Accounting for Biases in Black-Scholes (original) (raw)
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Stochastic skew in currency options☆
Journal of Financial Economics, 2007
We analyze the behavior of over-the-counter currency option prices across moneyness, maturity, and calendar time on two of the most actively traded currency pairs over the past eight years. We find that, on any given date, the conditional risk-neutral distribution of currency returns can show strong asymmetry. This asymmetry varies greatly over time and often switches signs. We develop and estimate a class of models that captures this stochastic skew behavior. Model estimation shows that our stochastic skew models significantly outperform traditional jump-diffusion stochastic volatility models both in sample and out of sample.
International Journal of Economics and Finance, 2013
Under risk neutrality and rational expectations, the future value of the option premium is an unbiased estimator of the future actual payoff of the option. In this paper, this unbiasedness hypothesis is tested for the Black-Scholes currency call option pricing model. Three currencies, against the US dollar, are considered: the British pound, the Swiss franc, and the Japanese yen. The data is monthly and starts from the late 1980s. A set of seven different strike prices are assumed for each currency. Unbiasedness is supported if the regression constants are statistically insignificant, and if the regression slopes are statistically insignificantly different from 1, and if there is no autocorrelation in the regression residuals. The results for the British pound are strongly supportive of this version of market option efficiency. For the other two currencies only long run cointegration relations are uncovered. The results, whether short run or long run, remain also strongly supportive when the theoretical constraints are imposed. In addition, the results are not materially different with alternative measures of currency volatility. It can be concluded that the Black-Scholes currency option pricing model is relevant not only theoretically but also empirically and practically.
2008
This paper looks at the consequences of introducing heteroscedasticity in option pricing. The analysis shows that introducing heteroscedasticity results in a better fitting of the empirical distribution of foreign exchange rates than in the Brownian model. In the Black-Scholes world the assumption is that the variance is constant, which is definitely not the case when looking at financial time series data. In this study we therefore price a European call option under a Garch model Framework using the Locally Risk Neutral Valuation Relationship. Option prices for different spot prices are calculated using simulations. We use the non-linear in mean Garch model in analyzing the Kenyan foreign exchange market.
SSRN Electronic Journal, 2000
This paper tests the predictive accuracy of the Black-Scholes (BS) model in pricing the Nifty index option contracts and examines whether the skewness and kurtosis adjusted BS model of gives better results than the original BS model. We also examine whether volatility smile in case of NSE Nifty options, if any, can be attributed to the non normal skewness and kurtosis of stock returns. We use S&P CNX NIFTY near-the-month call options for the period January 1, 2003 to December 24, 2008. The results show that BS model is misspecified as the implied volatility graph depicts the shape of a 'Smile' for the study period. There is significant underpricing by the original BS model and that the mispricing increases as the moneyness increases. Even the modified BS model misprices options significantly. However, pricing errors are less in case of the modified BS model than in case of the original BS model. On the basis of Mean Absolute Error (MAE) it can be concluded that the modified BS model is performing better than the original BS model. Moreover, volatility smile in case of NSE Nifty options for the study period cannot be attributed to the non normal skewness and kurtosis of stock returns.
SSRN Electronic Journal, 2000
We study a new class of three-factor affine option pricing models with interdependent volatility dynamics and a stochastic skewness component unrelated to volatility shocks. These properties are useful in order (i) to model a term structure of implied volatility skews more consistent with the data and (ii) to capture comovements of short and long term skews largely unrelated to the volatility dynamics. We estimate our models using about fourteen years of S&P 500 index option data and find that on average they improve the out-of-sample pricing accuracy of benchmark two-and three-factor affine models by 20%. Using an appropriate decomposition of volatility and skewness, highlighting the main directions of improvements produced by our setting, we show that the enhanced fit results from an improved modeling of the term structure of implied-volatility skews. The largest pricing improvements tend to concentrate during periods of financial crises or market distress, suggesting volatilityunrelated skewness as a potentially useful reduced-form risk factor for reproducing some of the crisis-related dynamics of index option smiles.
Pricing currency options in tranquil markets: modelling volatility frowns
Monash Econometrics and …, 2002
Volatility smiles arise in currency option markets when empirical exchange rate returns distributions exhibit leptokurtosis. This feature of empirical distributions is symptomatic of turbulent periods when exchange rate movements are in excess of movements based on the assumption of normality. In contrast, during periods of tranquility, movements in exchange rates are relatively small, resulting in unconditional empirical returns distributions with thinner tails than the normal distribution. Pricing currency options during tranquil periods on the assumption of normal returns yields implied volatility frowns, with over-pricing at both deep-in and deep-out-of-the-money contracts and underpricing for at-the-money contracts. This paper shows how a parametric class of thin-tailed distributions based on the generalised Student t family of distributions can price currency options during periods of tranquility.
Evaluation of Black-Scholes and GARCH Models Using Currency Call Options Data
Review of Quantitative Finance and Accounting, 2000
This paper empirically examines the performance of Black-Scholes and Garch-M call option pricing models using call options data for British Pounds, Swiss Francs and Japanese Yen. The daily exchange rates exhibit an overwhelming presence of volatility clustering, suggesting that a richer model with ARCH/GARCH effects might have a better fit with actual prices. We perform dominant tests and calculate average percent mean squared errors of model prices. Our findings indicate that the Black-Scholes model outperforms the GARCH models. An implication of this result is that participants in the currency call options market do not seem to price volatility clusters in the underlying process.
Skewed Generalized Error Distribution of Financial Assets and Option Pricing
SSRN Electronic Journal, 2000
This article provides a mathematical and empirical investigation of the reasons for the presence of skewness and kurtosis in financial data. The results indicate that this phenomenon is triggered by higher-order moment dependencies in the data, such as asymmetric and conditional volatility. Moreover, the article develops and tests successfully a skewed extension of the generalized error distribution (SGED), which is then used to model European call option prices. Under the standard assumptions of risk neutrality, normality of log-returns, and absence of arbitrage opportunities, the SGED model yields as special cases several well-known models for pricing options on stocks, stock indices, currencies, and currency futures.
Parameter Estimation of Local Volatility in Currency Option Valuation
International Review on Modelling and Simulations (IREMOS), 2016
In quantitative finance and option pricing, one of the basic determinants of option prices is the volatility of the underlying asset. In this paper, we therefore, present a concise study of volatility in option pricing in the sense of Dupire's approach. Thereafter, we outspread such study via the application of Ito formula to the modelling and valuation of currency option with local volatility. For the purpose of efficiency, we use the daily historical prices of stock-S&P 500 for a certain period to estimate the corresponding historical volatility. Graphical representation of the analysed daily historical data of stock prices with respect to a local volatility is presented.