Filters

2017 - 201922020 - 20211

More filters

2019 - 201912020 - 20222
Reset filters

Settings

Subject: European option pricing ×

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Extreme at-the-money skew in a local volatility model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Pigato, Paolo
    We consider a local volatility model, with volatility taking two possible values, depending on the value of the underlying with respect to a fixed threshold. When the threshold is taken at-the-money, we establish exact pricing formulas and compute short-time asymptotics of the implied volatility surface. We derive an exact formula for the at-the-money implied volatility skew, which explodes as T-1/2, reproducing the empirical "steep short end of the smile". This behavior does not depend on the precise choice of the parameters, but simply follows from the "regime-switch" of the local volatility at-the-money.
  • Thumbnail Image
    Item
    Short-time near-the-money skew in rough fractional volatility models
    (London : Taylor & Francis, 2018) Bayer, C.; Friz, P.K.; Gulisashvili, A.; Horvath, B.; Stemper, B.
    We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the ‘rough’ regime of Hurst parameter H<1/2. This regime recently attracted a lot of attention both from the statistical and option pricing point of view. With focus on the latter, we sharpen the large deviation results of Forde-Zhang [Asymptotics for rough stochastic volatility models. SIAM J. Financ. Math., 2017, 8(1), 114–145] in a way that allows us to zoom-in around the money while maintaining full analytical tractability. More precisely, this amounts to proving higher order moderate deviation estimates, only recently introduced in the option pricing context. This in turn allows us to push the applicability range of known at-the-money skew approximation formulae from CLT type log-moneyness deviations of order t1/2 (works of Alòs, León & Vives and Fukasawa) to the wider moderate deviations regime.
  • Thumbnail Image
    Item
    Short-dated smile under rough volatility: asymptotics and numerics
    (London : Taylor & Francis, 2021) Friz, Peter K.; Gassiat, Paul; Pigato, Paolo
    In Friz et al. [Precise asymptotics for robust stochastic volatility models. Ann. Appl. Probab, 2021, 31(2), 896–940], we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small-noise formulae for option prices, using the framework [Bayer et al., A regularity structure for rough volatility. Math. Finance, 2020, 30(3), 782–832]. We investigate here the fine structure of this expansion in large deviations and moderate deviations regimes, together with consequences for implied volatility. We discuss computational aspects relevant for the practical application of these formulas. We specialize such expansions to prototypical rough volatility examples and discuss numerical evidence.