24Lecture24

Use your long stock to close out your option position

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Unformatted text preview: n worth $29.73 = $29.00e +0.1×0.25 . Profit on the trade is $30.00 − $29.73 = $0.27 Derivatives III: R. J. Hawkins Econ 136: Financial Economics 6/ 10 Price Risk: Delta (∆) & Gamma (Γ) OPTION PRICE (arbitrary) 50 Options have price risk. 40 Slope = 0.95 Price risk changes with underlying-asset level. 30 20 10 Slope = 0.67 Slope = 0.20 0 -10 0 10 20 30 40 50 60 70 80 90 100 We want simple descriptors of price risk for small underlying-asset changes. UNDERLYING ASSET LEVEL (arbitrary) Let’s do a Taylor-series expansion of a call option price C : C (S + dS ) = C (S ) + ∂C 1 ∂2C dS + (dS )2 + . . . ∂S 2 ∂S 2 Derivatives IV: R. J. Hawkins Econ 136: Financial Economics 2/ 13 Price Risk: Delta (∆) & Gamma (Γ) Interpreting the call option price Taylor series: 1 ∂2C ∂C dS + (dS )2 + . . . 2 ∂S 2 ∂S ∂C 1 ∂2C C (S + dS ) − C (S ) ≈ dS + (dS )2 2 ∂S 2 ∂S C (S + dS ) = C (S ) + OPTION PRICE (arbitrary) 50 40 ∂C ≡ Delta (∆) ∂S = the slope Slope = 0.95 30 20 10 Slope = 0.67 Slope = 0.20 0 -10 0 10 20 30 40 50 6...
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This note was uploaded on 01/23/2014 for the course ECON 136 taught by Professor Szeidl during the Fall '08 term at Berkeley.

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