Improved Pricing on the Stock Market with Trading Agents

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would mean that we would be looking at a stable distribution of values, thus making iteasier to harness the subagent. Except for a few stray values, most values lie between–0.10 and 0.10, omitting the unit, as it has no bearing.Having obtained this result, I proceeded to test for all pairs of values ofthresholds of purchase and thresholds of sale, spanning the interval between –0.15 and0.15 (I chose to have an extra margin of 0.05) with an interval of 0.01 in betweenvalues. The outcome of these tests can be seen in Chart 2 and Chart 3 (next page). Ineach case the subagent was given an initial amount of 10,000 Swedish crowns (SEK).I made the rather simplifying assumption that the total cost of transaction would be0.05 per cent of the absolute worth of the stock traded, for both purchase and sale. Iopted for this low cost for a few reasons. Firstly, the Internet based broker Avanza(www.avanza.se) offers a brokerage of 0.12 per cent. That should set an upperboundary for the transaction fee. Second, as a trading agent initiates all transactionson its own, starting or stopping a full run of these agents could be looked upon as asingle separate type of order, just like an ordinary limit order, for example. Therewould not be any need for any communication with outer sources except at the verystart and at the very end of a run.Apart from the transaction fee, there is also the implicit transaction cost of thespread (the difference between the highest bid and the lowest ask price in a doubleauction). It would have been impossible for me to simulate a real stock market, andthereby the cost of the spread, in a realistic way. Instead I made the idealisticassumption that I could sell or buy stocks at the rate I had used for my predictivecalculations, i.e., the rates would not be affected by the agents’ orders and the stockmarket would be extremely liquid.In the charts (2 and 3) every crossing of two lines in the landscapes represents apair of parameters (threshold values). The performance of the corresponding ‘Buy andHold’ strategy is also given in the headings of the individual charts.Searching for patterns in these landscapes, I immediately recognised the plateauxand valleys in the lower and right quarters of the charts (looking at the charts as theyare displayed). In Chart 3, corresponding to a fall of the exchange, there is a plateau inthe right quarter and a valley in the lower quarter. This corresponds to high values forboth the threshold of sale and the threshold of purchase, and to high values for thethreshold of sale and low values for the threshold of purchase, respectively. Here Imust point out that at the very edge of the right corner, just a few or no transactionshave taken place. The threshold of purchase is set at a level too high for anytransaction to be initiated, except for possibly a few stray transactions. If bought, astock would immediately be sold owing to the very high-set threshold of sale. In thechart pertaining to a rise of the exchange (Chart 2), the reverse scenario arises. In thischart there is a plateau in the lower quarter and a lowland plain in the right quarter.The plateau corresponds to a high value for the threshold of sale and a low value forthe threshold of purchase, and the valley corresponds to high values for both thethreshold of sale and the threshold of purchase.The results are not too astonishing. They just state that it is always good to sellearly so that you can switch to the best performing stocks, that in bad times youshould only invest in stocks with really good prospects, and that in good times oneshould aim at always remaining invested in shares.I decided to take a closer look at this pattern, focusing on the area close to thecentre of the charts with their high peaks and deep valleys, i.e., the area where mostvalues of function (1) were centred, to see whether it had any kind of generality ornot. For this purpose I used samples 3 to 58 (appendix), in all 56 samples. 28 samples9
Chart 2, 26 Feb 99 - 25 Feb 00, sample 1. Interval in between threshold values 0.01.'Buy and Hold': 16070 SEK.40000350003000025000200001500010000Total sum at end of period(SEK).35000-4000030000-3500025000-3000020000-25000500015000-20000Threshold of sale-0.15-0.10000002-0.05-1.75E-090.0499999970.100000020.15 S1S10S19S28S37S46S550Threshold of purchase,S1= - 0.15, S61=0.15 .10000-150005000-100000-5000Chart 3, 28 Feb 00 - 23 Feb 01, sample 2. Interval in between threshold values 0.01.'Buy and Hold': 6960 SEK.20000-0.15-0.09500001-0.0400000030.0149999980.07Threshold of sale 0.12500003S1S8S15S22S29S36S43S50S57180001600014000120001000080006000400020000Threshold of purchase,S1=- 0.15, S61=0.15 .Total sum at end of period(SEK).18000-2000016000-1800014000-1600012000-1400010000-120008000-100006000-80004000-60002000-40000-200010
Page 1 and 2: Improved P
Page 3 and 4: mathematical sign that all is not a
Page 5 and 6: If the model corresponds well with
Page 7 and 8: this purpose I designed a subagent
Page 9: exceeded a threshold value, set bef
Page 13 and 14: Chart 4, Average of 28 samples, 26
Page 15 and 16: Table 4. The choice of subagent.The
Page 17 and 18: separately (compare with results of
Page 19 and 20: interesting to see how much time th
Page 21 and 22: As I have already indicated in a pr
Page 23 and 24: [Blume and Easley, 1990] L. Blume,
Page 25 and 26: B, SHB-ATEL2-B,VOLV-B,WM-B, STE-R,A

Improved Pricing on the Stock Market with Trading Agents

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