Advanced Option Risk Management

Advanced Option Risk Management - Option Risk Management...

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1 Option Risk Management Copyright © 2000 – 2006 Investment Analytics
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 2 Agenda ± Option sensitivity factors ± Delta ± Delta hedging ± Option time value ± Gamma and leverage ± Volatility sensitivity ± Gamma and Vega hedging
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 3 Option Sensitivity Factor ± What affects the price of an option ± the asset price, S ± the volatility, σ ± the interest rate, r ± the time to maturity, t ± the strike price, X
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 4 Black-Scholes Equation ± Consider delta-hedged option portfolio ± Must grow at risk free rate, else arbitrage ± Leads to following relationship: rV S V rS S V S t V = + + 2 2 2 2 2 1 σ Delta Gamma Theta
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 5 Option Greeks ± Delta (“price sensitivity”) ± change in option price due to change in stock price ± Gamma (“leverage”) ± change in delta due to change in stock price ± Vega (“volatility sensitivity”) ± change in option price due to change in volatility ± Theta (“time decay”) ± change in option value due to change in time to maturity
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 6 Option Delta ± Key sensitivity dV/dS ± Change in option value for infinitely small move ± In reality use: V/ S ± Better still: + = + S V S V Delta 2 1
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 7 The Delta of a Call Option ± Delta changes as stock price changes ± Gammameasures rate of change of delta X Stock Price Call Value 1 0.5 0 Out of the money At the money In the money
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 8 IBM Option Delta
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 9 A New Look at Delta Probability Delta = Probability of Option Finishing in- the-money S X.e -rt Out-of-the-Money
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 10 Delta: At-the-Money Probability S = X.e -rt At - the - Money
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 11 Delta: In-The-Money Probability S X.e -rt Delta 1 In-the-Money
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 12 Delta and Derivatives ± Forward FX Contracts ± F = e (r-rf)t S ± So delta of forward is e -rft ± Stock index with dividend yield d ± Delta = e -dt
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Copyright © 2000-2006 Investment Analytics Advanced Option Risk Management Slide: 13 Delta and Volatility ± How does (future) volatility affect delta?
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This document was uploaded on 11/04/2011 for the course ECON 421 at CUNY York.

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Advanced Option Risk Management - Option Risk Management...

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