Results 61 to 70 of about 1,119,588 (120)

A Gamma Ornstein-Uhlenbeck model driven by a Hawkes process. [PDF]

Math Financ Econ, 2021
Bernis G, Brignone R, Scotti S, Sgarra C.   +3 more
europepmc   +1 more source

Probability density of lognormal fractional SABR model [PDF]

arXiv, 2017
Instantaneous volatility of logarithmic return in the lognormal fractional SABR model is driven by the exponentiation of a correlated fractional Brownian motion. Due to the mixed nature of driving Brownian and fractional Brownian motions, probability density for such a model is less studied in the literature.
arxiv  

Mass at zero in the uncorrelated SABR model and implied volatility asymptotics [PDF]

arXiv, 2015
We study the mass at the origin in the uncorrelated SABR stochastic volatility model, and derive several tractable expressions, in particular when time becomes small or large. As an application--in fact the original motivation for this paper--we derive small-strike expansions for the implied volatility when the maturity becomes short or large.
arxiv  

Vanna-Volga Method for Normal Volatilities [PDF]

arXiv, 2018
Vanna-Volga is a popular method for the interpolation/extrapolation of volatility smiles. The technique is widely used in the FX markets context, due to its ability to consistently construct the entire Lognormal smile using only three Lognormal market quotes. However, the derivation of the Vanna-Volga method itself is free of distributional assumptions.
arxiv  

Unifying the BGM and SABR Models: A short Ride in Hyperbolic Geometry [PDF]

arXiv, 2006
In this short note, using our geometric method introduced in a previous paper \cite{phl} and initiated by \cite{ave}, we derive an asymptotic swaption implied volatility at the first-order for a general stochastic volatility Libor Market Model. This formula is useful to quickly calibrate a model to a full swaption matrix.
arxiv  

A Note on the Equivalence between the Normal and the Lognormal Implied Volatility : A Model Free Approach [PDF]

arXiv, 2011
First, we show that implied normal volatility is intimately linked with the incomplete Gamma function. Then, we deduce an expansion on implied normal volatility in terms of the time-value of a European call option. Then, we formulate an equivalence between the implied normal volatility and the lognormal implied volatility with any strike and any model.
arxiv  

Short-maturity asymptotics for VIX and European options in local-stochastic volatility models [PDF]

arXiv
We derive the short-maturity asymptotics for European and VIX option prices in local-stochastic volatility models where the volatility follows a continuous-path Markov process. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered.
arxiv  

Mean-Reverting SABR Models: Closed-form Surfaces and Calibration for Equities [PDF]

arXiv
In this paper, we consider three stochastic-volatility models, each characterized by distinct dynamics of instantaneous volatility: (1) a CIR process for squared volatility (i.e., the classical Heston model); (2) a mean-reverting lognormal process for volatility; and (3) a CIR process for volatility.
arxiv  

Efficient simulation of the SABR model [PDF]

arXiv
We propose an efficient and reliable simulation scheme for the stochastic-alpha-beta-rho (SABR) model. The two challenges of the SABR simulation lie in sampling (i) the integrated variance conditional on terminal volatility and (ii) the terminal price conditional on terminal volatility and integrated variance.
arxiv  

Option pricing in the moderate deviations regime. [PDF]

Math Financ, 2018
Friz P, Gerhold S, Pinter A.
europepmc   +1 more source