Binomial option pricing with stochastic parameters: A beta distribution approach

This research extends the binomial option-pricing model of Cox, Ross, and Rubinstein (1979) and Rendleman and Barter (1979) to the case where the up and down percentage changes of stock prices are stochastic. Assuming stochastic parameters in the discrete-time binomial option pricing is analogous to assuming stochastic volatility in the continuous-time option pricing. By assuming that the up and down parameters are independent random variables following beta distributions, we are able to derive a closed-form solution to this stochastic discrete-time option pricing. We also derive an upper and a lower bounds of the option price.     

Asian option pricing with orthogonal polynomials

In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black–Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any special functions are involved. We provide sufficient conditions to guarantee convergence of the series. The moment indeterminacy of the log-normal distribution introduces an asymptotic bias in the series, however we show numerically that the bias can safely be ignored in practice.     

A generalization of the Hull and White formula with applications to option pricing approximation

By means of Malliavin calculus we see that the classical Hull and White formula for option pricing can be extended to the case where the volatility and the noise driving the stock prices are correlated. This extension will allow us to describe the effect of correlation on option prices and to derive approximate option pricing formulas.A previous version of this paper has benefited from helpful comments by two anonymous referees.     

Location of hazardous materials plants in Israel

The study described in this article examines the distribution of hazardous materials plants in Israel during 2002–2010. In particular, it focuses on densely populated areas destined for future urban expansion, areas in proximity to rivers and water sources, and main transportation arteries. The survey identified certain hazardous materials plants (representing 10% of all such plants in Israel) as highly dangerous owing to the kinds of substances they contain, the nature of their industrial activities, and potential environmental hazards. The location of hazardous plants showed a correlation between population density and industry, with the highest concentration of plants found in Tel Aviv (30%), Haifa and adjacent industrial areas (25%), and Ashdod (12%). Significant concentrations of hazardous plants were also found in Ramat Hovav, Netanya, and Acre (Akko). From 2000 to 2010, the number of hazardous materials plants known to the Ministry of Environmental Protection increased by 62%, with most of the increase concentrated in such coastal cities as Haifa and Tel Aviv, the rest in Israel’s northern and southern (Negev) regions. Further analysis of these data revealed problems resulting from the proximity of these sites to potable and irrigation water sources and to transportation arteries. The main purposes of the study were, first, to develop a geo-tool for informed decision-making regarding the location of hazardous materials plants, and, second, to examine the distribution of such plants in Israel in order to prevent future industrial accidents. This article is part of a comprehensive study on the role of environmental policy in the planning of hazardous materials plants in Israel.     

An empirical investigation of the factors that determine the pricing of Dutch index warrants

This paper investigates the pricing of Dutch index warrants. It is found that when using the historical standard deviation as an estimate for the volatility, the Black and Scholes model underprices all put warrants and call warrants on the FT-SE 100 and the CAC 40, while it overprices the call warrants on the DAX. When the implied volatility of the previous day is used the model prices the index warrants fairly well. When the historical standard deviation is used the mispricing of the call and the put warrants depends in a strong way on the mispricing of the previous trading day, and on the moneyness (in a non-linear way), the volatility, and the dividend yield. When the implied standard deviation of the previous trading day is used the mispricing of the call warrants is only related to the moneyness and to the estimated volatility, while the mispricing of put index warrants depends in a strong way on the moneyness, the volatility, the dividend yield and the remaining time to maturity.     

Calibration of a nonlinear feedback option pricing model

We consider the option pricing model proposed by Mancino and Ogawa, where the implementation of dynamic hedging strategies has a feedback impact on the price process of the underlying asset. We present numerical results showing that the smile and skewness patterns of implied volatility can actually be reproduced as a consequence of dynamical hedging. The simulations are performed using a suitable semi-implicit finite difference method. Moreover, we perform a calibration of the nonlinear model to market data and we compare it with more popular models, such as the Black–Scholes formula, the Jump-Diffusion model and Heston's model. In judging the alternative models, we consider the following issues: (i) the consistency of the implied structural parameters with the times-series data; (ii) out-of-sample pricing; and (iii) parameter uniformity across different moneyness and maturity classes. Overall, nonlinear feedback due to hedging strategies can, at least in part, contribute to the explanation from a theoretical and quantitative point of view of the strong pricing biases of the Black–Scholes formula, although stochastic volatility effects are more important in this regard.     

A generalized approach to optimal hedging with option contracts

In this paper, we develop a theoretical model in which a firm hedges a spot position using options in the presence of both quantity (production) and basis risks. Our optimal hedge ratio is fairly general, in that the dependence structure is modeled through a copula function representing the quantiles of the hedged position, and hence any quantile risk measure can be employed. We study the sensitivity of the exercise price which minimizes the risk of the hedged portfolio to the relevant parameters, and we find that the subjective risk aversion of the firm does not play any role. The only trade-off is between the effectiveness and cost of the hedging strategy.     

Bond and option pricing for interest rate model with clustering effects

This paper analyzes an interest rate model with self-exciting jumps, in which a jump in the interest rate model increases the intensity of jumps in the same model. This self-exciting property leads to clustering effects in the interest rate model. We obtain a closed-form expression for the conditional moment-generating function when the model coefficients have affine structures. Based on the Girsanov-type measure transformation for general jump-diffusion processes, we derive the evolution of the interest rate under the equivalent martingale measure and an explicit expression of the zero-coupon bond pricing formula. Furthermore, we give a pricing formula for the European call option written on zero-coupon bonds. Finally, we provide an interpretation for the clustering effects in the interest rate model within a simple framework of general equilibrium. Indeed, we construct an interest rate model, the equilibrium state of which coincides with the interest rate model with clustering effects proposed in this paper.     

An empirical comparison of GARCH option pricing models

Recent empirical studies have shown that GARCH models can be successfully used to describe option prices. Pricing such contracts requires knowledge of the risk neutral cumulative return distribution. Since the analytical forms of these distributions are generally unknown, computationally intensive numerical schemes are required for pricing to proceed. Heston and Nandi (2000) consider a particular GARCH structure that permits analytical solutions for pricing European options and they provide empirical support for their model. The analytical tractability comes at a potential cost of realism in the underlying GARCH dynamics. In particular, their model falls in the affine family, whereas most GARCH models that have been examined fall in the non-affine family. This article takes a closer look at this model with the objective of establishing whether there is a cost to restricting focus to models in the affine family. We confirm Heston and Nandi's findings, namely that their model can explain a significant portion of the volatility smile. However, we show that a simple non affine NGARCH option model is superior in removing biases from pricing residuals for all moneyness and maturity categories especially for out-the-money contracts. The implications of this finding are examined. JEL Classification G13     

An efficient algorithm for pricing barrier options in arbitrage-free binomial models with calibrated drift terms

The interrelation between the drift coefficient of price processes on arbitrage-free financial markets and the corresponding transition probabilities induced by a martingale measure is analysed in a discrete setup. As a result, we obtain a flexible setting that encompasses most arbitrage-free binomial models. It is argued that knowledge of the link between drift and transition probabilities may be useful for pricing derivatives such as barrier options. The idea is illustrated in a simple example and later extended to a general numerical procedure. The results indicate that the option values in our fitted drift model converge much faster to closed-form solutions of continuous models for a wider range of contract specifications than those of conventional binomial models.     

An analysis of option pricing under systematic consumption risk using GARCH

An issue in the pricing of contingent claims is whether to account for consumption risk. This is relevant for contingent claims on stock indices, such as the FTSE 100 share price index, as investor’s desire for smooth consumption is often used to explain risk premiums on stock market portfolios, but is not used to explain risk premiums on contingent claims themselves. This paper addresses this fundamental question by allowing for consumption in an economy to be correlated with returns. Daily data on the FTSE 100 share price index are used to compare three option pricing models: the Black–Scholes option pricing model, a GARCH (1, 1) model priced under a risk-neutral framework, and a GARCH (1, 1) model priced under systematic consumption risk. The findings are that accounting for systematic consumption risk only provides improved accuracy for in-the-money call options. When the correlation between consumption and returns increases, the model that accounts for consumption risk will produce lower call option prices than observed prices for in-the-money call options. These results combined imply that the potential consumption-related premium in the market for contingent claims is constant in the case of FTSE 100 index options.     

On the duality principle in option pricing: semimartingale setting

The purpose of this paper is to describe the appropriate mathematical framework for the study of the duality principle in option pricing. We consider models where prices evolve as general exponential semimartingales and provide a complete characterization of the dual process under the dual measure. Particular cases of these models are the ones driven by Brownian motions and by Lévy processes, which have been considered in several papers. Generally speaking, the duality principle states that the calculation of the price of a call option for a model with price process S=e ^H (with respect to the measure P) is equivalent to the calculation of the price of a put option for a suitable dual model S′=e ^H′ (with respect to the dual measure P′). More sophisticated duality results are derived for a broad spectrum of exotic options. The second named author acknowledges the financial support from the Deutsche Forschungsgemeinschaft (DFG, Eb 66/9-2). This research was carried out while the third named author was supported by the Alexander von Humboldt foundation.     

Modeling time series information into option prices: An empirical evaluation of statistical projection and GARCH option pricing model

This paper compares the empirical performances of statistical projection models with those of the Black–Scholes (adapted to account for skew) and the GARCH option pricing models. Empirical analysis on S&P500 index options shows that the out-of-sample pricing and projected trading performances of the semi-parametric and nonparametric projection models are substantially better than more traditional models. Results further indicate that econometric models based on nonlinear projections of observable inputs perform better than models based on OLS projections, consistent with the notion that the true unobservable option pricing model is inherently a nonlinear function of its inputs. The econometric option models presented in this paper should prove useful and complement mainstream mathematical modeling methods in both research and practice.     

Two-dimensional risk-neutral valuation relationships for the pricing of options

The Black–Scholes model is based on a one-parameter pricing kernel with constant elasticity. Theoretical and empirical results suggest declining elasticity and, hence, a pricing kernel with at least two parameters. We price European-style options on assets whose probability distributions have two unknown parameters. We assume a pricing kernel which also has two unknown parameters. When certain conditions are met, a two-dimensional risk-neutral valuation relationship exists for the pricing of these options: i.e. the relationship between the price of the option and the prices of the underlying asset and one other option on the asset is the same as it would be under risk neutrality. In this class of models, the price of the underlying asset and that of one other option take the place of the unknown parameters.      

An option pricing approach to corporate dividends and the capital investment financing decision

In light of a growing trend toward viewing dividends as an investable asset class, this article opens up a new perspective on their valuation. We show that dividends can be viewed as options on the cash flow of the firm. That is, a firm either pays zero dividends, in which case the option expires out‐of‐the‐money, or it pays a positive dividend, the value of which corresponds to the option's moneyness. The exercise price is determined by the capital budget, the flexibility of the company to use external financing, and whether it has minimum and maximum dividends. The model is also capable of accommodating a stochastic capital budget, which allows for uncertain growth opportunities and their correlation with the firm's cash flows. We also present an application of the model using actual data for a large multinational company.     

An endogenous volatility approach to pricing and hedging call options with transaction costs

Standard delta hedging fails to exactly replicate a European call option in the presence of transaction costs. We study a pricing and hedging model similar to the delta hedging strategy with an endogenous volatility parameter for the calculation of delta over time. The endogenous volatility depends on both the transaction costs and the option strike prices. The optimal hedging volatility is calculated using the criterion of minimizing the weighted upside and downside replication errors. The endogenous volatility model with equal weights on the up and down replication errors yields an option premium close to the Leland [J. Finance, 1985 Leland, HE. 1985. Option pricing and replication with transaction costs. J. Finance, 40: 1283–1301. [Crossref], [Web of Science ®] , [Google Scholar], 40, 1283–1301] heuristic approach. The model with weights being the probabilities of the option's moneyness provides option prices closest to the actual prices. Option prices from the model are identical to the Black–Scholes option prices when transaction costs are zero. Data on S&P 500 index cash options from January to June 2008 illustrate the model.     

The role of co-skewness in the pricing of real estate

The current study investigates whether systematic skewness offers an alternative perspective as to why the risk-adjusted returns on real estate should be similar to that for stocks. This is not a trivial issue since an affirmative finding implies that we might be incorrectly measuring real estate risk from both a pricing and a portfolio allocation perspective. A multivariate test of the Kraus-Litzenberger model is used to investigate this skewness proposition with the K-L CAPM tested against several alternative versions of the CAPM. The study finds that the Kraus-Litzenberger model offers additional insights into the measurement of real estate risk. Evidence is also found that both the zero beta and the consumption-oriented CAPM hold, which is consistent with the recent literature in real estate.     

On option pricing models in the presence of heavy tails

We propose a modification of the option pricing framework derived by Borland which removes the possibilities for arbitrage within this framework. It turns out that such arbitrage possibilities arise due to an incorrect derivation of the martingale transformation in the non-Gaussian option models which are used in that paper. We show how a similar model can be built for the asset price processes which excludes arbitrage. However, the correction causes the pricing formulas to be less explicit than the ones in the original formulation, since the stock price itself is no longer a Markov process. Practical option pricing algorithms will therefore have to resort to Monte Carlo methods or partial differential equations and we show how these can be implemented. An extra parameter, which needs to be specified before the model can be used, will give market makers some extra freedom when fitting their model to market data.     

A perturbative approach to Bermudan options pricing with applications

In this paper we address the problem of the valuation of Bermudan option derivatives in the framework of multi-factor interest rate models. We propose a solution in which the exercise decision entails a properly defined series expansion. The method allows for the fast computation of both a lower and an upper bound for the option price, and a tight control of its accuracy, for a generic Markovian interest rate model. In particular, we show detailed computations in the case of the Bond Market Model. As examples we consider the case of a zero coupon Bermudan option and a coupon bearing Bermudan option; in order to demonstrate the wide applicability of the proposed methodology we also consider the case of a last generation payoff, a Bermudan option on a CMS spread bond.