Multi-asset Black-Scholes model as a variable second class constrained dynamical system

DOI10.1016/j.physa.2016.03.063zbMath1400.91582OpenAlexW2320020638MaRDI QIDQ1619629

R. Smith

Publication date: 13 November 2018

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physa.2016.03.063

zbMATH Keywords

option pricingpropagatorssingular Lagrangian systemsDirac's methodconstrained Hamiltonian path integralsmultiasset Black-Scholes equation

Mathematics Subject Classification ID

Applications of statistical and quantum mechanics to economics (econophysics) (91B80) Financial applications of other theories (91G80) Derivative securities (option pricing, hedging, etc.) (91G20) Path integrals in quantum mechanics (81S40)

Related Items (5)

Robust and accurate construction of the local volatility surface using the Black-Scholes equation ⋮ Dynamic optimization and its relation to classical and quantum constrained systems ⋮ The quantum dark side of the optimal control theory ⋮ Endogenous stochastic arbitrage bubbles and the Black-Scholes model ⋮ Optimal non-uniform finite difference grids for the Black-Scholes equations

Cites Work

• The Pricing of Options and Corporate Liabilities
• Penalty methods for the numerical solution of American multi-asset option problems
• The path integral approach to financial modeling and options pricing
• Option pricing, stochastic volatility, singular dynamics and constrained path integrals
• Stochastic volatility models at \(\rho = \pm 1\) as second class constrained Hamiltonian systems
• A Black-Scholes Schrödinger option price: `bit' versus `qubit'
• New analytical option pricing models with Weyl–Titchmarsh theory
• Classical Algebraic Geometry
• Generalized Hamiltonian dynamics
• DESSINS D'ENFANTS AND HYPERSURFACES WITH MANY $A_j$-SINGULARITIES
• A PATH INTEGRAL APPROACH TO DERIVATIVE SECURITY PRICING I: FORMALISM AND ANALYTICAL RESULTS
• Financial Modelling with Jump Processes
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Arbitrage Theory in Continuous Time
• A discussion on embedding the Black-Scholes option pricing model in a quantum physics setting
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