Implied Volatility Functions: Empirical Tests

Dumas, Bernard; Fleming, Jeff; Whaley, Robert E.

doi:10.1111/0022-1082.00083

Cited by 1,077 publications

(549 citation statements)

References 31 publications

Supporting

Mentioning

514

Contrasting

Unclassified

Order By: Relevance

“…However such estimation from historical data reflects only past data which may not be representative of the future. Several papers such as Bakshi, Cao and Chen (1997), Bates (1991), Dumas, Fleming, and Whaley (1998), Heston and Nandi (2000), Hsieh and Ritchken (2000) have followed the approach of minimizing the sum of squared errors between actual and theoretical option prices using a non-linear least squares (NLLS) procedure in order to obtain market-implied volatility and structural parameters. Parameters thus determined have the advantage of being based upon forward-looking information contained in option prices.…”

Section: Methodology and Model Calibrationmentioning

confidence: 99%

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

Bhat¹,

Arekar²

2016

IJEF

View full text Add to dashboard Cite

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.

show abstract

Section: Methodology and Model Calibrationmentioning

confidence: 99%

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

Bhat¹,

Arekar²

2016

IJEF

View full text Add to dashboard Cite

show abstract

“…To capture these variations, we include only one trading day's data in any cross sectional analysis. The daily implied volatility surface across strike prices and times to maturity could be estimated assuming a speciÞc function such as (see Dumas/Fleming/Whaley, 1998;Tompkins, 1999;Ané/Geman, 1999)…”

Section: Estimation Methodsmentioning

confidence: 99%

“…The rate of decrease is lower for options with longer time to maturity. In a recent empirical study Dumas/Fleming/Whaley (1998) conclude that the volatility proÞle is not stable through time. As far as S&P 500…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Dynamics of DAX Implied Volatilities

Hafner

Wallmeier²

2000

SSRN Journal

View full text Add to dashboard Cite

On the basis of transaction data, this paper analyzes the strike proÞle of implied volatilities of German DAX options for a time to expiration of 45 days. Beside the S&P option contract, the DAX option is one of the most heavily traded stock index options in the world. Using WLS spline regressions over the sample period from 1995 to 1999, we estimate a time series of smile characteristics, which we then try to attribute to economic fundamentals. Their choice is motivated by common theoretical explanations of the smile. The strike pattern almost exclusively appears as a "skew" rather than a "smile". We Þnd that the dynamics of the smile proÞle can be accurately modelled by a stationary AR(1) process. Market uncertainty, measured by volatility of volatility, and liquidity effects seem to play an important role in determining the pattern of DAX implied volatilities across exercise prices.

show abstract

“…At the very least, one would need to introduce strike dependence into the fractional volatility parameter in order to match the τ = 1 implied volatility skew, which is independent of Hurst exponent by construction. The simplest deterministic model used in practice that gives a reasonable description of the implied volatility skew around current spot levels is a quadratic equation (Dumas, Fleming & Whaley 1998):…”

Section: Implied Volatility In a Fractional Black-scholes Marketmentioning

confidence: 99%

Fractional Black–Scholes option pricing, volatility calibration and implied Hurst exponents in South African context

Flint

Maré

2017

SAJEMS

View full text Add to dashboard Cite

Background: Contingent claims on underlying assets are typically priced under a framework that assumes, inter alia, that the log returns of the underlying asset are normally distributed. However, many researchers have shown that this assumption is violated in practice. Such violations include the statistical properties of heavy tails, volatility clustering, leptokurtosis and long memory. This paper considers the pricing of contingent claims when the underlying is assumed to display long memory, an issue that has heretofore not received much attention.Aim: We address several theoretical and practical issues in option pricing and implied volatility calibration in a fractional Black–Scholes market. We introduce a novel eight-parameter fractional Black–Scholes-inspired (FBSI) model for the implied volatility surface, and consider in depth the issue of calibration. One of the main benefits of such a model is that it allows one to decompose implied volatility into an independent long-memory component – captured by an implied Hurst exponent – and a conditional implied volatility component. Such a decomposition has useful applications in the areas of derivatives trading, risk management, delta hedging and dynamic asset allocation.Setting: The proposed FBSI volatility model is calibrated to South African equity index options data as well as South African Rand/American Dollar currency options data. However, given the focus on the theoretical development of the model, the results in this paper are applicable across all financial markets.Methods: The FBSI model essentially combines a deterministic function form of the 1-year implied volatility skew with a separate deterministic function for the implied Hurst exponent, thus allowing one to model both observed implied volatility surfaces as well as decompose them into independent volatility and long-memory components respectively. Calibration of the model makes use of a quasi-explicit weighted least-squares optimisation routine.Results: It is shown that a fractional Black–Scholes model always admits a non-constant implied volatility term structure when the Hurst exponent is not 0.5, and that 1-year implied volatility is independent of the Hurst exponent and equivalent to fractional volatility. Furthermore, we show that the FBSI model fits the equity index implied volatility data very well but that a more flexible Hurst exponent parameterisation is required to fit accurately the currency implied volatility data.Conclusion: The FBSI model is an arbitrage-free deterministic volatility model that can accurately model equity index implied volatility. It also provides one with an estimate of the implied Hurst exponent, which could be very useful in derivatives trading and delta hedging.

show abstract

Implied Volatility Functions: Empirical Tests

Cited by 1,077 publications

References 31 publications

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

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

The Dynamics of DAX Implied Volatilities

Fractional Black–Scholes option pricing, volatility calibration and implied Hurst exponents in South African context

Contact Info

Product

Resources

About