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Exotic Options Pricing and Hedging

Exotic Options Pricing and Hedging. Dr Zili Zhu Quantitative Risk Management Mathematical & Information Sciences. 26 th February 2009. Background of CSIRO. Organization: Commonwealth Scientific and Industrial Research Organization (7000 staff members)

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Exotic Options Pricing and Hedging

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  1. Exotic Options Pricing and Hedging Dr Zili Zhu Quantitative Risk Management Mathematical & Information Sciences 26th February 2009

  2. Background of CSIRO Organization: • Commonwealth Scientific and Industrial Research Organization (7000 staff members) • Division of Mathematical and Information Sciences • Quantitative Risk Management Group (25 people) Commercial activities • CSIRO Exotic math for FX markets • Consulting assignments for major banks • Development of new options models for hedge funds. • Development of major risk-management software. CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  3. Content Exotic Options Pricing • Some examples • Pricing • Practical issues Hedging • General principle in hedging • Conventional approaches • CVaR minimisation approach CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  4. What is An Exotic Option: Reverse Knockout Call t K t K S B B CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  5. An Exotic Option: two-asset options • 2 asset Black-Scholes equation: • Payoff function S2 S2 S2 S1 CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  6. A Typical Exotic Option: Two-Asset No-Touch FENICS FX Pricing Page: CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  7. Other Exotic Options Compound Call/Put Quanto options Lookbacks Asian average options Trans-Atlantic options Holder Extendible options Knock-out and Knock-in barrier options Multiple window barrier options One-touch/No-touch options Range accrual options Target redemption options Best/Worst options Basket options Beta Basket options. Two-asset digitals Two-asset Knock-out/in options ……. CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  8. Pricing Exotic Options Stochastic Processes for Asset Prices i=1,2,…..N CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  9. S Tree Methods S SU pu pm SM pL SL Time S CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  10. Monte-Carlo Simulations: CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  11. Finite Difference, Element, Volume Methods S S0 CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  12. Practical Issues in Pricing Exotic Options • Volatility is not constant. • Correlation is dependent on ATM price. • Correlation should be dependent on strike levels? • Less than 20 seconds Is needed for pricing CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  13. Hedging Principles • Hedging to eliminate risk due to market movements in asset prices, volatility, interest-rates and correlations. • The cost of hedging reflects the premium received from clients. • Limit large down-side risk to P/L. • Trading in derivatives without hedging is speculation. • The objective of hedging is to protect business from unpredictable market movements on a daily basis. CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  14. Greek Hedging: Using Sensitivity Parameters • Delta: • Gamma: • Vega • Rho • Time decay CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  15. Example: Window No-Touch Option FENICS FX Pricing Page: CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  16. Example: Window No-Touch Option CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  17. Example: Greeks of Window No-Touch Option CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  18. Greeks: Window No-Touch Option CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  19. Example: Window No-Touch Option CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  20. Portfolio Approach • Delta hedging is automatically set for each individual option through the purchase/sell of underlying assets. • Other greek parameters such as gamma, vega, rho are balanced through the purchase/sell of vanilla and/or more liquid exotic options at portfolio level. • For options with discontinuous risk profiles or path-dependency (e.g. barrier options), hedging is difficult. CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  21. Loss Distribution without Hedges CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  22. A Greek Delta-Gamma Hedge To Reduce Risk CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  23. Hedging Strategy • Risk can only be reduced but not eliminated via hedging through greeks even if the Black-Scholes model is appropriate. • Hedging through greeks is model dependent. • For commodities and energies (e.g. electricity), model dependency can make hedging ineffective. • Other hedging approaches should be explored. CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  24. Using An Alternative Hedging Strategy • We use a Conditional Value-at-Risk as a risk measure. CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  25. Hedging Through CVaR Minimisation CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  26. Optimal Hedging Through CVaR Minimisation • CVaR Minimisation hedge can be naturally extended to incorporate the selection of the optimal instruments for hedging. • For example, six options are available for hedging, which is more effective and low-cost for hedging? CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  27. Optimal Hedging • Automatically select the most efficient instruments for hedging • Hedging performance is enhanced and cost is reduced. CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  28. Summary • Exotic options are used as specialist products to accommodate specific risk appetites and market views of end-users. • Exotic options are high-margin products. • Full understanding of down-side risk of exotic options is paramount before trading in these instruments. • The hedging of exotic options can be implemented as part of a structure. • Discontinuous payoffs or path-dependent features need to be considered. • Standard hedging is through Greek sensitivity parameters. • Hedging does not eliminate risks entirely. • Hedging through CVaR minimisation is an alternative approach. • Optimal hedging can be implemented through CVaR minimisation and a penalty on transaction cost. CSIRO Mathematical & Information Sciences www.cmis.csiro.au

  29. Acknowledgments • Thanks to FENICS FX the global standard in FX options pricing and analysis for the use of their trading system. • Thanks for China Finance Online for the invitation. CSIRO Mathematical & Information Sciences www.cmis.csiro.au

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