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# lecture10 - Recap Hedging using futures Lecture 10 Hedging...

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Recap Hedging using futures Lecture 10 - Hedging with futures BUSI 588, Fall 2011 Diego Garc´ ıa Kenan-Flagler Business School UNC at Chapel Hill September 28th, 2011 c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 10 - Hedging with futures 1 / 25 Recap Hedging using futures Outline 1 Recap Homework 4 2 Hedging using futures Metastrugentrigen Common hedging questions Handouts today: Class slides. Case 10 solutions. Homework 4 solutions. 2010 MBA783 final exam (solutions for last day of class). c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 10 - Hedging with futures 2 / 25

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Recap Hedging using futures Where are we? I. Static trades . Trades with options. Put-call parity. Futures and one-period binomial (trinomial). II. Dynamic trades . Binomial and Black-Scholes. Using and interpreting the binomial and Black-Scholes models. III. Applications . Hedging using futures. Capital structure and options (risky debt and convertibles). Real options (projects as options). c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 10 - Hedging with futures 3 / 25 Recap Hedging using futures On the final Closed-book 3-hour in-class exam. Copy/paste from cases/homeworks. It will be easier than in 2010. It’s a race against each other. My job is to make the race fair. You can use a computer. Only pre-programmed Excel will be a barebones Black-Scholes calculator (with Γ, Θ, vega, . . . ). My goal is to get you to hug me after the exam. Meaning you had a good time. I do not mean it literally. c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 10 - Hedging with futures 4 / 25
Recap Hedging using futures Preparing for the final Read over slides Reproduce examples. Go over homeworks (* and **). Go over cases: \$\$s: 2-6, 8, 10-13. Go over the 2010 final. c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 10 - Hedging with futures 5 / 25 Recap Hedging using futures Gamma Stock price Gamma 800 1000 1200 1400 1600 1800 0.0 0.001 0.002 0.003 0.004 Rule of thumb: options are tough to replicate when they are at-the-money and close to maturity. c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 10 - Hedging with futures 6 / 25

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Recap Hedging using futures Straddles’ value Underlying asset value Payoffs 800 1000 1200 1400 1600 0 100 200 300 400 c Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 10 - Hedging with futures 7 / 25 Recap Hedging using futures Straddles replication Delta of straddle N ( x ) Δ - call + ( N ( x ) - 1) Δ - put = 2 N ( x ) - 1 Cash position - K (1 + r f ) T - t N ( x - σ T - t ) borrow call + K (1 + r f ) T - t (1 - N ( x - σ T - t )) lend put = - 2 K (1 + r f ) T - t N ( x - σ T - t ) - 0 . 5 Whether we are long or short depends on N ( x ) - 1 / 2 0.
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