Pricing American options with stochastic volatility and small nonlinear price impact: A PDE approach

Dong Yan, Sha Lin, Zhihao Hu and Ben-Zhang Yang

Chaos, Solitons & Fractals, 2022, vol. 163, issue C

Abstract: In this paper, transaction costs as small nonlinear price impact are introduced into American option pricing under the Heston stochastic volatility model, forming a gap between option prices of the holder and writer. Through the use of a dynamic hedging strategy together with a known option independent of transaction costs, we derive two different nonlinear pricing partial differential equation systems for the holder and writer, respectively. A numerical algorithm is designed to solve the systems so that American option prices as well as the optimal exercise boundary can be simultaneously obtained. Examples are presented to illustrate the effect of transaction costs on both option prices and optimal exercise prices.

Keywords: American option pricing; Nonlinear partial differential equations; Stochastic volatility; Nonlinear price impact (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007718

DOI: 10.1016/j.chaos.2022.112581

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