Stochastic Implied Volatility

Hafner, Reinhold

doi:10.1007/978-3-642-17117-8

Cited by 33 publications

(8 citation statements)

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“…In particular, for the applications that we discuss in the above paragraph, one needs to fit an econometric model to the estimated factors Z t . For example, Hafner (2004) and Cont and da Fonseca (2002) fitted an AR(1) process to each factor, and Fengler et al (2007) considered a multivariate VAR(2) model. The main question that arises from these applications is whether the inference based on Z t is equivalent to the one based on Z t .…”

Section: Introductionmentioning

confidence: 99%

Time Series Modelling With Semiparametric Factor Dynamics

Park

Mammen

Härdle

et al. 2009

Journal of the American Statistical Association

126

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High-dimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the low-dimensional time series analysis. Such highdimensional problems occur frequently in many different fields of science. In this paper we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modelling approach poses an important question: Is it justified, from inferential point of view, to base statistical inference on the estimated times series factors? We show that the difference of the inference based on the estimated time series and 'true' unobserved time series is asymptotically negligible. Our results justify fitting vector autoregressive processes to the estimated factors, which allows one to study the dynamics of the whole high-dimensional system with a low-dimensional representation. We illustrate the theory with a simulation study.Also, we apply the method to a study of the dynamic behavior of implied volatilities and discuss other possible applications in finance and economics.

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Section: Introductionmentioning

confidence: 99%

Time Series Modelling With Semiparametric Factor Dynamics

Park

Mammen

Härdle

et al. 2009

Journal of the American Statistical Association

126

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“…The explicit derivation of (3.5) and a detailed treatment of implied volatilities can be found in Hafner (2004) and Fengler (2005). Clearly, lower dimension objects describing V may be used to analyze the RN surface H. A functional dataset containing realizations of the implied volatility surface V is, however, not available, as in an exchange only discretized values of V t corrupted by noise are registered from trades.…”

Section: Estimationmentioning

confidence: 99%

Dynamic semiparametric factor models in risk neutral density estimation

2009

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“…Having the data-driven basis m l in hand we can estimate daily factors by the ordinary least squares (OLS) method. Afterwards one fits the econometric model to Z t , as it has been done by Cont and Da Fonseca (2002) and Hafner (2004), who fitted AR(1) to every Z t,l , l ∈ {1, . .…”

Section: Model Characterizationmentioning

confidence: 99%

Implied basket correlation dynamics

Härdle

Silyakova

2016

Statistics &Amp; Risk Modeling

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Equity basket correlation is an important risk factor. It characterizes the strength of linear dependence between assets and thus measures the degree of portfolio diversification. It can be estimated both under the physical measure from return series, and under the risk neutral measure from option prices. The difference between the two estimates motivates a so called "dispersion strategy". We study the performance of this strategy on the German market over the recent 2 years and propose several hedging schemes based on implied correlation (IC) forecasts. Modeling IC is a challenging task both in terms of computational burden and estimation error. First the number of correlation coefficients to be estimated would grow with the size of the basket. Second, since the IC is implied from option prices it is not constant over maturities and strikes. Finally, the IC changes over time. The dimensionality of the problem is reduced by an assumption that the correlation between all pairs of equities is constant (equicorrelation). The IC surface (ICS) is then approximated from implied volatilities of stocks and implied volatility of the basket. To analyze this structure and the dynamics of the ICS we employ a dynamic semiparametric factor model (DSFM).JEL classification codes: C14, C32, G12, G13, G15, G17

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Stochastic Implied Volatility

Cited by 33 publications

References 0 publications

Time Series Modelling With Semiparametric Factor Dynamics

Time Series Modelling With Semiparametric Factor Dynamics

Dynamic semiparametric factor models in risk neutral density estimation

Implied basket correlation dynamics

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