A Neural Network Approach For Options Pricing

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A Neural Network Approach For Options Pricing

• By Jing Wang
• Course CS757 Computational Finance
• Instructor Dr. Ruppa Thulasiram
• Project CFWin03-35
• Email jingwang_at_cs.umanitoba.ca
• Date May 26, 2003

2
Overview

• Background Motivation
• Problem Statement
• Solution Strategy
• Results and Comparison
• Conclusion
• Future work
• Reference

3
Background Motivation

• Option Pricing
• Determine a risk-free price for options
• Approaches
• Lattice Models
• Black-Sholes Model
• Monte Carlo Simulation
• Artificial Neural Network (ANN)
• Non-parametric, non-linear
• Data driven
• Capture the dynamics

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Problem Statement

• Type of options
• European call / put
• American call / put
• Objective
• Train the ANN with a set of option pricing data
  with certain inputs (current stock price, strike
  price, maturity time, option type, risk-free
  rate), then use the neural network calculate
  risk-free option prices
• Assume option price upper bound 50

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Solution Strategy

• Supervised ANN
• Multi-Layer Perceptron (MLP)
• Training method Back-Propagation
• One ANN for a specific type of options
• Benchmark Binomial tree
• Provides data to train the ANN
• Implementation
• Sequential implementation using C
• Parallel implementation using MPI

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ANN Structure

• One Input Layer
• 5 Inputs current underlying asset price, strike
  price, maturity date, risk-free interest and
  sigma
• Hidden Layers
• No threshold, but an active function
• Different number of hidden layers and nodes on
  hidden layers are compared while implementation
• Output Layer
• Use the above active function
• Three different strategies

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Output Layer Structure

• Solution 1 One node
• Output value output_node_value 50
• Sigmoid function produces a value 0,1
• Above function produced a value 0,50
• i.e. Output node gets value 0.249 to produce
  option price 12.45
• Solution 2 Fifty nodes
• Only node K has a value
• Output Value (K-1) value_of_node_K
• i.e. For option price 12.45, only node 13 has a
  value of 0.45, all others produce 0

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Output Layer Structure (cont.)

• Solution 3 Fifty nodes
• First K nodes produce values
• First K-1 nodes produce 1
• Node K produce the value which is
• option_price (K-1)
• Output Value
• i.e. For option price 12.45, node 13 has a value
  of 0.45, node 1 to node 12 produce 1, and the
  rests produce 0

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Parallel Design

• Use the best structure of the three strategies
• One processor has a portion of the ANN
• all input nodes, all hidden layers, n1/p hidden
  nodes, and n2/p output nodes
• n1 of hidden nodes on a full ANN
• n2 of output nodes on a full ANN
• p of working processors.

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Result Comparison

• Learning accuracy compared between the three
  strategies
• of data used
• European Call Train 336, Test 2892
• American Put Train 319, Test 2600

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Result Comparison (cont.)
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Conclusion

• Artificial Neural Network is able to pricing
  options
• An ANN produce a better result when the output
  value rely on more output nodes than only one
• An ANN with more less hidden layer and more
  hidden layer nodes learns quicker

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Future Work

• Real data to Train and Test ANN
• Train ANN for different options
• More time to finish parallel implementation

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Reference

• 1 Rashedur M. Rahman, Ruppa K. Thulasiram, and
  Parimala Thulasiraman. Forecasting Stock Prices
  using Neural Networks on a Beowulf Cluster. 2003.
• 2 Christian Schittenkopf. A neural
  network-based approach to extracting risk-neural
  density and to derivative pricing.
• 3 Rudy De Winne, Alain Francois-Heude, and
  Benoît Meurisse. Market Microstructure and Option
  Pricing A Neural Network Approach. Book of
  Research, Catholic University of Leuwen. August
  2001