A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Researchers develop Malliavin calculus for signatures, simplifying option Greeks computation.
Enhancing the Black-Scholes model with Lévy processes and Malliavin calculus
The extremely useful method of Malliavin calculus has not yet gained adequate popularity because of the complicated analytic apparatus of this method. The author attempts here to propose a simplified algebraic formalism similar to Malliavin calculus, but based on the notion of creation-annihilation operators instead of…
Develops a method to approximate convexity adjustments for interest rate products.
This study introduces computation of option sensitivities (Greeks) using the Malliavin calculus under the assumption that the underlying asset and interest rate both evolve from a stochastic volatility model and a stochastic interest rate model, respectively. Therefore, it integrates the recent developments in the Mall…
Study short-term behavior of up-and-in barrier options using Malliavin calculus.
Optimizes reinsurance and investment strategies to minimize ruin probability.
This paper uses Malliavin calculus to price and compute delta of financial derivatives in jump-diffusion models.
This paper is devoted to pricing American options using Monte Carlo and the Malliavin calculus. Unlike the majority of articles related to this topic, in this work we will not use localization fonctions to reduce the variance. Our method is based on expressing the conditional expectation E[f(St)/Ss] using the Malliavin…
Paper develops methods for solving complex stochastic equations using Malliavin calculus.
Study examines how risk tolerance impacts long-term investment returns.
Volatility roughness studied using fractional noise-driven models.
An explicit martingale representation for random variables described as a functional of a Levy process will be given. The Clark-Ocone theorem shows that integrands appeared in a martingale representation are given by conditional expectations of Malliavin derivatives. Our goal is to extend it to random variables which a…
In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later we study the case of Asian options where clos…
Researchers compute Greeks for rough Volterra SV models using Malliavin calculus.
In a 2006 article (\cite{A1}), Allouba gave his quadratic covariation differentiation theory for Itô's integral calculus. He defined the derivative of a semimartingale with respect to a Brownian motion as the time derivative of their quadratic covariation and a generalization thereof. He then obtained a systematic diff…
The paper provides an efficient method to price path-dependent derivatives using multiscale stochastic volatility models.
Study large deviations for hypoelliptic diffusion on sub-Riemannian manifolds.
New approach to score function in diffusion models using Malliavin calculus.
We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin …
New financial model with sandwiched volatility for option pricing.
Study on skew and curvature of implied and local volatilities using Malliavin calculus.
Myopic optimization outperforms reinforcement learning in portfolio management, leading to lower returns and higher risks.
Paper proves SVV model reproduces power-law skew in implied volatilities.
Abstract: Generalizes SGMs to infinite-dimensional Hilbertian setting.
Researchers develop explicit approximations for European put options in stochastic volatility models.
New method modifies diffusions for singular rewards.
The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The form of the density function of the random variable, which expresses the average of…
Dupire's functional Itô calculus provides an alternative approach to the classical Malliavin calculus for the computation of sensitivities, also called Greeks, of path-dependent derivatives prices. In this paper, we introduce a measure of path-dependence of functionals within the functional Itô calculus framework. Name…
We consider a standard optimal investment problem in a complete financial market driven by a Wiener process and derive an explicit formula for the optimal portfolio process in terms of the vertical derivative from functional It^o calculus. An advantage with this approach compared to the Malliavin calculus approach is t…
The paper provides formulas for volatility in various models, including rough volatility.
Paper introduces MSPD for multivariate risk processes with dependencies.
In the framework of risk management, for the study of the sensitivity of pricing and hedging in stochastic financial models to changes of parameters and to perturbations of the stock prices, we propose an error calculus which is an extension of the Malliavin calculus based on Dirichlet forms. Although useful also in ph…
This paper extends Heston model to fractional Brownian motion for option pricing.
In this paper we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process, by using the Malliavin calculus. In analogy with the celebrated Black-Scholes formula, we aim at expressing the expected cash flow in terms of a building block. The former is r…
We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function.
Researchers tackle insider trading in incomplete markets using a discrete-time jump process approach.
Using Malliavin Calculus techniques, we derive closed-form expressions for the at-the-money behaviour of the forward implied volatility, its skew and its curvature, in general Markovian stochastic volatility models with continuous paths.
Study on implied volatility of Asian options with stochastic volatility.
The paper explores anticipative binary information in financial markets using Brownian motion and Poisson processes.
The paper analyzes implied volatility for European and Asian options under stochastic volatility Bachelier model.
We develop a technique based on Malliavin-Bismut calculus ideas, for asymptotic expansion of dual control problems arising in connection with exponential indifference valuation of claims, and with minimisation of relative entropy, in incomplete markets. The problems involve optimisation of a functional of Brownian path…
We obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for Levy processes, Arai and Suzuki (2015) obtained a formula for locally risk-minimiz…
We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to …
Study on short-term behavior of ATM-IV for jump-diffusion model.
We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in infinitely many equivalent martingale measures. We find the set equivalent marting…
We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and "payoff" functions depending on the process at multiple future times. In the spirit of Fournie et al [13] and Davis and Johansson [9] this can improve Monte Carlo numerics for stochastic volatility models with jumps. To this end one needs so…
Study on implied volatility of Inverse options under stochastic volatility models.