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Hedging Process in Detail Hedging Strategy – Goal of hedging is for Asset and Liability Risks to be offsetting – Many different possible strategies and hedging instruments • Dynamic Hedging Continuous rebalancing of assets to match liabilities Many different possible rebalancing rules • Static Hedging

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United, Delta Profit at Risk From `Silent Killer' in Fuel Hedges By Mary Jane Credeur, Mary Schlangenstein and Paul Burkhardt - Jan 31, 2011 U.S. airlines including United Continental Holdings Inc. and Delta Air Lines Inc. may see 2011 profits eroded as an indicator of jet-fuel costs surges to a two-year high.

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To hedge delta to zero, buy 6 TF futures. Can only trade whole futures contracts. Hedging, requires rounding up or down. CHICAGO BOARD OPTIONS EXCHANGE. 30.

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Dynamic Hedging CVA FX Hedge Credit Hedge Net PnL (21) 21 0 0 PnL Inception FX 5y Credit CVA T=0 1.3500 93 382 FX Moves Only FX 5y Credit CVA T = 0 1.3600 93 403 FX Moves +100 pips Expected Loss increases 21k; offset by gain in FX Hedge No net gain or loss FX hedge is unchanged at EUR 2.1mm CDS hedge is increased to 8mm delta-hedge? • Recall that the delta-hedging strategy consists of selling one option, and buying a certain number ∆ shares • An example of Delta hedging for 2 days (daily rebalancing and mark-to-market): Day 0: Share price = $40, call price is $2.7804, and ∆ = 0.5824 Sell call written on 100 shares for $278.04, and buy 58.24 shares.

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7 Delta Hedging and Trading Systems Any derivatives trading and risk management system (for equities, foreign exchange and bond derivatives) should accommodate conversions as described above. The following delta hedging conversions should be included † Hedging a future by its underlying stock or vice versa | e.g., hedging an ALSI futures

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The delta hedge is perfect in the sense that if we follow it we will have no variability in final outcome – it is a complete replication strategy. To understand what is happening here imagine the unit time interval divided into 1/𝛿 sub-intervals Delta-Hedging a... Contact Information mathfinance.com Title Page JJ II J I Page 6 of 40 Go Back Full Screen Close Quit 2.3. Delta Hedging the Short Option The delta is the slope of the value function ∂ ∂S t v(S t,t) = ... Black-Scholes delta vanilla 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000

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