Evolutionary Foundations of Equilibria in Irrational Markets by Guo Ying Luo

Author:Guo Ying Luo
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

5.4 Numerical Examples and Results

To see how the futures price moves over time in this market, a set of simulations is now conducted. For t = 1, 2, . . . , define θ1 t  = Pr(u s t  > 0. 10),  and The vector (θ1 t , θ2 t , θ3 t ) characterizes trader t’s probability distribution of his or her prediction error with respect to the fundamental value.

Consider a futures market with a random shock, ω s , where s ≥ 1, is a random draw from an interval according to a symmetric doubly truncated normal distribution where the density function is with parameter σ and B = 2. 999. Z ⋅is the unit normal probability density function and Φ( ⋅) is the corresponding cumulative distribution function.11 As σ goes up (down), the variation in random shock also goes up (down). Other detailed characteristics of the market are described by (1), (2), (3), and (4) in Appendix A.

First, with σ = 5. 0, 100 simulations are conducted and the market is followed from time period 1 to 3,000. The histogram in Fig. 5.3a shows that at time period 500, on average across 100 simulations, the percentages of time that | P s f  − Z s  | ≥ 0. 10 and are 40% and 16%, respectively. By time period 3, 000, on average across 100 simulations, the percentage of time that | P s f  − Z s  | ≥ 0. 10 has decreased to 28% whereas the percentages of time that has increased to 19%. That is, as time goes by there is a lower proportion of time that | P s f  − Z s  | is greater than 0. 10 and there is a higher proportion of time that is less than 0.025.

Fig. 5.3Histogram of | P s f  − Z s  | as a percentage of times: (a) ω t obeys a truncated normal distribution σ = 5, (b) ω t obeys a truncated normal distribution σ = 1. 5, and (c) No random shock to the economy

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