arXiv research

Carr and Wu (2004), henceforth CW, developed a framework that encompasses almost all of the continuous-time models proposed in the option pricing literature. Their framework hinges on the stopping time property of the time changes. By analyzing the measurability of the time changes with respect to the underlying filtra…

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and the implied volatility sur…

In quantitative finance, we often model asset prices as a noisy Ito semimartingale. As this model is not identifiable, approximating by a time-changed Levy process can be useful for generative modelling. We give a new estimate of the normalised volatility or time change in this model, which obtains minimax convergence …

We derive precise transformation formulas for synthetic lower Ricci bounds under time change. More precisely, for local Dirichlet forms we study how the curvature-dimension condition in the sense of Bakry-Emery will transform under time change. Similarly, for metric measure spaces we study how the curvature-dimension c…

We present a new and easy-to-implement sequential sampling method for CGMY processes with either finite or infinite variation, exploiting the time change representation of the CGMY model and a decomposition of its time change. We find that the time change can be decomposed into two independent components. While the fir…

Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first passage problem for such processes. We are lead to consider modifying the standard f…

The paper prices weather contracts using a complex temperature model.

The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process $(X,D)$ of a diffusion state variable $X$ driving default intensity and a default indicator process $D$ and time change it wi…

The paper improves energy contract pricing models by incorporating jumps and varying parameters.

In this paper we propose a general derivative pricing framework which employs decoupled time-changed (DTC) Lévy processes to model the underlying asset of contingent claims. A DTC Lévy process is a generalized time-changed Lévy process whose continuous and pure jump parts are allowed to follow separate random time scal…

The Kelly rule fails to maximize growth in a time-changed return setting.

This paper studies subordinate Ornstein-Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean-reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigro…

The paper approximates CARMA models for option pricing.

Develops a new model for multi-currency volatility using CBI-time-changed Lévy processes.

We address the problem of parameter estimation for diffusion driven stochastic volatility models through Markov chain Monte Carlo (MCMC). To avoid degeneracy issues we introduce an innovative reparametrisation defined through transformations that operate on the time scale of the diffusion. A novel MCMC scheme which ove…

This paper extends subordinated models to include stochastic time changes, improving financial modeling.

This paper proposes a new model for SPX and VIX derivatives markets.

The paper optimizes RV estimation by efficient sampling in time-changed diffusion models.

The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stoc…

New findings show independent subordination is not relevant for accurate option pricing.

We consider structural credit modeling in the important special case where the log-leverage ratio of the firm is a time-changed Brownian motion (TCBM) with the time-change taken to be an independent increasing process. Following the approach of Black and Cox, one defines the time of default to be the first passage time…

We consider flows, called $W^{\rm u}$ flows, whose orbits are the unstable manifolds of a codimension one Anosov flow. Under some regularity assumptions, we give a short proof of the strong mixing property of $W^{\rm u}$ flows and we show that $W^{\rm u}$ flows have purely absolutely continuous spectrum in the orthocom…

The accurate prediction of time-changing covariances is an important problem in the modeling of multivariate financial data. However, some of the most popular models suffer from a) overfitting problems and multiple local optima, b) failure to capture shifts in market conditions and c) large computational costs. To addr…

We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross (possibly coupled with compounded Poisson jumps, JCIR), are tractable…

New GLPs split Lévy bridges into non-overlapping subprocesses.

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function parameters are usually learned using maximum likelihood, which can lead to overfitt…

No-arbitrage models of term structure have the feature that the return on zero-coupon bonds is the sum of the short rate and the product of volatility and market price of risk. Well known models restrict the behavior of the market price of risk so that it is not dependent on the type of asset being modeled. We show tha…

TCNF models SDEs using time deformation of Brownian motion.

We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a Lévy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent Lévy measure, local stochastic volatility and have a local stochastic default intensity. Moreover, the Lévy subordina…

Credit Valuation Adjustment (CVA) pricing models need to be both flexible and tractable. The survival probability has to be known in closed form (for calibration purposes), the model should be able to fit any valid Credit Default Swap (CDS) curve, should lead to large volatilities (in line with CDS options) and finally…

We prove that the variance swap rate (fair strike) equals the price of a co-terminal European-style contract when the underlying is an exponential Markov process, time-changed by an arbitrary continuous stochastic clock, which has arbitrary correlation with the driving Markov process, provided that the payoff function …

We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a number of widely used models. In particular, we use the variance-gamma model, the CG…

We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily enables to enforce the martingale pricing requirement. The martingale condition is i…

Subordination is an often used stochastic process in modeling asset prices. Subordinated Levy price processes and local volatility price processes are now the main tools in modern dynamic asset pricing theory. In this paper, we introduce the theory of multiple internally embedded financial time-clocks motivated by beha…

Paper solves PDEs for optimal investment strategies in volatile markets.

Paper presents adaptive minimax risk classifiers for multidimensional concept drift.

We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under polynomial transformations and Lévy time change. We present a generic method for…

We derive asymptotic expansions for option data to detect infinite variation volatility.

Enlargement of filtrations is a classical topic in the general theory of stochastic processes. This theory has been applied to stochastic finance in order to analyze models with insider information. In this paper we study initial enlargement in a Markov chain market model, introduced by R. Norberg. In the enlargened fi…

We will study metric measure spaces $(X,d,m)$ beyond the scope of spaces with synthetic lower Ricci bounds. In particular, we introduce distribution-valued lower Ricci bounds BE$_1(κ,\infty)$ $\bullet$ for which we prove the equivalence with sharp gradient estimates, $\bullet$ the class of which will be preserved under…

Modeling price dynamics in AMMs with fees using geometric Brownian motion.

Time changes of noise level at Warsaw Stock Market are analyzed using a recently developed method basing on properties of the coarse grained entropy. The condition of the minimal noise level is used to build an efficient portfolio. Our noise level approach seems to be a much better tool for risk estimations than standa…

We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, then its discrete realized variance…

For a given Markov process $X$ and survival function $\overline{H}$ on $\mathbb{R}^+$, the inverse first-passage time problem (IFPT) is to find a barrier function $b:\mathbb{R}^+\to[-\infty,+\infty]$ such that the survival function of the first-passage time $τ_b=\inf \{t\ge0:X(t)<b(t)\}$ is given by $\overline{H}$. In …

Time-subordinated Brownian motion models improve financial market stochastic distribution.

New Dynkin condition for manifolds with boundary yields bi-Lipschitz equivalence and spectral properties.

By adopting the polynomial interpolation method, we propose an approach to hedge against the interest-rate risk of the default-free bonds by measuring the nonparallel movement of the yield-curve, such as the translation, the rotation and the twist. The empirical analysis shows that our hedging strategies are comparable…

The present paper aims at locating the breakings of the integration process of an international system observed during about 50 years in the 19th century. A historical study could link them to special events, which operated as exogenous shocks on this process. The indicator of integration used is the spread between the…