Course Project Presentation for 74.757 Computational Finance Algorithm for Pricing European Asian Op

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Course Project Presentation for 74.757
Computational FinanceAlgorithm for Pricing
European Asian Options

• Supervisor Dr. Ruppa Thulasiram Presenter Kai
  Huang

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Presentation Outline

• Introduction
• Problem Statement
• Binomial tree
• Solutions
• Recombining Tree
• Non-recombining Tree
• Analysis Results
• Conclusion Future Work

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Introduction

• Options
• Exercise price maturity date
• Call option put option
• Complex options options with more complicated
  payoff than standard calls and puts.
• The option pricing problem
• Determining a fair price to pay for an option.

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Introduction

• Asian Options
• path-dependent options
• Whose payoff depends on the average price of the
  underlying asset during the life of the option
• popular in the real financial market
• Call max (0, Save-X)
• Put max (0, X-Save)
• Save is the average value of the underlying asset
  calculated over the option life.
• arithmetic average and geometric average.

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Problem Statement

• My aim for this project is to find the path,
  which can give the best payoff, and calculate the
  best payoff for an European Arithmetic Asian Put.

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Binomial Tree Method

• Binomial tree method is a common approach.
• The difficulty with the binomial tree method in
  the case of Asian options lies in its exponential
  nature.
• 2n paths have to be individually evaluated for a
  binomial tree with n periods.

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Solution for the Recombining Tree
u
u
d
d
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Solution for the Recombining Tree

• An adapted Dijkstra shortest path algorithm is
  designed to solve this pricing problem.
• In this adapted Dijkstra shortest path
  algorithm,the recombining binomial tree can be
  treated as a directional graph and the price of
  the underlying asset on different node can be
  thought as the weight of the former arc in the
  graph (The root node is the exception).
• In this way, the shortest path means the path
  that can give maximal payoff for this European
  Asian put.
• problem is that the u and d do not change during
  the whole computation

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Solution for the Non-recombining Tree
u
u
u
d
u
d
d
d
10
Solution for the Non-recombining Tree

• In the non-recombining tree, the u and d may
  change in each step, thus make the underlying
  asset more variable and has some application
  values.

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Analysis

• Theoretic analysis
• practical analysis
• Pricing arithmetic Asian option is a difficult
  problem and no closed-form equation can be used
  to test.
• Therefore, one binomial tree is created by hand
  whose time step equals to 10, and the best path
  for an European Asian put can also be found by
  hand. Then two results are compared and I found
  they are exactly same, which means that in this
  level my algorithm is right in practice.

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Results
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Conclusion

• Option pricing problem is a significant problem.
• Asian Options are widely used in financial
  market.
• Pricing Asian options is a significant problem
  for computer scientists and mathematicians.
• My solution can calculate European Asian options
  correctly.

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Future Work

• Parallel computation can be applied in this
  problem,which may have more accurate computing
  results with shorter running time.

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• Thanks ! Questions ?