The Stochastic Balance Equation for the American Option Value Function and its Gradient

2021/02/25 by Malkhaz Shashiashvili, Shashiashvili, Malkhaz
Economics, Econometrics and Finance · #60H10 #65M06 #91B28 #FOS: Economics and business #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2102.12800

openalex publication_date 2021/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the paper we consider the problem of valuation and hedging of American options written on dividend-paying assets whose price dynamics follow the multidimensional diffusion model. We derive a stochastic balance equation for the American option value function and its gradient. We prove that the latter pair is the unique solution of the stochastic balance equation as a result of the uniqueness in the related adapted future-supremum problem.

Related

• Option prices in stochastic volatility models
• Viscosity Solutions and American Option Pricing in a Stochastic Volatility Model of the Ornstein-Uhlenbeck Type
• Properties of the American price function in the Heston-type models
• Reflected Backward Stochastic Differential Equations for a Finite State Markov Chain Model and Applications to American Options
• Probabilistic solution of the American options