Transcript No Slide Title

Course Project Presentation
for
74.757 Computational Finance
Algorithm for Pricing
European Asian Options
Supervisor: Dr. Ruppa Thulasiram
Presenter: Kai Huang
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
d’
u’
d’
d’’
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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 ?
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