Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes

In this paper we develop a constructive approach to studying continuously and discretely sampled functionals of Lévy processes. Estimates for the rate of convergence of the discretely sampled functionals to the continuously sampled functionals are derived, reducing the study of the latter to that of the former. Laguerre reduction series for the discretely sampled functionals are developed, reducing their study to that of the moment generating function of the pertinent Lévy processes and to that of the moments of these processes in particular. The results are applied to questions of contingent claim valuation, such as the explicit valuation of Asian options, and illustrated in the case of generalized inverse Gaussian Lévy processes.

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Comment: “On Approximating Deep in-the-money Asian Options Under Exponential Lévy Processes”

Journal of Futures Markets ◽

10.1002/fut.21733 ◽

2015 ◽

Vol 35 (12) ◽

pp. 1220-1221

Author(s):

Xianming Sun ◽

Dorien Haesen ◽

Michèle Vanmaele

Keyword(s):

Lévy Processes ◽

Levy Processes ◽

Asian Options

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Continuous-time methods in the study of discretely sampled functionals of Lévy processes. I. The positive process case

Advances in Applied Probability ◽

10.1017/s0001867800001683 ◽

2007 ◽

Vol 39 (01) ◽

pp. 245-270

Author(s):

Michael Schröder

Keyword(s):

Lévy Processes ◽

Generalized Inverse ◽

Moment Generating Function ◽

Levy Processes ◽

Asian Options ◽

Inverse Gaussian ◽

Contingent Claim Valuation ◽

Reduction Series ◽

Generalized Inverse Gaussian ◽

The Moment

In this paper we develop a constructive approach to studying continuously and discretely sampled functionals of Lévy processes. Estimates for the rate of convergence of the discretely sampled functionals to the continuously sampled functionals are derived, reducing the study of the latter to that of the former. Laguerre reduction series for the discretely sampled functionals are developed, reducing their study to that of the moment generating function of the pertinent Lévy processes and to that of the moments of these processes in particular. The results are applied to questions of contingent claim valuation, such as the explicit valuation of Asian options, and illustrated in the case of generalized inverse Gaussian Lévy processes.

Download Full-text