The importance of the loss function in option valuation

Christoffersen, Peter; Jacobs, Kris

doi:10.1016/j.jfineco.2003.02.001

Cited by 330 publications

(231 citation statements)

References 31 publications

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“…Starting with the assumption that the forecast user is interested in the conditional variance, we effectively take the solution of the optimisation problem above (the conditional variance) as given, and consider the loss functions that will generate the desired solution. This approach is unusual in the economic forecasting literature: the more common approach is to take the forecast user's loss function as given and derive the optimal forecast for that loss function; related papers here are Granger (1969), Engle (1993), Christoffersen and Diebold (1997), Christoffersen and Jacobs (2004) and Patton and Timmermann (2007), amongst others. The fact that we know the forecast user desires a variance forecast places limits on the class of loss functions that may be used for volatility comparison, ruling out 3 All of the results in this paper apply directly to the problem of forecasting integrated variance (IV), which Andersen et al (2010), amongst others, argue is a more ''relevant'' notion of variability.…”

Section: Introductionmentioning

confidence: 99%

Volatility forecast comparison using imperfect volatility proxies

Patton

2011

Journal of Econometrics

953

391

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a b s t r a c tThe use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts. We motivate our study with analytical results on the distortions caused by some widely used loss functions, when used with standard volatility proxies such as squared returns, the intra-daily range or realised volatility. We then derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some useful special cases of this class of ''robust'' loss functions. The methods are illustrated with an application to the volatility of returns on IBM over the period 1993 to 2003.

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Section: Introductionmentioning

confidence: 99%

Volatility forecast comparison using imperfect volatility proxies

Patton

2011

Journal of Econometrics

953

391

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“…6 Christoffersen and Jacobs (2004) conclude that the squared pricing error is a "good general-purpose loss function in option valuation applications. "…”

Section: Ranking Forecastsmentioning

confidence: 99%

Density forecast comparisons for stock prices, obtained from high‐frequency returns and daily option prices

Fan¹,

Taylor

Sandri

2017

Journal of Futures Markets

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This paper presents the first comparison of the accuracy of density forecasts for stock prices. Six sets of forecasts are evaluated for DJIA stocks, across four forecast horizons. Two forecasts are risk-neutral densities implied by the Black-Scholes and Heston models. The third set are historical lognormal densities with dispersion determined by forecasts of realized variances obtained from 5-min returns. Three further sets are defined by transforming risk-neutral and historical densities into realworld densities. The most accurate method applies the risk transformation to the Black-Scholes densities. This method outperforms all others for 87% of the comparisons made using the likelihood criterion.

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“…To explain the parabolic smile/smirk pattern of Black-Scholes implied volatility, Dumas et al (1998) modeled implied volatility as DVFs with strike price and maturity adjustments. The model was also analyzed and improved upon by Christoffersen and Jacobs (2004). Dumas, Fleming and Whaley furnished modeling of implied volatility, through various DVFs.…”

Section: Deterministic Volatility Functions (Dvfs)mentioning

confidence: 99%

“…The parabolic shape of the volatility smile, and its dependence on moneyness and maturity, has motivated Dumas et al (1998) to model implied volatility as a quadratic function of moneyness and maturity: they called it ad hoc Black-Scholes model. The same was also analyzed and improved upon by Christoffersen and Jacobs (2004) and they named it Practitioner BlackScholes model. The Deterministic Volatility Function (DVF) approach has been extensively studied in Monte Carlo settings by Dumas et al (1998) and Pena et al (1999), Heston and Nandi (2000) and Christoffersen and Jacobs (2004).…”

Section: Introductionmentioning

confidence: 99%

“…The same was also analyzed and improved upon by Christoffersen and Jacobs (2004) and they named it Practitioner BlackScholes model. The Deterministic Volatility Function (DVF) approach has been extensively studied in Monte Carlo settings by Dumas et al (1998) and Pena et al (1999), Heston and Nandi (2000) and Christoffersen and Jacobs (2004). In recent times, the model has been evaluated by many.…”

Section: Introductionmentioning

confidence: 99%

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Modeling volatility smile: Empirical evidence from India

Singh

2013

J Deriv Hedge Funds

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The objective of this article is twofold. The first and foremost objective is to investigate the information content of the volatility smile and to model its parabolic smile/ skew pattern having advance quadratic formulations, to serve the best of requirements of derivative and capital market. The second relative objective is to find out the impeccable option pricing model capable of expanding the smile/smirk phenomenon of Black-Scholes, which can meet the requirements of option traders and practitioners, specifically during the period of high financial flux as capital market is subject to high unpredictability and may continue to be so. For modeling the volatility smile, we have identified a set of traditional Deterministic Volatility Functions (DVFs) of Dumas et al (1998), and endeavored in restructuring and redesigning of DVFs and further analytically examining the empirical effect of it. The underlying focus of this article remains to emphasize on the analytical investigation of the parameters of DVF models and its relative performance with respect to the classical Black-Scholes model. Furthermore, to search the most apt DVF model that could emerge as the most potential framework for the prediction of volatility smile and the market option price, this article utilizes the data of the most turbulent recent period of Indian and world economy, year [2007][2008][2009], and finds the practical implications of hypothecated DVF models during the uncertain upheavals of financial forces.

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The importance of the loss function in option valuation

Cited by 330 publications

References 31 publications

Volatility forecast comparison using imperfect volatility proxies

Volatility forecast comparison using imperfect volatility proxies

Density forecast comparisons for stock prices, obtained from high‐frequency returns and daily option prices

Modeling volatility smile: Empirical evidence from India

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