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OptionsMarketWithJumps

by William Elliott (Submitted: 10/22/2013)

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## WHAT IS IT?

This simulated options market creates a grid of traders who use the Black-Scholes formula to determine when to buy and sell options. Values such as the starting price and the risk free rate of interest can be adjusted by the user to see what effects different variables have on the market.

## HOW IT WORKS

The agents are arranged on the grid based on their level of "patience" (the range of the market they analyze) and "judgement" (how much they deviate from the Black-Scholes formula). The traders gain and lose money as they trade options with the Black-Scholes formula. Lighter green means success, lighter red means loss, and darker colors or black indicates small success or small loss. Successive markets are averaged into the main display in a Monte-Carlo type model.

## HOW TO USE IT

Adjust or input variables with slider bars and boxes. The "Seed" value enables one to run each market with a seed (a value of zero means disregard the seed value). In addition to the default judgement vs. patience graph, the dropdown menu allows the user to change the graph to "Scattered" so that the traders' judgement and patience values are not dependent on their position. The finalMarket value tells the program how many markets to run before the program stops. The putMarket switch enables one to decide whether to simulate a put option market or a call option market.

## THINGS TO NOTICE

The four graphs on the left side of the display show the stock price, the options market, the average sigma, and the rate of activity. The main graph often starts out with wild variations, but eventually smooths out over time. In addition, the trader with the best patience and judgement is marked with a blue square, and the trader with the worst patience and judgement is marked with a yellow square.

## THINGS TO TRY

It is suggested that the user simulate both a put market and a call market to see how the main graph differs between the two over time. For a more accurate reading of what patience and judgement values yield success in this particular market, leave the market running for several hundered runs.

## EXTENDING THE MODEL

## NETLOGO FEATURES

The main grid feature of NetLogo enabled a color-coded simulation of traders in an options market.

## RELATED MODELS

Artificial Financial Market
OptionsMarket

## AUTHOR

William Elliott
william.elliott@magprep.com

## CREDITS AND REFERENCES

http://code.google.com/p/stock-market-simulation/
http://bradley.bradley.edu/~arr/bsm/pg04.html
Zhang, Shu Lin; Feng, De Yu; Wang, Shu Ping. “Option Pricing under Unknown Volatility : An Agent-Based Modeling and Simulation Approach.” 2009 International Conference on Information and Financial Engineering (2009): 130-134
Joshi, Mark. The Concepts and Practice of Mathematical Finance.
Merton, Robert. “Option Pricing when Underlying Stock Returns are Discontinuous.”
http://demonstrations.wolfram.com/OptionPricesInMertonsJumpDiffusionModel/

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