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C1,α  regularity for degenerate parabolic equations arising from the Heston model
Journal article   Open access   Peer reviewed

C1,α regularity for degenerate parabolic equations arising from the Heston model

Lihe Wang and Yaoyuan Zhang
Communications on pure and applied analysis, Vol.22(12), pp.3430-3460
2023
DOI: 10.3934/cpaa.2023122
url
https://doi.org/10.3934/cpaa.2023122View
Published (Version of record) Open Access

Abstract

This paper addresses a class of parabolic equations with boundary degeneracy associated with the Heston stochastic volatility process, a well-known degenerate mean-reverting diffusion process in mathematical finance. Solutions to our equations correspond to the pricing problem for perpetual timer options, which can be regarded as European options with random expiration time. After establishing the necessary maximum principles and the Harnack inequality, we prove local regularity up to the degenerate boundary using the dilation technique and the truncation iteration method. This result holds significant importance for degenerate parabolic equations involving the Heston operator and has practical applications in asset pricing problems.

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