Related papers: From characteristic functions to implied volatilit…
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility…
We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential L\'evy models. This…
We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and…
We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied…
We investigate the asymptotic behaviour of the implied volatility in the Bachelier setting, extending the large-strike results established for the Black-Scholes framework. Exploiting the theory of regular variation, we derive explicit…
We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear…
We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential L\'evy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the…
We introduce a new class of local volatility models. Within this framework, we obtain expressions for both (i) the price of any European option and (ii) the induced implied volatility smile. As an illustration of our framework, we perform…
We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms. This parameterization is flexible enough to fit market implied…
The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing…
We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution 1) is properly normalized and 2) obeys the tower law (semigroup property), so we can construct martingales…
We extend upon the saddle-point equation presented in [1] to derive large-time model-implied volatility smiles, providing its theoretical foundation and studying its applications in classical models. As long as characteristic function…
We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity…
We consider the at-the-money strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behavior of the slope for infinite activity exponential L\'evy models including a Brownian component. As…
We provide a full characterisation of the large-maturity forward implied volatility smile in the Heston model. Although the leading decay is provided by a fairly classical large deviations behaviour, the algebraic expansion providing the…
We provide explicit conditions on the distribution of risk-neutral log-returns which yield sharp asymptotic estimates on the implied volatility smile. We allow for a variety of asymptotic regimes, including both small maturity (with…
We propose a randomised version of the Heston model-a widely used stochastic volatility model in mathematical finance-assuming that the starting point of the variance process is a random variable. In such a system, we study the small-and…
The paper studies estimation of parameters of diffusion market models from historical data. The standard definition of implied volatility for these models presents its value as an implicit function of several parameters, including the…
The main purpose of this work is to examine the behavior of the implied volatility smiles around jumps, contributing to the literature with a high-frequency analysis of the smile dynamics based on intra-day option data. From our…
We develop a method to study the implied volatility for exotic options and volatility derivatives with European payoffs such as VIX options. Our approach, based on Malliavin calculus techniques, allows us to describe the properties of the…