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The purpose of this paper is to present an arbitrarily accurate approximation for the value of European options written on a Black‐Scholes stock paying a discrete dividend.

The proposed method is a computational method for the analytical solution of the problem.

It was found that the proposed method is computationally faster than any other exact computational available method, including Monte‐Carlo simulations.

The method is applied for a single dividend payment, but can be extended for several payments. The exact amount of the dividend must be known ex‐ante, as well as the precise date of payment.

The paper provides the most efficient way to compute with absolute precision the value of European options on dividend‐paying assets, under the Black‐Scholes assumption.

The computing time in the approach is several orders of magnitude faster than with traditional Monte Carlo methods, for the same desired accuracy.

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.

The paper employs simple accounting concepts and an argument part based on business need.

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.

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.

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.

A number of hedging approaches proposed to improve the hedging results and final returns of Black-Scholes model are analyzed and compared.

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.

This paper offers a new method for volatility arbitrage in Chinese financial market.

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.

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.

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.

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.

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.

Empirical results mostly show positive implied skewness, which suggests extreme price rises were more likely than extreme price decreases.

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.

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.

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.

The purpose of this article is to propose a detailed methodology to estimate, model and incorporate the non-constant volatility onto a numerical tree scheme, to evaluate a real option, using a quadrinomial multiplicative recombination.

This article uses the multiplicative quadrinomial tree numerical method with non-constant volatility, based on stochastic differential equations of the GARCH-diffusion type to value real options when the volatility is stochastic.

Findings showed that in the proposed method with volatility tends to zero, the multiplicative binomial traditional method is a particular case, and results are comparable between these methodologies, as well as to the exact solution offered by the Black–Scholes model.

The originality of this paper lies in try to model the implicit (conditional) market volatility to assess, based on that, a real option using a quadrinomial tree, including into this valuation the stochastic volatility of the underlying asset. The main contribution is the formal derivation of a risk-neutral valuation as well as the market risk premium associated with volatility, verifying this condition via numerical test on simulated and real data, showing that our proposal is consistent with Black and Scholes formula and multiplicative binomial trees method.

Ex ante tests of the efficiency of the London options market explain alternative hedging strategies to fund managers who seek to comprehend the opportunities in the options markets and profit by potential market inefficiencies. Over and under valued options were used to form hedge portfolios, which were mostly positive indicating potential inefficiencies in LIFFE. Therefore options appear to incorporate the role of an investment strategy on their own and not only as a hedge against positions in the underlying stocks while the Black‐Scholes formula proved to be an easily computed and implemented way to make above normal, zero risk profits. This paper also confirms the ability of a weighted implied standard deviation to explain future volatility more accurately than historical volatility by use of regression analysis.