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This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the…

Statistical Finance · Quantitative Finance 2015-02-04 Jozef Barunik , Tomas Krehlik , Lukas Vacha

We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…

Probability · Mathematics 2016-07-26 Viktor Bezborodov , Luca Di Persio , Yuliya Mishura

The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range…

Other Condensed Matter · Physics 2008-12-02 Sergei Fedotov , Abby Tan

The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is…

Computational Finance · Quantitative Finance 2014-08-06 Tetsuya Takaishi

In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or…

Computational Finance · Quantitative Finance 2015-09-14 Edgardo Brigatti , Felipe Macias , Max O. Souza , Jorge P. Zubelli

In this work, we give a generalized formulation of the Black-Scholes model. The novelty resides in considering the Black-Scholes model to be valid on 'average', but such that the pointwise option price dynamics depends on a measure…

Mathematical Finance · Quantitative Finance 2024-04-09 Nizar Riane , Claire David

Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general,…

Computation · Statistics 2016-08-12 Deborshee Sen , Ajay Jasra , Yan Zhou

We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the…

Physics and Society · Physics 2009-11-11 J. L. McCauley , G. H. Gunaratne , K. E. Bassler

This paper is concerned with portfolio selection for an investor with exponential, power, and logarithmic utility in multi-asset financial markets allowing jumps. We investigate the classical Merton's portfolio optimization problem in a…

Optimization and Control · Mathematics 2026-05-04 Sigui Brice Dro , Emmanuel Gnabeyeu

In a seminal paper in 1973, Black and Scholes argued how expected distributions of stock prices can be used to price options. Their model assumed a directed random motion for the returns and consequently a lognormal distribution of asset…

Computational Engineering, Finance, and Science · Computer Science 2009-11-07 Joseph L. McCauley , Gemunu H. Gunaratne

The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state…

Mathematical Finance · Quantitative Finance 2025-10-13 Nicola F. Zaugg , Lech A. Grzelak

This paper presents a discrete-time option pricing model that is rooted in Reinforcement Learning (RL), and more specifically in the famous Q-Learning method of RL. We construct a risk-adjusted Markov Decision Process for a discrete-time…

Computational Finance · Quantitative Finance 2019-09-04 Igor Halperin

We investigate a statistical-static hedging technique for pricing assets considered as single-step stochastic cash flows. The valuation is based on constructing in a canonical way a European style derivative on a benchmark security such…

Pricing of Securities · Quantitative Finance 2018-03-13 Jarno Talponen

Stochastic volatility models have existed in Option pricing theory ever since the crash of 1987 which violated the Black-Scholes model assumption of constant volatility. Heston model is one such stochastic volatility model that is widely…

Computational Finance · Quantitative Finance 2021-12-10 Kumar Yashaswi

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes…

Computational Finance · Quantitative Finance 2010-04-14 Masaaki Fukasawa

New simulation approaches to evaluating path-dependent options without matrix inversion issues nor Euler bias are evaluated. They employ three main contributions: Stochastic approximation replaces regression in the LSM algorithm; Explicit…

Pricing of Securities · Quantitative Finance 2018-04-13 Michael A. Kouritzin

A new method is proposed to obtain the risk neutral probability of share prices without stochastic calculus and price modeling, via an embedding of the price return modeling problem in Le Cam's statistical experiments framework.…

Pricing of Securities · Quantitative Finance 2014-11-19 Yannis G. Yatracos

This paper presents a novel way to predict options price for one day in advance, utilizing the method of Quasi-Reversibility for solving the Black-Scholes equation. The Black-Scholes equation solved forwards in time with Tikhonov…

Analysis of PDEs · Mathematics 2022-03-21 Mikhail V. Klibanov , Kirill V. Golubnichiy , Andrey V. Nikitin

This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with fixed delays in the drift and diffusion…

Probability · Mathematics 2008-12-02 Mercedes Arriojas , Yaozhong Hu , Salah-Eldin Mohammed , Gyula Pap

First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback.…

Physics and Society · Physics 2008-12-02 J. L. McCauley , G. H. Gunaratne , K. E. Bassler