arXiv research

We develop a dynamic version of the SSVI parameterisation for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the constraint that the total implied variance needs to be null at the maturity of t…

Flexible model captures commodity skews with maturity effects.

Large batch sizes reduce gradient variance in DP-SGD, improving privacy.

Symbolic regression finds simple formulas for implied volatility.

Characterizes no Butterfly arbitrage in SVI model parameters.

No-arbitrage constraints on implied variance slope are weak, leading to almost guaranteed arbitrage in many cases.

In the recent years, banks have sold structured products such as worst-of options, Everest and Himalayas, resulting in a short correlation exposure. They have hence become interested in offsetting part of this exposure, namely buying back correlation. Two ways have been proposed for such a strategy : either pure correl…

W-shaped vol curves in liquid options can be modeled with two variance-gamma models.

We create precise formulas for VIX option implied volatility.

Before training a neural net, a classic rule of thumb is to randomly initialize the weights so the variance of activations is preserved across layers. This is traditionally interpreted using the total variance due to randomness in both weights \emph{and} samples. Alternatively, one can interpret the rule of thumb as pr…

We undertake a systematic comparison between implied volatility, as represented by VIX (new methodology) and VXO (old methodology), and realized volatility. We compare visually and statistically distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. We find that t…

Monotonicity of normalized implied-volatility coordinates under no-arbitrage

Improves diffusion models by controlling total variance and signal-to-noise-ratio.

We study distributions of realized variance (squared realized volatility) and squared implied volatility, as represented by VIX and VXO indices. We find that Generalized Beta distribution provide the best fits. These fits are much more accurate for realized variance than for squared VIX and VXO -- possibly another indi…

This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumpt…

Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.

New framework improves option pricing models by addressing volatility dynamics.

New formula for implied volatility from Black-Scholes model.

The paper proposes a new method to calibrate option pricing models that accurately match both volatility surfaces and variance term structures.

New Monte Carlo method outperforms existing strategy for estimating Sobol' indices.

We extend Dupire's formula for stochastic interest rates and local volatility.

This paper examines Bachelier implied volatility at extreme strikes.

Proposes deep hedging for index options using implied volatility surface.

The paper develops estimators for variance in graph structures using fused lasso.

We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European options which are written in terms of the implied volatility are given. In particular…

Two approaches integrate qualitative views into portfolio optimization, showing aggregation methods outperform robust optimization.

The paper analyzes the bias-variance tradeoff for Bregman divergences.

We quantify predictive uncertainty using the posterior predictive variance.

We investigate the joint dynamics of spot and implied volatility from an empirical perspective. We focus on the equity market with the SPX Index our underlying of choice. Using only observable quantities, we extract the instantaneous variance curves implied by the market and study their daily variations jointly with sp…

We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of 'forward implied variance' in the original derivation of Gatheral, who introduced this representation in his book 'The Vol…

This notes explores angle structures on ideally triangulated compact $3$-manifolds with high genus boundary. We show that the existence of angle structures implies the existence of a hyperbolic metric with totally geodesic boundary, and conversely each hyperbolic $3$-manifold with totally geodesic boundary has an ideal…

Study finds adding more information to robust option pricing does not improve bounds.

The paper calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.

We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by $α$-stable processes with $α\in(1,2]$. In this framework, we examine the implied volatility and its asymptotic behaviors for both asset and variance options. Furthermore, we examine the jump clus…

The study classifies flows of finite curvature in 3D space.

The rough Bergomi model, introduced by Bayer, Friz and Gatheral [Quant. Finance 16(6), 887-904, 2016], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in e…

The paper connects semi-parametric estimates to European option pricing.

Contextual bandits study how reward variance affects regret bounds.

We extend the model-free formula of [Fukasawa 2012] for $\mathbb E[Ψ(X_T)]$, where $X_T=\log S_T/F$ is the log-price of an asset, to functions $Ψ$ of exponential growth. The resulting integral representation is written in terms of normalized implied volatilities. Just as Fukasawa's work provides rigourous ground for Ch…

New algorithm reduces MDP regret by accounting for state suboptimality gaps and variance.

We consider multi-level composite optimization problems where each mapping in the composition is the expectation over a family of random smooth mappings or the sum of some finite number of smooth mappings. We present a normalized proximal approximate gradient (NPAG) method where the approximate gradients are obtained v…

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 in the log strike. We illustrate the versatility of our expansion by computing t…

In this paper, we implement and test two types of market-based models for European-type options, based on the tangent Levy models proposed recently by R. Carmona and S. Nadtochiy. As a result, we obtain a method for generating Monte Carlo samples of future paths of implied volatility surfaces. These paths and the surfa…

In this paper, we consider minimal hypersurfaces in the product space $\mathbb{H}^n \times \mathbb{R}$. We begin by studying examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations. We then consider minimal hypersurfaces with finite total curvature. This assumption implies that the …

Paper proves uniqueness of a complex construction.

The paper introduces a method to decompose variance in twin networks for better treatment effect estimation.

Minimal surfaces in hyperbolic space have a renormalized area criterion.

Totally geodesic submanifolds in product spaces imply special curvature properties.