Implied Lévy volatility

Corcuera, José Manuel; Guillaume, Florence; Leoni, Peter; Schoutens, Wim

doi:10.1080/14697680902965548

Cited by 25 publications

(13 citation statements)

References 6 publications

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“…20 The Whaley (1993) model is simply the Black (1976b) model applied to VIX options. Corcuera, Guillaume, Leoni, and Schoutens (2009) develop the Black and Scholes (1973) implied volatility concept under a Lévy framework and show (among other things) how the NIG distribution translates into Black and Scholes (1973) implied volatilities. Implied volatility term structure of at-the-money VIX call options.…”

Section: Estimation Results and Discussionmentioning

confidence: 99%

A Term Structure Model for VIX Futures

Huskaj

Nossman²

2012

Journal of Futures Markets

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This study develops a term structure model for VIX futures. Instead of deriving the VIX futures price from a model for the instantaneous variance of the S&P 500 or a model for the VIX, the VIX futures price dynamics are specified exogenously. The empirical features of VIX futures returns (positive skewness, excess kurtosis, and a decreasing volatility term structure for longer term expirations) are captured by assuming that they are normal inverse Gaussian distributed and scaled by a volatility function that is dependent on the maturity. The usefulness of the resulting model is illustrated in two applications: risk management (via calculating value at risk (VaR)) and asset pricing (via pricing hypothetical VIX options). The results show that the model provides a good fit for the empirical term structure of VIX futures, produces good VaR estimates, and is promising for use in pricing VIX options. C 2012 Wiley Periodicals, Inc. Jrl Fut Mark

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Section: Estimation Results and Discussionmentioning

confidence: 99%

A Term Structure Model for VIX Futures

Huskaj

Nossman²

2012

Journal of Futures Markets

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“…The dash-dotted line in Figure 2 represents the standard VG density function. For a detailed discussion on how to build standardized Lévy distributions and how to calibrate the VG distribution using historical data or option data, we refer to Seneta (2004), Corcuera et al (2009), andSchoutens (2016). The quantile-quantile plots (see Figure 3) show that a standard VG distribution is better capable of fitting the tail behavior of the standardized log stock returns than a standard Gaussian distribution.…”

Section: Estimating the Stock Return Processmentioning

confidence: 99%

“…Schoutens (2016)), CDO prices (Albrecher et al (2007)), and implied volatility smiles (Corcuera et al (2009)).…”

Section: Valuation Of the Hedgeable Partmentioning

confidence: 99%

Affordable and adequate annuities with stable payouts: Fantasy or reality?

Bilsen

Linders

2019

Insurance: Mathematics and Economics

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This paper introduces a class of unit-linked annuities that extends existing annuities by allowing portfolio shocks to be gradually absorbed into the annuity payouts. Consequently, our new class enables insurers to offer an affordable and adequate annuity with a stable payout stream. We show how to price and adequately hedge the annuity payouts in a general financial environment.In particular, our model accounts for various stylized facts of stock returns such as asymmetry and heavy-tailedness. Furthermore, the generality of our framework makes it possible to explore the impact of a parameter misspecification on the annuity price and the hedging performance.JEL Classification: G11, G13, G22. .Substituting (110) into (112), we findHence, the budget constraint can be approximated as follows:

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“…Indeed, instead of a normal distribution, we allow for a Lévy distribution, while the Gaussian copula is generalized to a Lévy-based copula. 2 This model can also, at least to some extent, be considered as a generalization to the multidimensional case of the model proposed in Corcuera et al [17] and the parameter σ j in (4) can then be interpreted as the Lévy space (implied) volatility of stock j. The idea of building a multivariate asset model by taking a linear combination of a systematic and an idiosyncratic process can also be found in Kawai [26] and Ballotta and Bonfiglioli [3].…”

Section: The Modelmentioning

confidence: 99%

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

Linders

Schoutens

2016

Innovations in Derivatives Markets

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In this paper we employ a one-factor Lévy model to determine basket option prices. More precisely, basket option prices are determined by replacing the distribution of the real basket with an appropriate approximation. For the approximate basket we determine the underlying characteristic function and hence we can derive the related basket option prices by using the Carr-Madan formula. We consider a three-moments-matching method. Numerical examples illustrate the accuracy of our approximations; several Lévy models are calibrated to market data and basket option prices are determined. In the last part we show how our newly designed basket option pricing formula can be used to define implied Lévy correlation by matching model and market prices for basket options. Our main finding is that the implied Lévy correlation smile is flatter than its Gaussian counterpart. Furthermore, if (near) atthe-money option prices are used, the corresponding implied Gaussian correlation estimate is a good proxy for the implied Lévy correlation.

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Implied Lévy volatility

Cited by 25 publications

References 6 publications

A Term Structure Model for VIX Futures

A Term Structure Model for VIX Futures

Affordable and adequate annuities with stable payouts: Fantasy or reality?

Basket Option Pricing and Implied Correlation in a One-Factor Lévy Model

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