Case Study on Modeling the Silver and Nasdaq Financial Time Series with Simulated Annealing

Abstract

This paper reports a case study on modeling the SPDR Silver Trust (SLV) and Nasdaq Composite Index timeseries by using a financial agent based system using simulated annealing. We show here how adding financial information to the modeling system can significantly improve the modeling results. The learning system LFABS, previously developed by the author, will be used as a testbed for the empirical evaluation of the proposed methodology on the two case studies.

A The Simple Financial Agent Based Simulator

Please note that the description of the LFABS system appearing in the Appendix has already been reported in our previous publications such as [16]. We will repeat here the description of LFABS’ architectures for improving the readability of the paper. Before proceeding, we would like to point out the two main assumptions that we made about the economic behavior of an individual. We hypothesize that each investment decision for each individual depends on two main components:

• (a) his/her propensity to take some risks today, by buying a financial asset, in exchange for a future uncertain reward, when selling the asset. Indeed any investor has to decide if it is good for her/him to buy, for instance, a Treasury Bond (very safe, but low return), a corporate obligation (not safe as a treasury bond, giving a discrete return), or a company share (no guarantee on the capital as the company may fail, but good return). The investment decision is made according to the investor’s risk/reward profile which we will model as a risk/reward propensity rate in the system.

• (b) the common and public consensus about the future behavior of the asset. Public knowledge about the economic outlook diffused by financial news, economic reports, etc. will influence the investment decision of every one operating in the market. If the economic outlook is forecast negative, on average people will tend to sell some of their assets. If the economic future looks positive, investors tend by more assets. In the paper, we call market sentiment, or just sentiment, the common perception of economy outlook and we will model it accordingly in our system.

Let’s move now to explaining the architecture of our system. We start by describing the basic component of our simulator: the FinancialAgent. The FinancialAgent implements the simple decision making process underlying the investment decision of buying, selling or holding an asset. The algorithm is:

Said in plain words, a Financial Agent will decide to buy some asset with probability P(X $<\,$BuyThreshold), it will hold to its assets with probability P(BuyThreshold < X < SellThreshold), and it will sell some of its assets with probability P(SellThreshold < X). As it can be seen in the algorithm, the probabilities are dependent on the current level of sentiment about the economy. In fact the probability to buy assets increases along with the sentiment, while the probability to sell assets decreases when the sentiment is raising and vice versa. Also the amount of assets to be bought or sold is set to 2% of the total assets of the investors. The value 2% has been chosen as it represents twice the average daily variation of the timeseries we have investigated. We verified empirically in earlier works [16] that it provides reasonable simulation results and has been kept constant since then. It might be changed in case the time series under investigation displays an average daily variation higher than 1%.

Given FinancialAgent, the algorithm for simulating a simulation of the entire financial market can be obtained by creating several FinancialAgents, each one with its own status in terms of own assets, invested assets and risk/reward propensity, and then performing a sequence of investment rounds where each agent decides if buying, selling, or holding taking into account the current Sentiment value. At the end of each round, it is possible to measure the percentage of invested assets, this percentage can then be used as an estimated for one data point of the target time serie. If the simulation is repeated for n rounds, the output will represent an estimate for an n-length time serie. After explaining what the financial simulator S-FABS does, here is its algorithm:

S-FABS take as input the vector of risk/rewards propensity rates for each Financial Agent. During each round, the risk/rewards propensity rates are used in combination with the current value of the economic sentiment by each Financial Agent.