Filters

2017 - 20193

More filters

2021 - 20223
Reset filters

Settings

End date: 2019 × Start date: 2010 × DDC: 330 × DDC: 510 × WGL Institute: WIAS ×

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    A regularity structure for rough volatility
    (Oxford [u.a.] : Wiley-Blackwell, 2019) Bayer, Christian; Friz, Peter K.; Gassiat, Paul; Martin, Jorg; Stemper, Benjamin
    A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility. First observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, rough volatility captures parsimoniously key-stylized facts of the entire implied volatility surface, including extreme skews (as observed earlier by Alòs et al.) that were thought to be outside the scope of stochastic volatility models. On the mathematical side, Markovianity and, partially, semimartingality are lost. In this paper, we show that Hairer's regularity structures, a major extension of rough path theory, which caused a revolution in the field of stochastic partial differential equations, also provide a new and powerful tool to analyze rough volatility models.
  • Thumbnail Image
    Item
    Option pricing in the moderate deviations regime
    (Oxford [u.a.] : Wiley-Blackwell, 2017) Friz, Peter; Gerhold, Stefan; Pinter, Arpad
    We consider call option prices close to expiry in diffusion models, in an asymptotic regime (“moderately out of the money”) that interpolates between the well-studied cases of at-the-money and out-of-the-money regimes. First and higher order small-time moderate deviation estimates of call prices and implied volatilities are obtained. The expansions involve only simple expressions of the model parameters, and we show how to calculate them for generic local and stochastic volatility models. Some numerical computations for the Heston model illustrate the accuracy of our results.
  • Thumbnail Image
    Item
    The invariant distribution of wealth and employment status in a small open economy with precautionary savings
    (Amsterdam : North-Holland, 2019) Bayer, Christian; Rendall, Alan D.; Wälde, Klaus
    We study optimal savings in continuous time with exogenous transitions between employment and unemployment as the only source of uncertainty in a small open economy. We prove the existence of an optimal consumption path. We exploit that the dynamics of consumption and wealth between jumps can be expressed as a Fuchsian system. We derive conditions under which an invariant joint distribution for the state variables, i.e., wealth and labour market status, exists and is unique. We also provide conditions under which the distribution of these variables converges to the invariant distribution. Our analysis relies on the notion of T-processes and applies results on the stability of Markovian processes from Meyn and Tweedie (1993a, b,c). © 2019 The Author(s)