Alternative asset-price dynamics and volatility smile

Brigo, Damiano; Mercurio, Fabio; Sartorelli, Giulio

doi:10.1088/1469-7688/3/3/303

Cited by 26 publications

(25 citation statements)

References 14 publications

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“…as in Mercurio (2000, 2002) (with μ(t, x, i) ≡ μ-see also Brigo et al 2003). Clearly the conditions for the existence and uniqueness of the solution of the SDE (11) depend on the densities…”

Section: Is the Joint Pdf Of (X(t) Y(t)); (Ii) For Any Integrable Fumentioning

confidence: 93%

“…, X n (t)). As a consequence of the risk-neutrality assumption, we can restrict the drift term of the asset price component to be of the form μ(t, s, i) = μs, where the parameter μ is specified by the pricing measure Q (μ = r − q, where r is the risk-free rate and q the continuous dividend yield, μ = r − r f , r f the foreign risk-free rate, for underlyings that are exchange rates-see Brigo et al 2003). Finally, let (s) be the integrable payoff of the derivative maturing at time T. Then, from Theorem 2.1, its price at time t = 0 is simply given by…”

Section: Application To Option Pricing Modelsmentioning

confidence: 99%

“…The case of one-dimensional log-normal mixture dynamics has been considered by Mercurio (2000, 2002) and Brigo et al (2003) and fully exploited for pricing European call/put options. In the following we present firstly a simulation scheme for RS diffusions to improve the classical discretization approach for generating sample paths from Eq.…”

Section: Application To Option Pricing Modelsmentioning

confidence: 99%

“…Ramponi (B) Dept. S.E.F.eME.Q., University of via Columbia,2,00133 Rome, In a series of papers Mercurio (2000, 2002) and Brigo et al (2003) proposed a class of one-dimensional diffusion models characterized by a local volatility function which implies a mixture distribution for the asset price. In particular, the case of log-normal mixtures has been considered and applied to various pricing problems.…”

Section: Introductionmentioning

confidence: 99%

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Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing

Ramponi

2009

Methodol Comput Appl Probab

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In this paper we present a class of regime switching diffusion models described by a pair (X(t), Y(t)) ∈ R n × S, S = {1, 2, . . . , N}, Y(t) being a Markov chain, for which the marginal probability of the diffusive component X(t) is a given mixture. Our main motivation is to extend to a multivariate setting the class of mixture models proposed by Brigo and Mercurio in a series of papers. Furthermore, a simple algorithm is available for simulating paths through a thinning mechanism. The application to option pricing is considered by proposing a mixture version for the Margrabe Option formula and the Heston stochastic volatility formula for a plain vanilla.

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Section: Is the Joint Pdf Of (X(t) Y(t)); (Ii) For Any Integrable Fumentioning

confidence: 93%

Section: Application To Option Pricing Modelsmentioning

confidence: 99%

Section: Application To Option Pricing Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing

Ramponi

2009

Methodol Comput Appl Probab

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“…The Multi Variate Mixture Dynamics model (MVMD) introduced by Brigo, Mercurio and Rapisarda [8] and recently described in a deeper way in Brigo, Rapisarda and Sridi [10] is a tractable dynamical arbitrage-free model defined as the multidimensional version of the lognormal mixture dynamics model (LMD) in [4] and [5] (see also [9]). The singleasset LMD model is a no-arbitrage model widely used among practitioners because of its practical advantages in calibration and pricing (analytical formulae for European options, explicit expression for the local volatility) and of its flexibility and accuracy.…”

Section: Introduction To the Multivariate Mixture Dynamicsmentioning

confidence: 99%

The Multivariate Mixture Dynamics Model: Shifted Dynamics and Correlation Skew

2015

Self Cite

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The Multi Variate Mixture Dynamics model is a tractable, dynamical, arbitragefree multivariate model characterized by transparency on the dependence structure, since closed form formulae for terminal correlations, average correlations and copula function are available. It also allows for complete decorrelation between assets and instantaneous variances. Each single asset is modelled according to a lognormal mixture dynamics model, and this univariate version is widely used in the industry due to its flexibility and accuracy. The same property holds for the multivariate process of all assets, whose density is a mixture of multivariate basic densities. This allows for consistency of single asset and index/portfolio smile.In this paper, we generalize the MVMD model by introducing shifted dynamics and we propose a definition of implied correlation under this model. We investigate whether the model is able to consistently reproduce the implied volatility of FX cross rates once the single components are calibrated to univariate shifted lognormal mixture dynamics models. We consider in particular the case of the Chinese renminbi FX rate, showing that the shifted MVMD model correctly recovers the CNY/EUR smile given the EUR/USD smile and the USD/CNY smile, thus highlighting that the model can also work as an arbitrage free volatility smile extrapolation tool for cross currencies that may not be liquid or fully observable.We compare the performance of the shifted MVMD model in terms of implied correlation with those of the shifted Simply Correlated Mixture Dynamics model where the dynamics of the single assets are connected naively by introducing correlation among their Brownian motions. Finally, we introduce a model with uncertain volatilities and correlation. The Markovian projection of this model is a generalization of the shifted MVMD model.

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Lognormal Mixture Diffusion Model

Mercurio

2010

Encyclopedia of Quantitative Finance

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Alternative asset-price dynamics and volatility smile

Cited by 26 publications

References 14 publications

Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing

Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing

The Multivariate Mixture Dynamics Model: Shifted Dynamics and Correlation Skew

Lognormal Mixture Diffusion Model

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