Related papers: An Expanded Local Variance Gamma model
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…
The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the…
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…
Following an approach originally suggested by Balland in the context of the SABR model, we derive an ODE that is satisfied by normalized volatility smiles for short maturities under a rough volatility extension of the SABR model that…
Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it…
In [1], we calibrated a one-factor Cheyette SLV model with a local volatility that is linear in the benchmark forward rate and an uncorrelated CIR stochastic variance to 3M caplets of various maturities. While caplet smiles for many…
We apply convex regularization techniques to the problem of calibrating the local volatility surface model of Dupire taking into account the practical requirement of discrete grids and noisy data. Such requirements are the consequence of…
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 develop an expansion approach for the pricing of European quanto options written on LIBOR rates (of a foreign currency). We derive the dynamics of the system of foreign LIBOR rates under the domestic forward measure and then consider the…
In the current literature, the analytical tractability of discrete time option pricing models is guaranteed only for rather specific types of models and pricing kernels. We propose a very general and fully analytical option pricing…
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 non-parametric extension with leverage functions to the Andersen commodity curve model. We calibrate this model to market data for WTI and NG including option skew at the standard maturities. While the model can be calibrated…
This paper addresses the approximation of the local volatility function in the Cheyette interest rate model. Its main contribution is an explicit analytical formula for approximating local volatility, derived by extending the classical…
In this paper we provide evidence that financial option markets for equity indices give rise to non-trivial dependency structures between its constituents. Thus, if the individual constituent distributions of an equity index are inferred…
For any strictly positive martingale $S = \exp(X)$ for which $X$ has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials…
Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the…
We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [5, 6, 8] for…
We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest…
This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation…
We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is…