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A study of the Chan and Shelton learning model for market making

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Overview

This is a study of An Electronic Market-Maker by Nicholas Tung Chan and Christian Shelton.

01 - Expected Profit

This is a Monte Carlo simulation of the basic model that computes the expected profit. The following is a reproduction of Figure 3 from the paper:

ExpectedProfit-Result

These are plots of the true price and market price for strategies 1, 2, and 3, respectively, when the noise factor alphaU = 0.4:

ExpectedProfit-Prices-alphaU-0.4-imbalance-1 ExpectedProfit-Prices-alphaU-0.4-imbalance-2 ExpectedProfit-Prices-alphaU-0.4-imbalance-3

These are plots of the true price and market price for strategies 1, 2, and 3, respectively, when the noise factor alphaU = 1.0:

ExpectedProfit-Prices-alphaU-1.0-imbalance-1 ExpectedProfit-Prices-alphaU-1.0-imbalance-2 ExpectedProfit-Prices-alphaU-1.0-imbalance-3

These are plots of the true price and market price for strategies 1, 2, and 3, respectively, when the noise factor alphaU = 1.6:

ExpectedProfit-Prices-alphaU-1.6-imbalance-1 ExpectedProfit-Prices-alphaU-1.6-imbalance-2 ExpectedProfit-Prices-alphaU-1.6-imbalance-3

02 - Basic Model (SARSA)

This is an implementation of the basic model that uses the SARSA learning method to choose the optimum strategy. The following is a reproduction of Figure 5 from the paper:

  • Episode 25

BasicModel-Prices-025

  • Episode 100

BasicModel-Prices-100

  • Episode 200

BasicModel-Prices-200

  • Episode 500

BasicModel-Prices-500

The following is a reproduction of Figure 6a from the paper:

BasicModel-EndOfEpisodeProfitSum

The following is a reproduction of Figure 6b from the paper:

BasicModel-EndOfEpisodeInventory

The following is a reproduction of Figure 6c from the paper:

BasicModel-AveragePriceDeviation

03 - Extended Model (SARSA)

This is an implementation of the extended model that uses the SARSA learning method to choose the optimum spread. The following is a reproduction of Figure 9 from the paper:

  • Episode 25

ExtendedModel-Prices-025

  • Episode 100

ExtendedModel-Prices-100

  • Episode 200

ExtendedModel-Prices-200

  • Episode 500

ExtendedModel-Prices-500

The following is a reproduction of Figure 10a from the paper:

ExtendedModel-EndOfEpisodeProfitSum

The following is a reproduction of Figure 10b from the paper:

ExtendedModel-AverageEpisodicSpread

The following is a reproduction of Figure 10c from the paper:

ExtendedModel-AveragePriceDeviation

The following is a reproduction of Figure 10d from the paper:

ExtendedModel-EndOfEpisodeInventory

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