ANALYSIS OF AN OPTION MARKET DYNAMICS BASED ON A HETEROGENEOUS AGENT MODEL

• Author: Saki Kawakubo,Shinobu Yoshimura,Kiyoshi Izumi
• Date: 01 April 2014
• Published date: 01 April 2014
• DOI: http://doi.org/10.1002/isaf.1353

ANALYSIS OF AN OPTION MARKET DYNAMICS BASED ON A

HETEROGENEOUS AGENT MODEL

SAKI KAWAKUBO,

a

*KIYOSHI IZUMI

a,b

AND SHINOBU YOSHIMURA

a

a

School of Engineering, The University of Tokyo,Bunkyo-ku, Tokyo, Japan

b

CREST, JST, Chiyoda-ku, Tokyo, Japan

SUMMARY

We propose a two-market model in which an option market and its underlying market interact. Many artificial

markets representing stock markets have been developed, and these models have been actively used to investigate

the effects of market rules. However, no artificial market model for derivatives has been intensively studied, even

though derivative markets are increasingly important. We tested stylized facts that can be observed in an option

market and our model can replicate fat-tailed distributions, positive skew of the return and positive autocorrelation

of the square of return of implied volatility. We found that the speed of volatility mean reversion for fundamental-

ists and the existence of chartists are important factors for replicating the positive skew of an option market. The

value of fat-tailed distributions and positive skewnessof the return getcloser to the real value by coupling an option

market and an underlying market. Copyright © 2014 John Wiley & Sons, Ltd.

Keywords: option market; multi agent model; artificial market; financial market simulation

1. INTRODUCTION

Technologies applied in current financial markets and the environments within which these markets

operate are changing drastically. High-frequency trading, trans-border transactions and algorithmic

trading can be seen in almost any financial market. The relationships among markets have become

more complex and elusive, and the dynamics of markets have become more difficult to understand.

To make the complexity in financial markets better understood, many engineering and mathematical

models have been studied.

Computer simulation using heterogeneous agents is an engineered approach. Several influential

artificial stock markets have been developed, but most of these targeted a single stock market. These

artificial markets have been academically useful for finding reasons for market anomalies and looking

at the effect of regulations on stock markets. NASDAQ, a major US stock market, applied a multi-agent

simulation when a change in the market tick size was being considered (Darley & Outkin, 2007). As the

application of artificial markets becomes more prevalent, a more realistic model is needed as an

effective solution for verifying the efficacy of financial regulations.

In contrast to stock markets, no artificial derivatives market has been intensively studied, even though

the trading volume of derivative markets has surged because of the increased use of financial engineer-

ing and the important effects of derivative markets. Derivative markets are generally grouped into two

categories: futures markets and options markets. Many investors trade derivative products as a risk

* Correspondence to: Saki Kawakubo, School of Engineering, The University of Tokyo, Bunkyo-ku, Tokyo, Japan. E-mail:

d2012s.kawakubo@socsim.org

Copyright © 2014 John Wiley & Sons, Ltd.

INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE AND MANAGEMENT

Intell. Sys. Acc. Fin. Mgmt. 21, 105–128 (2014)

Published online 7 May 2014 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/isaf.1353

management tool to offset price changes of their underlying assets. Derivativestrading also serves other

purposes. The leverage effects of derivativeprodu cts allow funds to trade more efficiently. In addition, a

derivative market and its underlying market can be linked through hedge trading and arbitrage trading,

and these types of trading offer new sources of return for investors.

We developed an artificial option market using heterogeneous agents and have investigated the

statistical features of the model. We selected an option market because it required a unique approach

since the pricing mechanism of an option is totally different from that of a stock or a futures contract.

While most financial products trade with the price level rising or falling according to supply and

demand, option values are determined by multiple factors, such as implied volatility (IV), time to

maturity and the difference between the strike price and the underlying asset’s price. Moreover, there

are several statistical features that differ from those of other financial markets.

Creating an artificial option market requires a whole new approach, and such a model can provide a

useful platform for testing financial regulations being considered for application to derivative markets.

The existing artificial markets have targeted a single market and investigated some anomalies,

mechanism for bubbles and crashes, and impacts of regulations (Brock & Hommes, 1998). In an actual

environment the financial markets interact with each other, and such interaction may trigger anomalies,

bubbles and crashes. Our simulation model deals with an asset and its derivative markets simulta-

neously and sets out to make the interaction between markets clear. However, current artificial m arket

models do not pay much attention to modelling of the derivative markets. So, we work on establishing

the basic model for an artificial market for derivatives.

In the latter part of this section we discuss the background to this work. Previous studies on artificial

option markets are introduced, and we look at the stylized facts of option markets and a volatility index

in Section 2. Section 3 explains the details of our model. We did several experiments to see how our

model works and which parameters are responsible for replicating the stylized facts in Section 4. In

Section 5 we summarize this study and our findings.

1.1. Multi-agent Model for an Option Market

Option contracts are usually priced based on the Black–Scholes model. In this model, the price is

derived by a partial differential equation under a no-arbitrage condition and the assumption of a normal

distribution for the return of an underlying asset. However, it is well known that the return of an under-

lying asset does not follow the normal distribution; instead, the distribution is generally fat tailed. In

fact, several important features are not considered under the Black–Scholes model’s assumptions.

The most noticeable feature is about the characteristics of IV. IV is the future volatility that investors

expect. It is usually calculated from a market option price by using the Black–Scholes model. IV is

considered as a single value over both strike prices and maturities under the Black–Scholes model’s

assumption, but it is widely known that IV is different among each strike price and maturity.

Extensional models have tried to replicate these stylized facts of an option market more accurately.

These models are constructed on the basis of stochastic differential equations and incorporate a special

function to make a theoretical price close to the actual market price. Unfortunately, these models fail to

explain what causes the anomalies observed in option markets. A multi-agent model can identify micro

factors, such as the impact of market regulation or investor behaviour, and this information will be

useful for creating a more effective market. We have examined a mechanism that produces the stylized

facts of an option market by developing an artificial option market with a multi-agent model.

As mentioned, most artificial markets focus on a single stock market. However, a few artificial

market models for an option market have been reported. Ecca et al. (2008) developed an artificial

106 S. KAWAKUBO ET AL.

Copyright © 2014 John Wiley & Sons, Ltd. Intell. Sys. Acc. Fin. Mgmt., 21, 105–128 (2014)

DOI: 10.1002/isaf