Alternative Methods to Derive Option Pricing Models: Review and Comparison

Cheng Few Lee, Yibing Chen and John Lee

Chapter 102 in Handbook of Financial Econometrics, Mathematics, Statistics, and Machine Learning:(In 4 Volumes), 2020, pp 3573-3617 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The main purposes of this paper are: (i) to review three alternative methods for deriving option pricing models (OPM), (ii) to discuss the relationship between binomial OPM and Black–Scholes OPM, (iii) to compare the Cox et al. method and the Rendleman and Bartter method for deriving Black–Scholes OPM, (iv) to discuss lognormal distribution method to derive the Black–Scholes OPM, and (v) to show how the Black–Scholes model can be derived by stochastic calculus. This paper shows that the main methodologies used to derive the Black–Scholes model are: binomial distribution, lognormal distribution, and differential and integral calculus. If we assume risk neutrality, then we do not need stochastic calculus to derive the Black–Scholes model. However, the stochastic calculus approach for deriving the Black–Scholes model is still presented in Section 102.6. In sum, this paper can help statisticians and mathematicians understand how alternative methods can be used to derive the Black–Scholes option model.

Keywords: Financial Econometrics; Financial Mathematics; Financial Statistics; Financial Technology; Machine Learning; Covariance Regression; Cluster Effect; Option Bound; Dynamic Capital Budgeting; Big Data (search for similar items in EconPapers)
JEL-codes: C01 C1 G32 (search for similar items in EconPapers)
Date: 2020
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Journal Article: Alternative methods to derive option pricing models: review and comparison (2016)
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