ABSTRACT:
Financial markets are among the most complex systems in reality and many phenomena observed in real markets are still poorly understood. Traditional analytical approaches in economics to study aggregative phenomena either are purely macroscopic, or rely on top-down construction based on a number of unrealistic assumptions mainly for the sake of analytical tractability. In contrast, microsimulation (MS) explores complex dynamics from the bottom up. It enables us to relax unrealistic assumptions and study complex systems which do not yield to analytic treatment. In addition, it is appropriate for studying large scale markets which are difficult to investigate experimentally. Microsimulation has shown great potential for more accurately understanding the mechanisms of complex economic systems, and will play an increasingly important role in risk management, regulation, and policy making.
The general motivation of my PhD research is to apply MS for understanding the complex dynamics of financial markets characterized by some stylized features. In the research, I focused on two of the most active markets, namely stock markets and options markets.
Here I take the volatility smile phenomenon observed in options markets as an example. It is intrinsically related to the well-known and widely-used Black-Scholes (BS) model for pricing options. The only unobservable parameter of this Nobel Prize winning model is the volatility of the underlying asset which by nature should be independent of the strike of the option contract. However, the volatilities required to match option prices quoted in real markets, i.e., implied volatilities (IV), exhibit a remarkable curvature against strikes and may change strongly over time. Understanding the origin of the volatility smile has eluded the financial world for more than two decades.
We have developed a MS model for explaining the smile. It focuses on those traders who are highly active and in majority in real markets, namely speculators and arbitrageurs. The traders in the model apply the most typical speculative or arbitraging strategies and the option prices are determined by supply and demand. Our results agree with empirical studies in respect to the shape and dynamic properties of the smile, and suggest that this phenomenon is a natural consequence of traders’ heterogeneous behavior and expectations about the future. Specifically, the entire (implied volatility)-(strike price) phase space becomes a basin of attraction from which the volatility smile emerges as a stochastic attractor, as a result of the (indirect) competition between traders with heterogeneous interests. These findings pave the way for a new generation of risk management tools which implicitly incorporate such collective human behavior.
SCS colloquium: N. Javaheri
De rekenregels van de natuur
