Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes. Issue 9 (1st September 2016)

• Record Type: Journal Article
• Authors: Zeng, Pingping; Kwok, Yue Kuen
• Is Part Of: Quantitative finance. Volume 16:Issue 9(2016)
• Page Start: 1375
• Page End: 1391
• Publication Date: 2016-09-01
• Subjects: Time-changed Lévy processes -- Arithmetic Asian options -- Conditioning variable approach -- Partially exact and bounded approximations; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2016.1149610
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : We derive efficient and accurate analytical pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes. By extending the conditioning variable approach, we derive the lower bound on the Asian option price and construct an upper bound based on the sharp lower bound. We also consider the general partially exact and bounded (PEB) approximations, which include the sharp lower bound and partially conditional moment matching approximation as special cases. The PEB approximations are known to lie between a sharp lower bound and an upper bound. Our numerical tests show that the PEB approximations to discrete arithmetic Asian option prices can produce highly accurate approximations when compared to other approximation methods. Our proposed approximation methods can be readily applied to pricing Asian options under most common types of underlying asset price processes, like the Heston stochastic volatility model nested in the class of time-changed Lévy processes with the leverage effect.