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Numerical studies on approximate option prices

Authors
Yoon, JeongyoenSeung, JisuSong, Seongjoo
Issue Date
4월-2017
Publisher
KOREAN STATISTICAL SOC
Keywords
asymptotic option price; Gram-Charlier expansion; Heston model; normal inverse gaussian process
Citation
KOREAN JOURNAL OF APPLIED STATISTICS, v.30, no.2, pp.243 - 257
Indexed
KCI
Journal Title
KOREAN JOURNAL OF APPLIED STATISTICS
Volume
30
Number
2
Start Page
243
End Page
257
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/83947
DOI
10.5351/KJAS.2017.30.2.243
ISSN
1225-066X
Abstract
In this paper, we compare several methods to approximate option prices: Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method using normal inverse gaussian (NIG) distribution, and an asymptotic method using nonlinear regression. We used two different types of approximation. The first (called the RNM method) approximates the risk neutral probability density function of the log return of the underlying asset and computes the option price. The second (called the OPTIM method) finds the approximate option pricing formula and then estimates parameters to compute the option price. For simulation experiments, we generated underlying asset data from the Heston model and NIG model, a well-known stochastic volatility model and a well-known Levy model, respectively. We also applied the above approximating methods to the KOSPI200 call option price as a real data application. We then found that the OPTIM method shows better performance on average than the RNM method. Among the OPTIM, A type Gram-Charlier expansion and the asymptotic method that uses nonlinear regression showed relatively better performance; in addition, among RNM, the method of using NIG distribution was relatively better than others.
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Song, Seongjoo
정경대학 (통계학과)
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