Abstract
Option pricing using artificial neural networks (ANN) model while relaxing the assumption of constant volatility still remains a challenge. The conventional practice for pure ANN models has been to either model volatility using the very ANN model and have the model output fed as an input to the ANN option pricing model, or to make allowances for a large number of lags directly as inputs to the option pricing model with the belief that the ability of ANN to incorporate flexibility and redundancy creates a more robust model. This has been done in spite of a well-known fact-that financial time series data harbors a set of characteristics such as volatility clustering, leptokurtosis and leverage effects-features that ANNs in their pure forms have proved inadequate in capturing. Consequently, this study sought to follow the conventional methods employed by other studies and developed two pure ANN option pricing models-one with constant volatility and the other while violating the assumption of constant volatility with an aim of establishing whether significant differences exist in the outputs of the two models. The intraday data for the AAPL stock option for the period between December 2016 and March 2017 with 56,238 data points was used in validating the developed models. Results indicate that the ANN model (with varying volatility) makes better predictions than the model with constant volatility. However, the difference between the performance of the two models is not significant at 0.05 level of significance.
Highlights
For the past two decades, the Black-Scholes Model (BSM) has continuously received considerable attention especially in underlying probability attributes of an European call option on a non-dividend stock (Al Saedi and Tularam, 2018) and has been identified as the basic building block of the financial derivatives theory (Wilmott et al, 1995)
Time-dependent parameters of the Black-Scholes PDE (Rodrigo and Mamon, 2006), use of the Adomain approximate decomposition technique (Bohner and Zheng, 2009), application of the Projected Differential Transformation Method (PDTM), a modification of the Differential Transformation Method (DTM) on the Black-Scholes Equation (BSE) for European option valuation (Edeki et al, 2015) and the use of Laplace transform to provide a solution to the Black-Scholes terminal value (Shin and Kim, 2016), all as reviewed in detail by Al Saedi and Tularam (2018)
Since our objective in this subsection is to price under the no arbitrage assumptions, with constant interest rate and constant volatility, the model inputs consists of time to maturity and moneyness, λ, which is the ratio of the strike price to the underlying asset price defined by: the transformation: X λ=
Summary
For the past two decades, the Black-Scholes Model (BSM) has continuously received considerable attention especially in underlying probability attributes of an European call option on a non-dividend stock (Al Saedi and Tularam, 2018) and has been identified as the basic building block of the financial derivatives theory (Wilmott et al, 1995). The advances made on the analytical solutions include but are not limited to: the use of the generalization technique in which parabolic partial differential equations were reduced to canonical form (Harper, 1994); the finitedifference methods to provide the exact solution of the. A detailed review on the use of these techniques can be found on Al Saedi and Tularam (2018)
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