An Analytical Approximation Formula for Barrier Option Prices Under the Heston Model

Xin-Jiang He and Sha Lin ()
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Xin-Jiang He: Zhejiang University of Technology
Sha Lin: Zhejiang Gongshang University

Computational Economics, 2022, vol. 60, issue 4, No 9, 1413-1425

Abstract: Abstract In this paper, we investigate the pricing problem of barrier options under the Heston model. We innovatively develop a two-step solution process and present an analytical approximation formula of high efficiency and accuracy. In specific, upon assuming that all the future information of the volatility is known at the current time, the Heston model becomes a time-dependent Black-Scholes model, under which an analytical approximation for barrier option price is presented. The target barrier option price is essentially the expectation of the obtained conditional price with respect to the volatility, working out of which leads to an approximation involving a Fourier cosines series. Finally, the results of numerical experiments demonstrate that our formula has the potential to be applied in practice.

Keywords: Barrier options; Heston model; Analytical approximation; Fourier cosine series; Accuracy (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10614-021-10186-7

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