case08sol

case08sol - Introduction to derivatives Fall 2011 BUSI 588...

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Unformatted text preview: Introduction to derivatives, Fall 2011 BUSI 588, Case 8 solutions Solutions to Aureliano Buend´ ıa and hedging Using Black-Scholes one can easily verify that the value and the “Greeks” of the call options under consideration are given by the following table. Option Call Put Call Strike 100 120 150 Value 10.386 17.502 0.354 Delta 0.6346-0.7149 0.0462 Gamma 0.0188 0.0170 0.0048 Theta-6.3496 0.9460-1.1752 1. (*) From the above table, for each $1 that copper goes up in price, the call option with a strike of $100 goes up in value by (approximately) 63.46 cents. The call option with a strike of $150 goes up in value by (approximately) 4.62 cents for each $1 move in copper. Similarly, the put option with a strike of $120 will go down in value by (approximately) 71.49 cents if copper goes up by $1. Since UBS sold this options, the delta of this portfolio will be the oppositive sign of the delta of the individual options, i.e. Δ =- 200(0 . 6346)- 100(- . 7149)- 150(0 . 0462) =- 62 . 35 If UBS traded x units of the underlying asset, the delta of the portfolio would be Δ P =- 62 . 35 + x , so that if they want to be delta-neutral, UBS shoudl buy 62.35 units of copper....
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This note was uploaded on 11/25/2011 for the course BUSI 588 taught by Professor Staff during the Fall '10 term at UNC.

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case08sol - Introduction to derivatives Fall 2011 BUSI 588...

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