Daniel HERLEMONT. Financial Risk Management. Non Linear Risks: Options. Following P. Jorion 2001. Financial Risk Manager Handbook, Chapter 15. Daniel ...
Non Linear Risks: Options Following P. Jorion 2001 Financial Risk Manager Handbook, Chapter 15
Daniel HERLEMONT
Introduction In practice we have to deal with options positions in options embedded non linear payoff pattern
Summary Option pricing and Taylor approximation Greeks Dynamic Hedging
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Notations
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Taylor Expansion • Option pricing is about to find f
Option Hedging use partial derivative Taylor expansion
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Long Call
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Options Pricing The price of the option is the expected present value of the future payoff in a risk neutral world
European call
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Options Greeks Delta for the long call
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Gamma for the European call or put
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Gamma
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Vega Vega of a long European call
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Implied Volatility
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Theta - the Time Decay
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Dynamic Hedging Holding an option is equivalent to hold a fraction (detla) to the underlying asset, where this fraction dynamically change over time rebalance periodically Hedging risks Delta - Gamma Hedging
