arXiv research

New models avoid probability in option pricing, matching historical and implied volatilities.

The paper offers a pricing-hedging method for prediction sets.

We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer's pathwise Itō calculus. Price trajectories are $d$-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategie…

New method reduces errors in pricing and sensitivities for discontinuous payoffs.

Develops pathwise analysis for log-optimal portfolios using rough paths theory.

This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a path…

Unified treatment of option pricing deviations scaled for financial models.

This paper gives several simple constructions of the pathwise Ito integral $\int_0^tφdω$ for an integrand $φ$ and a price path $ω$ as integrator, with $φ$ and $ω$ satisfying various topological and analytical conditions. The definitions are purely pathwise in that neither $φ$ nor $ω$ are assumed to be paths of stochast…

A new method for pricing and hedging options without using probability theory.

Unified approach to financial market modeling in discrete time.

Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times. The local time is constructed from discrete approximations, and it is shown that it is $α$-Hölder …

Develops strategies to minimize trading costs in volatile markets.

We provide a model-free pricing-hedging duality in continuous time. For a frictionless market consisting of $d$ risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of a path dependent European option has the same value as the purely probabi…

Exact simulation method for market impact estimation under various execution strategies.

We study the small-time behaviour of the rough Bergomi model, introduced by Bayer, Friz and Gatheral (2016), and prove a large deviations principle for a rescaled version of the normalised log stock price process, which then allows us to characterise the small-time behaviour of the implied volatility.

We consider idealized financial markets in which price paths of the traded securities are cadlag functions, imposing mild restrictions on the allowed size of jumps. We prove the existence of quadratic variation for typical price paths, where the qualification "typical" means that there is a trading strategy that risks …

The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.

A new model for S&P 500 and VIX options pricing and calibration.

This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.

Pathwise uniqueness shown for specific stochastic equations.

Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast…

Develops portfolio theory without probabilistic analysis, focusing on pathwise decomposition.

Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are s…

Efficient pathwise gradient estimators for multivariate distributions.

A new approach to continuous-time universal portfolios using pathwise Itô calculus.

New method computes pathwise gradients for non-reparameterizable distributions.

The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: {\it warm start initialization}, {\it active set updating}, and {\it …

Estimates roughness of volatility from discrete variance data.

We develop a class of pathwise inequalities of the form $H(B_t)\ge M_t+F(L_t)$, where $B_t$ is Brownian motion, $L_t$ its local time at zero and $M_t$ a local martingale. The concrete nature of the representation makes the inequality useful for a variety of applications. In this work, we use the inequalities to derive …

Develops a new framework for financial price processes without stochastic calculus.

New Monte Carlo method for calculating sensitivities of barrier options.

We use pathwise Itô calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of Föllmer's pathwise Itô calculus and works for portfolios generated from functions that may depend on the current states of the market port…

While absence of arbitrage in frictionless financial markets requires price processes to be semimartingales, non-semimartingales can be used to model prices in an arbitrage-free way, if proportional transaction costs are taken into account. In this paper, we show, for a class of price processes which are not necessaril…

This paper simplifies hedge ratios in financial models using pathwise algorithmic differentiation.

New findings on option pricing under bounded bid-ask spreads, showing minimal obstruction and explicit operator.

Validates economic scenarios using statistical tests on stochastic processes.

This dissertation advances scalable Gaussian processes using iterative methods and pathwise conditioning.

This work introduces efficient sampling methods for Gaussian processes by focusing on pathwise conditioning.

MuRiT efficiently computes multi-parameter persistence barcodes.

We show that a trader, who starts with no initial wealth and is not allowed to borrow money or short sell assets, is theoretically able to attain positive wealth by continuous trading, provided that she has perfect foresight of future asset prices, given by a continuous semimartingale. Such an arbitrage strategy can be…

We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of Itô's integral and based on a certain topology which is induced by the outer measure corresponding to the minimal superhedging price. The second one is based on the controlle…

We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes …

Optimizes selling bonds with non-negative prices using a Brownian bridge model.

Efficient estimators for smooth Hilbert-valued parameters with theoretical guarantees.

We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted variance swap along with super- and sub- replicating strategies which enforce t…

The paper optimizes bridge-type estimators for sparse models using pathwise methods.

We consider a class $\mathscr{X}$ of continuous functions on $[0,1]$ that is of interest from two different perspectives. First, it is closely related to sets of functions that have been studied as generalizations of the Takagi function. Second, each function in $\mathscr{X}$ admits a linear pathwise quadratic variatio…

A new method in finance without probabilities or integrals.