Stock-price volatility, mean-reverting diffusion, and noise

Merville, Larry J.; Pieptea, Dan R.

doi:10.1016/0304-405x(89)90078-0

Cited by 72 publications

(44 citation statements)

References 26 publications

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“…The MRSRP has been widely used to model the stochastic evolution of volatility over time (see among others, Hull and White 1988, Heston 1993, Ball and Roma 1994, Grünbichler and Longstaff 1996, and Psychoyios et al 2003 for a review on the continuous time stochastic volatility processes). This is because it is consistent with the empirical evidence that volatility follows a mean-reverting process (see e.g., Scott 1987, Merville and Pieptea 1989, and Sheikh 1993, and it precludes volatility from taking negative values.…”

Section: A Generating the Data: The Simulation Setupsupporting

confidence: 79%

Volatility options: Hedging effectiveness, pricing, and model error

Psychoyios

Skiadopoulos

2005

Journal of Futures Markets

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Section: A Generating the Data: The Simulation Setupsupporting

confidence: 79%

Volatility options: Hedging effectiveness, pricing, and model error

Psychoyios

Skiadopoulos

2005

Journal of Futures Markets

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“…Several studies have examined the efficacy of alternative measures of volatility to be input into the model. Although early work used historical volatility of the underlying asset as an input to the BSM several researchers such as Latane and Rendleman (1976), Chiras and Manaster (1978), Merville and Pieptea (1989) showed that the underlying volatility implied in the traded prices of options is a better predictor of ex-post volatility than volatility estimated from historical time-series. This measure of volatility is known in the literature as "implied volatility".…”

Section: Black-scholes-merton Model (Bsm)mentioning

confidence: 99%

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

Bhat¹,

Arekar²

2016

IJEF

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Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models -the Black-Scholes-Merton Option Pricing Model (BSM) and Duan"s NGARCH option pricing model -for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the "volatility smile". This bias of the BSM results from its assumption of a constant volatility over the option"s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

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“…These multifactor models have been validated by empirical studies that show that the deterministic volatility assumption is inconsistent with real data [2]. Instead, studies find that volatility is strongly mean-reverting [15] and show the presence of multiple time scales (or dimensions) of volatility variation [7,16]. More recently, Lorig et al [14] adopted a general class of multifactor Local-Stochastic Volatility (LSV) models with hybrid dynamics.…”

mentioning

confidence: 99%

Robust Numerical Calibration for Implied Volatility Expansion Models

Baltean-Lugojan¹,

Parpas²

2016

SIAM J. Finan. Math.

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Abstract. Implied volatility expansions allow calibration of sophisticated volatility models. They provide an accurate fit and parametrization of implied volatility surfaces that is consistent with empirical observations. Fine-grained higher order expansions offer a better fit but pose the challenge of finding a robust, stable and computationally tractable calibration procedure due to a large number of market parameters and nonlinearities. We propose calibration schemes for second order expansions that take advantage of the model's structure via exact parameter reductions and recoveries, reuse and scaling between expansion orders where permitted by the model asymptotic regime and numerical iteration over bounded significant parameters. We perform a numerical analysis over 12 years of real S&P 500 index options data for both multiscale stochastic and general local-stochastic volatility models. Our methods are validated empirically by obtaining stable market parameters that meet the qualitative and numerical constraints imposed by their functional forms and model asymptotic assumptions.Key words. implied volatility expansions, numerical calibration, parameter reductions, nonlinear least squares AMS subject classifications. 91G20, 91G60, 90C30, 60-081. Introduction. Research into implied volatility modelling both in academia and industry is focused on addressing the unrealistic assumption of constant asset volatility in the well-known Black-Scholes framework for pricing financial options (see [13] for an overview). A robust model parametrization of implied volatility needs to capture both characteristics and dynamics of the implied volatility surface along different strikes and maturities (or expiries). In addition, volatility models need to balance parameter stability with quality of fit over market data. Practitioners often prioritize tight fits and re-calibrate daily due to overfits that are not stable over multiple days. Meanwhile, existing literature focuses more on consistency. The downside of models that focus on consistency is that they can be computationally expensive to calibrate or are narrowly applicable in pricing a range of derivative contracts. The literature around volatility models is substantial, and we refer the reader to [10] for an extensive overview and comparison of volatility model classes.Models that consistently capture detailed volatility dynamics typically require calibration via numerical-based approaches that are often computationally expensive or lead to numerical instabilities. In order to address these issues, theoretical results have been proposed that translate model formulations into explicit implied volatility expansions for an alternative faster parameter calibration. Fouque et al [8,9] studied Stochastic Volatility (SV) models with multiple factors driving volatility on different time scales. These multifactor models have been validated by empirical studies that show that the deterministic volatility assumption is inconsistent with real data [2]. Instead, studies find that vol...

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Stock-price volatility, mean-reverting diffusion, and noise

Cited by 72 publications

References 26 publications

Volatility options: Hedging effectiveness, pricing, and model error

Volatility options: Hedging effectiveness, pricing, and model error

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

Robust Numerical Calibration for Implied Volatility Expansion Models

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