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Option Hedging Examples

Option Hedging Examples. 2-factor Hedging. Assume the IBM stock position from before. 100 shares of IBM covered by 1.32 call options. Remember slippage with only delta hedge (1.3% Stock Price change met with only .04% change in portfolio). Eliminate Slippage. Delta – Gamma hedge

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Option Hedging Examples

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  1. Option Hedging Examples

  2. 2-factor Hedging • Assume the IBM stock position from before. • 100 shares of IBM covered by 1.32 call options. • Remember slippage with only delta hedge (1.3% Stock Price change met with only .04% change in portfolio)

  3. Eliminate Slippage • Delta – Gamma hedge • Stock: Delta = 1, Gamma = 0 • Call Option: Delta = .7580, Gamma = .02944 • Need additional option: • IBM 6-mo., X=80 call • Delta = .4035 Gamma = .03651

  4. Simultaneous Equations • In general: S Ns + C1 NC1 + C2 NC2 = 0  ( S) Ns +  (C1) NC1 +  (C2) NC2 = 0, where: S = 1, C1 = C1 , C2 = C2 ,  ( S) = 0 ,  ( C1) = C1,  ( C2) = C2 • Point is to solve for NC1 and NC2.

  5. Fill-In and Plug&Chug 1 Ns + 0.758 NC1 + .4035 NC2 = 0 0 Ns + 0.02944 NC1 + 0.03651 NC2 = 0 • If we deal with Ns = 1, then NC1 = -2.311 and NC2 = +1.864

  6. Delta-Gamma Hedge • Thus, to hedge a long position in 100 shares of IBM at $75, and also insure the hedge will not detriorate, Sell 2.311 IBM 6 mo. X=70 calls & Buy 1.864 IBM 6 mo. X=80 calls

  7. Starting Position Long IBM (100 shares @ $75) 7500.00 Short X=70 calls (2.311@ $8.015) -1852.66 Long X=80 calls (1.864@ $2.829) 527.23 Total Cost of Position 6174.57

  8. IBM = 74 • Long IBM (100 shares @ $74) 7400.00 • Short X=70 calls (2.311@$7.272) -1680.93 • Long X=80 calls (1.864@$2.443) 455.41 • Total Value of Position 6174.47 • A change of $0.10 or 0.0017% • (Delta-only, change = $2.00 or 0.03%)

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