Design New Exotic Instruments through Generic FiniteElement Platform

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Design New Exotic Instruments through Generic
Finite-Element Platform

• Mathematical Information Sciences

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A New Product Reditus

• One-Factor product series.
• Two-factor product series...
• Quants can freely add new products.
• Dealers interact with quants to develop new
  products.
• Traders can price deals straightaway.

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Objectives Approaches

• To price exotic options with irregular barriers
• To develop innovative products quickly
• Use Partial-Deferential-Equation (PDE) approach
• Use Finite-Element formulation.

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Why Finite-Element Method

• More stable pricing algorithms.
• Ideal for complex exotic options.
• Efficient for developing innovative products.

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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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Advantages of using Reditus

• Any equations of the business can be solved.
• Easy to build up your own unique products.
• 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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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)
Expiry date
Tag 1
t
X2
Tag 2
Tag 4
S
t0
X1
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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
• Reditus 824.75 pts
• Monte Carlo 824.52 pts

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Example Binary call with 3 one-day barriers

• Two-year option
• one-day barrier every 6 months.

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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.

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knock-ins
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Options with Stochastic Volatility
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Results from a stochastic volatility model
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Two-Asset Barrier Options
2
3
1
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Asian Options
A
A
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Pricing Results for Asian Options
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Jump Conditions for Discretely monitored Asian
Options
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Pricing Discrete Asian Options
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Lookback Options
J
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Discrete Lookback Options
J
1
2
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Pricing Discrete Lookback Options
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Parisian Options
J
2
1
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Pricing Parisian Options
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ParAsian Options
J
2
1
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ParAsian Options
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Options with Delayed Strike
K
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Pricing Options with Delayed Strike
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Reditus a new product-development platform

• 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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Using Reditus as part of 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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Using Reditus 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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Summary

• Reditus is a finite-element platform
• a versatile and efficient proto-typing
  tool
• powerful for researching new products
• a robust/stable method for risk check.
• a Monte-Carlo engine, and a finite-difference
  engine will be added soon.

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For the future

• Develop new numerical techniques for options
  pricing, trading strategy portfolio analysis.
• Provide research/consulting services to the
  financial energy markets.
• Use Reditus as an efficient platform to deliver
  innovative products.
• Other research groups within CSIRO provide
  intellectual backup.

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3 factor results