research opportunities are in the stepwise R&D project with fuzzy compound real option.
Originality/value
Many papers on economic analysis of R&D project are focused on NPV or cost‐benefit analysis in the public sector. Several attempts with real option have been conducted in the pharmaceutical field or the aerospace (NASA) industry but are not concerned with the fuzziness of expected benefit. Hence, in this paper, fuzzy logic is added to handle imprecise information on the Black‐Scholes‐Merton model with dividend paying.
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Farshid Mehrdoust, Amir Hosein Refahi Sheikhani, Mohammad Mashoof and Sabahat Hasanzadeh
The purpose of this paper is to evaluate a European option using the fractional version of the Black-Scholes model.
Abstract
Purpose
The purpose of this paper is to evaluate a European option using the fractional version of the Black-Scholes model.
Design/methodology/approach
In this paper, the authors employ the block-pulse operational matrix algorithm to approximate the solution of the fractional Black-Scholes equation with the initial condition for a European option pricing problem.
Findings
The fractional derivative will be described in the Caputo sense in this paper. The authors show the accuracy and computational efficiency of the proposed algorithm through some numerical examples.
Originality/value
This is the first paper that considers an alternative algorithm for pricing a European option using the fractional Black-Scholes model.
Details
Keywords
The Black Scholes option pricing model has been put to extensive application both in research and in actual market place. However, the inputs for the model are generally obtained…
Abstract
The Black Scholes option pricing model has been put to extensive application both in research and in actual market place. However, the inputs for the model are generally obtained from the stock market which is considered less efficient than the options market. This leads to a difference in calculated price and observed price. This paper studies the bias empirically.