Elsevier

Applied Soft Computing

Volume 10, Issue 1, January 2010, Pages 74-78
Applied Soft Computing

Using a non-uniform self-selective coder for option pricing

https://doi.org/10.1016/j.asoc.2009.06.003Get rights and content

Abstract

We propose a non-uniform self-selective coder for option pricing. The system has one switch and four subsystems, which fits the need of advanced financial analysis. Using the system, we can obtain the following important information: (1) the most powerful explanatory variable, (2) the length of most representative sample period, and (3) the optimal updated model. In addition, with the non-uniform self-selective coder, the mean absolute errors have been decreased significantly.

Introduction

In the early 1970s, Black and Scholes made a major breakthrough in the pricing of stock options, and this has had a huge influence on the way in which market participants price and hedge options. The key assumptions underlying the Black–Scholes option pricing model (OPM) are: (1) stock prices follow a random walk. (2) There are no riskless arbitrage opportunities. (3) Investors can borrow or lend at the same risk-free rate of interest.

However, empirical results show that the assumed normal distribution of the logarithmic stock return cannot be supported. In addition, the stock price volatility may change randomly in practice. Finally, the estimated bias may increase or decrease as the time to maturity of the option decreases.

Neural networks outperform the conventional Black–Scholes model when using both historical volatility and implied volatility [4]. In online mode during the process of control, some of the new data reinforce and confirm the information contained in the previous data. Other data, however, bring new information, which could indicate a change in operating conditions, development of a fault or simply a more significant change in the dynamic of the process. This type of data may posses enough new information to form a new rule or to modify an existing one. The judgment of the information potential and importance of the data is based on adaptive neural fuzzy rules [10], [11]. In this paper, we propose a non-uniform coder in the adaptive neural fuzzy system for option pricing.

Section snippets

Estimation errors of the OPM

Empirically, there are significant estimation errors that come from the Black–Scholes related option pricing model, the derived put-call parity, and the inverse implied volatility (to obtain the implied volatility from the Black–Scholes model). In general, the estimation errors are significant and enormous. In addition, the estimation errors are not diminished, whether for a just-in-the-money option, a just-out-of-the-money option, or a nearby option.

The only European option listed in Taiwan

ANFIS

Grid computing technologies provide advanced computational capabilities in recent years. The dynamic data-driven systems entail the ability to incorporate dynamically updated data into an executing application simulation. Such dynamic data inputs can be acquired in real-time workshop [7], [15], [16], [17]. In addition, fuzzy logic controllers of the so-called Takagi–Sugeno type have gained impetus recently for applications to complex systems [2], [5], [6], [12], [14].

Information system now

Simulink

Simulink is a software package in MATLAB for modeling, simulating, and analyzing dynamic systems. It supports linear and nonlinear systems, modeled in continuous time, sampled time, or a hybrid of the two. Systems can be multi-rate, i.e., have different parts that are sampled or updated at different rates. The non-uniform coder can therefore be implemented in the system.

Simulink can be used to explore the behavior of a wide range of real-world dynamic systems. Simulating a dynamic system is a

Problems of chaotic data

It is well known that stability and convergence are prerequisites for designing neural networks. A dynamic system frequently causes oscillation, divergence, or instability in neural networks. However, time-varying delays are very common in time-series data.

Chaos theory instead describes the behavior of certain nonlinear dynamical systems that are highly sensitive to initial conditions. As a result, this sensitivity manifests itself as an exponential growth of perturbations in the initial

Conclusion

The modified ANFIS can learn online information. This learning method works similarly to that of neural networks. From the modified ANFIS, we can obtain the following important information: (1) the most powerful explanatory variable, (2) the length of most representative sample period, and (3) the optimal updated model.

Simulating the system, we find that the most powerful explanatory variable and the optimal sampling size are changed over time. On the contrary, the optimal model is always the

Acknowledgement

The author gratefully acknowledges the constructive comments of anonymous referees, which have been very helpful in improving the paper.

References (17)

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    The crisp weighted possibilistic mean normal jump-diffusion model was obtained as well. Yen [23] gave a non-uniform coder in the adaptive neural fuzzy system for option pricing. Zhang et al. [24] proposed the fuzzy pricing formula of American options under the assumption that the price of stock, discount rate, the volatility, and interest rate are all fuzzy numbers.

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