Related papers: To sigmoid-based functional description of the vol…
Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an…
This study delves into the intricate realm of risk evaluation within the domain of specific financial derivatives, notably options. Unlike other financial instruments, like bonds, options are susceptible to broader risks. A distinctive…
This article proposes a calibration framework for complex option pricing models that jointly fits market option prices and the term structure of variance. Calibrated models under the conventional objective function, the sum of squared…
We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at…
Albeit of crucial interest for both financial practitioners and researchers, market-implied volatility data of European swaptions often exhibit large portions of missing quotes due to illiquidity of the various underlying swaption…
Using the large deviation principle (LDP) for a re-scaled fractional Brownian motion $B^H_t$ where the rate function is defined via the reproducing kernel Hilbert space, we compute small-time asymptotics for a correlated fractional…
We present a deep learning framework for pricing options based on market-implied volatility surfaces. Using end-of-day S\&P 500 index options quotes from 2018-2023, we construct arbitrage-free volatility surfaces and generate training data…
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…
Due to the lack of reliable market information, building financial term-structures may be associated with a significant degree of uncertainty. In this paper, we propose a new term-structure interpolation method that extends classical spline…
We present a dynamic hedging scheme for S&P 500 options, where rebalancing decisions are enhanced by integrating information about the implied volatility surface dynamics. The optimal hedging strategy is obtained through a deep policy…
The implied volatility is a crucial element of any financial toolbox, since it is used for quoting and the hedging of options as well as for model calibration. In contrast to the Black-Scholes formula its inverse, the implied volatility, is…
Implied volatility is at the very core of modern finance, notwithstanding standard option pricing models continue to derive option prices starting from the joint dynamics of the underlying asset price and the spot volatility. These models…
We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models…
We present a method for computing all the symmetries of a rational ruled surface defined by a rational parametrization which works directly in parametric rational form, i.e. without computing or making use of the implicit equation of the…
Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and…
We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…
This paper presents static and dynamic versions of univariate, multivariate, and multilevel functional time-series methods to forecast implied volatility surfaces in foreign exchange markets. We find that dynamic functional principal…
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
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…
In this paper we study the short-time behavior of the at-the-money implied volatility for European and arithmetic Asian call options with fixed strike price. The asset price is assumed to follow the Bachelier model with a general stochastic…