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The Journal of Derivatives

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Article

American Option Pricing: An Accelerated Lattice Model with Intelligent Lattice Search

Qianru Shang and Brian Byrne
The Journal of Derivatives Fall 2019, jod.2019.1.080; DOI: https://doi.org/10.3905/jod.2019.1.080
Qianru Shang
is a PhD candidate in finance at the College of Business of Technological University Dublin, in Dublin, Ireland
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Brian Byrne
is a lecturer in finance and MSc Finance co-ordinator at the College of Business of Technological University Dublin, in Dublin, Ireland
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Abstract

We introduce to the literature an intelligent lattice search algorithm to efficiently locate the optimal exercise boundary for American options. Lattice models can be accelerated by incorporating intelligent lattice search, truncation, and dynamic memory. We reduce computational runtime from over 18 minutes down to less than 3 seconds to estimate a 15,000-step binomial tree where the results obtained are consistent with a widely acclaimed literature. Delta and Implied Volatility can also be accelerated relative to standard models. Lattice estimation, in general, is considered to be slow and not practical for valuing large books of options or for promptly rebalancing a risk neutral portfolio. Our technique transforms standard binomial trees and renders them to be at least on par with commonly used analytical formulae. More importantly, intelligent lattice search can be tweaked to reach varying levels of accuracy with different step size, while conventional analytical formulae are less flexible.

TOPICS: Options, derivatives

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The Journal of Derivatives: 29 (5)
The Journal of Derivatives
Vol. 29, Issue 5
Summer 2022
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American Option Pricing: An Accelerated Lattice Model with Intelligent Lattice Search
Qianru Shang, Brian Byrne
The Journal of Derivatives Jul 2019, jod.2019.1.080; DOI: 10.3905/jod.2019.1.080

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American Option Pricing: An Accelerated Lattice Model with Intelligent Lattice Search
Qianru Shang, Brian Byrne
The Journal of Derivatives Jul 2019, jod.2019.1.080; DOI: 10.3905/jod.2019.1.080
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  • Article
    • Abstract
    • EXTENDING KIM-BYUN-CURRAN: THE OPTIMAL EXERCISE BOUNDARY ADAPTED FOR UNRESTRICTED CONTINUOUS DIVIDENDS
    • TWO ACCELERATION TECHNOLOGIES: TRUNCATION AND DYNAMIC MEMORY
    • THE EFFICIENT PRICING PROCESS OF AN ACCELERATED CRR MODEL: APPLYING INTELLIGENT LATTICE SEARCH ALGORITHM, TRUNCATION, AND DYNAMIC MEMORY
    • NUMERICAL RESULTS
    • CONCLUSION
    • ADDITIONAL READING
    • ENDNOTES
    • REFERENCES
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