arXiv · arXiv q-fin · 2026
We develop a semi-static framework for the variance-optimal hedging of multi-asset derivatives exposed to correlation and covariance risk. The approach combines continuous-time dynamic trading in the underlying assets with a static portfolio of auxiliary contingent claims. Using a multivariate Galtchouk--Kunita--Watanabe decomposition, we show that the resulting global mean-variance problem decouples naturally into a…
Konstantinos Chatziandreou, Sven Karbach
arXiv · arXiv q-fin · 2021
In this study we consider the pricing of energy derivatives when the evolution of spot prices is modeled with a normal tempered stable driven Ornstein-Uhlenbeck process. Such processes are the generalization of normal inverse Gaussian processes that are widely used in energy finance applications. We first specify their statistical properties calculating their characteristic function in closed form. This result is ins…
Piergiacomo Sabino
arXiv · arXiv q-fin · 2021
In this study we consider the pricing of energy derivatives when the evolution of spot prices follows a tempered stable or a CGMY driven Ornstein- Uhlenbeck process. To this end, we first calculate the characteristic function of the transition law of such processes in closed form. This result is instrumental for the derivation of non-arbitrage conditions such that the spot dynamics is consistent with the forward curv…
Piergiacomo Sabino
arXiv · arXiv q-fin · 2018
Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around $\mathbb{R}\subset \mathbb{C}$. The Fourier transform techniques reduces calculation of probability distributions and option prices to evaluation of integrals whose integrands are analytic in domains enjoying these properties. In the paper, we suggest to use changes…
Svetlana Boyarchenko, Sergei Levendorskiĭ
arXiv · arXiv q-fin · 2011
This describes a statistical technique called "tonsuring" for exploratory data analysis in finance. Instead of rejecting "outlier" data that conflicts with the model, this strips out "inlier" data to get a clearer picture of how the market changes for larger moves.
Martin Goldberg
arXiv · arXiv q-fin · 2026
This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a canonical parametrization of the bonding curve that ensures dimensional consistency across diverse trading functions, such as those employed by Uniswap and Balancer, and demonstrate that …
Jimmy Risk, Shen-Ning Tung, Tai-Ho Wang
arXiv · arXiv q-fin · 2021
We consider the problem of calculating risk-neutral implied volatilities of European options without relying on option mid prices but solely on bid and ask prices. We provide an approach, based on the conic finance paradigm, that allows to uniquely strip risk-neutral implied volatilities from bid and ask quotes, and that does not require restrictive assumptions. Our methodology also allows to jointly calculate the im…
Matteo Michielon, Asma Khedher, Peter Spreij
arXiv · arXiv q-fin · 2026
We study caplet stripping, the problem of recovering a caplet volatility term structure consistent with quoted cap volatilities. Many academic papers on the Libor market model assume caplet volatilities are readily available, whereas practitioners know they are not and extracting them is a complex task. This paper presents a practical workflow, structuring the presentation around a constructive algorithm. We start wi…
Fabien Le Floc'h
arXiv · arXiv q-fin · 2014
We study the problem of the execution of a moderate size order in an illiquid market within the framework of a solvable Markovian model. We suppose that in order to avoid impact costs, a trader decides to execute her order through a unique trade, waiting for enough liquidity to accumulate at the best quote. We find that despite the absence of a proper price impact, such trader faces an execution cost arising from a n…
Iacopo Mastromatteo
arXiv · arXiv q-fin · 2026
We address the attribution problem for apparent slow collective dynamics: is the observed persistence intrinsic, or inherited from a persistent driver? For the leading eigenvalue fraction $ψ_1=λ_{\max}/N$ of S\&P 500 60-day rolling correlation matrices ($237$ stocks, 2004--2023), a VIX-coupled Ornstein--Uhlenbeck model reduces the effective relaxation time from $298$ to $61$ trading days and improves the fit over bar…
Yuda Bi, Vince D Calhoun
arXiv · arXiv q-fin · 2025
We investigate the asymptotic behaviour of the Bachelier implied volatility tails, extending the large-strike results established for the Black-Scholes implied volatility. Exploiting the theory of regular variation, we derive explicit expressions for the Bachelier implied volatility in the wings of the smile, directly linking them to the tail decay of the underlying returns' distribution. Furthermore, we establish a …
Roberto Baviera, Michele Domenico Massaria
arXiv · arXiv q-fin · 2025
We study nearly unstable bivariate cumulative heavy-tailed INAR($\infty$) processes and show that, under a one-factor parameterization and a suitable scaling, they converge to the rough Heston model. This yields a discrete-time microstructural route to the joint price-variance dynamics and gives explicit formulas linking the INAR asymmetry parameters to the leverage correlation and diffusion scale of the limiting vol…
Yingli Wang, Zhenyu Cui, Lingjiong Zhu
arXiv · arXiv q-fin · 2021
We study the convergence properties of the short maturity expansion of option prices in the uncorrelated log-normal ($β=1$) SABR model. In this model the option time-value can be represented as an integral of the form $V(T) = \int_{0}^\infty e^{-\frac{u^2}{2T}} g(u) du$ with $g(u)$ a "payoff function" which is given by an integral over the McKean kernel $G(s,t)$. We study the analyticity properties of the function $g…
Alan L. Lewis, Dan Pirjol
arXiv · arXiv q-fin · 2020
In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalised to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options with weights that are directly related to trading intuition. Additionally, we derive first and second order hedges for volatility swaps using only variance swaps. As dynamically tra…
Frido Rolloos
arXiv · arXiv q-fin · 2019
There is an observed basis between repo discounting, implied from market repo rates, and bond discounting, stripped from the market prices of the underlying bonds. Here, this basis is explained as a convexity effect arising from the decorrelation between the discount rates for derivatives and bonds. Using a Hull-White model for the discount basis, expressions are derived that can be used to interpolate the repo rates…
Paul McCloud
arXiv · arXiv q-fin · 2017
You are a financial analyst. At the beginning of every week, you are able to rank every pair of stochastic processes starting from that week up to the horizon. Suppose that two processes are equal at the beginning of the week. Your ranking procedure is time consistent if the ranking does not change between this week and the next one. In this paper, we propose a minimalist definition of Time Consistency (TC) between t…
Henri Gérard, Michel de Lara, Jean-Philippe Chancelier
arXiv · arXiv q-fin · 2014
We consider the supOU stochastic volatility model which is able to exhibit long-range dependence. For this model we give conditions for the discounted stock price to be a martingale, calculate the characteristic function, give a strip where it is analytic and discuss the use of Fourier pricing techniques. Finally, we present a concrete specification with polynomially decaying autocorrelations and calibrate it to obse…
Robert Stelzer, Jovana Zavišin
arXiv · arXiv q-fin · 2010
We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still being highly analytically tractable. First we derive the characteristic function and give conditions that ensure its analyticity and absolute integrability in some open complex strip around zero. Therefore we can use Four…
Johannes Muhle-Karbe, Oliver Pfaffel, Robert Stelzer