Pricing Exotic Options through Generic FiniteElement Platform

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Pricing Exotic Options through Generic
Finite-Element Platform

• Mathematical Information Sciences

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PDE platform Fastflo

• A generic partial-differential equation solver.
• Easy handling of complex exotic options.
• Several nonlinear PDEs can be linked,
  e.g. PL, share number can be solved together.

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Generic PDE platform Fastflo

• Developed by CSIRO.
• In syndicate with BHP and Compumod.
• 40 man-year development in 6 years.
• Commercially distributed by NAG worldwide
  (www.nag.com)

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Finite-Element Methodbeing partitioned into
small elements
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Why Finite-Element Method

• More stable numerical algorithms.
• Suitable for complex equation systems.
• Ideal for fast development of more exotic
  products.

S
FDM
FEM
t
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What is Finite-Element Method

• Finite-Difference Method
  weighting function is a delta function.
• Finite-Element Method
  weighting function is a
  triangle.

FDM
FEM
i-1
i-1
i1
i
i
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This is how the Black-Scholes equation is solved
A scholes e D_js2hafX1X1,0.0,0.0,0.0_jk D_k
U1 \ -s2m1X1,1.0_j D_jU1 - rU1 0 b 2
U1X1-strikeexp(-rX2) b 4 U10.0 b 1
U1cut(X1-strike)
T1
Tag 1
t
X2
Tag 2
Tag 4
S
t0
X1
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Results from a stochastic volatility model
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Advantages of using Fastflo

• Any PDEs can be solved.
• Exotic options pricing, trading/portfolio
  analysis.
• Code is open and transparent.
• Code is modular for easy sharing.
• Easy and fast to modify and check models.

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Using Fastflo stand-alone

• An alternative for double-checking predictions.
• Stable and robust for risk-management.
• A fast proto-typing tool for pricing models and
• before major code
  development.
• An effective tool for developing new products.

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Using Fastflo as a system

• Close interaction between Quants and traders
• Product-development cycle is reduced drastically
• A transparent risk-management engine

Price
Exotic option models Parisian Asian Lookbacks T
wo-factors . ...
System
Quants
add-on
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An example Rate Term Structure Volatility
Surface
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Example Late-start barriers

• Partial barrier from 4-5 years.
• Volatility surface and term structure.
• E65, B60
• Fastflo 828.75 pts
• Monte Carlo 824.52 pts

S
E
B
t
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Example Knock-ins

• Any knock-in barrier types
• volatility surface
• interest rate term structure
• any complex barriers can be handled easily.

S
knock-ins
t
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Options with Stochastic Volatility
?
S
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Two-Asset Barrier Options
2
3
1
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Asian Options
A
S
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Discrete Asian Options
A
S
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Lookback Options
J
S
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Discrete Lookback Options
J
1
2
S
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Parisian Options
J
2
1
S
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ParAsian Options
J
2
1
S
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Options with Delayed Strike
K
S
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Summary

• Fastflo is
• a versatile and efficient proto-typing
  tool
• powerful for researching new products
• a robust/stable method for risk check.

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For the future

• Conduct research in financial mathematics.
• Develop new numerical techniques for options
  pricing, portfolio analysis.
• Provide research/consulting services to the
  financial market.
• Use Fastflo as an efficient platform to deliver
  innovative products.

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3 factor results