Analytic approach to solve a degenerate parabolic PDE for the Heston model

DOI10.1002/mma.4363zbMath1370.35184arXiv1406.2292OpenAlexW2964344960MaRDI QIDQ5348435

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Publication date: 15 August 2017

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.2292

zbMATH Keywords

semigroup of operatorsweighted Sobolev spacesvariational formulationmathematical financeHeston modeldegenerate parabolic PDEstochastic volatility processeuropean option

Mathematics Subject Classification ID

Variational inequalities (49J40) One-parameter semigroups and linear evolution equations (47D06) Degenerate parabolic equations (35K65) Diffusion processes (60J60)

Related Items (6)

Weighted multipolar Hardy inequalities and evolution problems with Kolmogorov operators perturbed by singular potentials ⋮ A class of weighted Hardy inequalities and applications to evolution problems ⋮ Computational technique for simulating variable-order fractional Heston model with application in US stock market ⋮ A class of weighted Hardy type inequalities in \(\mathbb{R}^N\) ⋮ A semigroup approach to generalized Black-Scholes type equations in incomplete markets ⋮ Local and non-local improved Hardy inequalities with weights

Uses Software

• Matlab

Cites Work

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• The Pricing of Options and Corporate Liabilities
• A Theory of the Term Structure of Interest Rates
• EFFICIENT, ALMOST EXACT SIMULATION OF THE HESTON STOCHASTIC VOLATILITY MODEL
• Variational Analysis for the Black and Scholes Equation with Stochastic Volatility
• A partial differential equation connected to option pricing with stochastic volatility: Regularity results and discretization
• The semigroup governing the generalized Cox-Ingersoll-Ross equation

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