Option Risk Management

Option Risk Management - Option Risk Management Copyright...

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1 Option Risk Management Copyright © 2000-2006 Investment Analytics
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Copyright © 2000-2006 Investment Analytics 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 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 Option Risk Management Slide: 4 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 Option Risk Management Slide: 5 Option Delta ± Key sensitivity ± Change in option value for $1 change in underlying stock ± Range –1 to +1 ± Option Delta ± Put options: negative delta ± Call options: positive delta
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Copyright © 2000-2006 Investment Analytics Option Risk Management Slide: 6 Delta Example ± Call option with Delta 0.5 ± Delta tells us how the call price changes ± If stock moves up by $10, call price increases by $5 ± If stock drops by $10, call price decreases by $5
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Copyright © 2000-2006 Investment Analytics Option Risk Management Slide: 7 Delta Position ± Delta Position ± The call ‘behaves’ like 0.5 units of stock ± If we hold 10 calls, our position behaves like 5 units of stock ± we say we are “long 5 deltas”
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Copyright © 2000-2006 Investment Analytics Option Risk Management Slide: 8 Position Deltas ± Call options ± have positive delta ± like being long stock ± Put options ± have negative delta ± like being short stock ± Stock - has a delta of 1! ± Bonds - have a delta of zero ± Combinations ± may have positive, negative or zero delta
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Copyright © 2000-2006 Investment Analytics Option Risk Management Slide: 9 Delta Hedging ± If you know the position’s delta, you can hedge it ± Example, 10 calls, each of delta 0.5 ± How to hedge: Sell Delta units of stock ± This creates a portfolio of 10 calls plus -5 units of stock ± The combined position has a delta of +5 - 5 = 0 ± Like being long 5 stock & short 5 stock = net zero stock ± The value of the portfolio will be unchanged, no matter whether the stock moves up or down
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Copyright © 2000-2006 Investment Analytics Option Risk Management Slide: 10 Delta Neutral Positions ± A portfolio is hedged when its position delta is zero ± We say we have a delta-neutral position ± Examples: assume call delta 0.5, put delta -0.5 ±
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Option Risk Management - Option Risk Management Copyright...

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