2_option_greeks

# 2_option_greeks - OPTION GREEKS, HEDGING AND INTEREST RATE...

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OPTION GREEKS, HEDGING AND INTEREST RATE RISK J. Wei, Department of Management, U of T 1 MGTD78 delta, gamma, vega, theta LIBOR and swap rates duration, convexity, immunization

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OPTION GREEK: DELTA J. Wei, Department of Management, U of T 2 MGTD78 Option Greeks: option’s sensitivity to model inputs Delta (C71) change of option value w.r.t. change of stock price call: delta → 0 when S → 0; delta → 1 when S → put: delta → -1 when S → 0; delta → 0 when S → T σ )T σ σ (r X S ln d ), d N( S P ), N(d S C σ σ σ σ + + = - - = = where
OPTION GREEK: DELTA J. Wei, Department of Management, U of T 3 MGTD78 Example: You have a call option, S = \$30, X = \$31, T = 0.5, σ = 0.25, r = 0.06. 1 2

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OPTION GREEK: GAMMA J. Wei, Department of Management, U of T 4 MGTD78 change of option’s or portfolio’s delta w.r.t. change of stock price gamma is the highest at S = X, and goes to zero as S → 0 or S → ∞ (see Figure 3.5 in book) small gamma: delta changes slowly rebalancing of delta-neutral portfolio needn’t be too frequent gamma neutral: If portfolio’s gamma is Γ and an option’s gamma is Γ T then adding w T units of options can make the portfolio T 2 e S P S C 2 d - 2 2 2 2 2 1 π = = = Γ
OPTION GREEK: GAMMA J. Wei, Department of Management, U of T 5 MGTD78 Example: Continue the previous delta example,

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OPTION GREEK: GAMMA J. Wei, Department of Management, U of T 6 MGTD78 can add two options to portfolio to make delta and gamma neutral example: Your portfolio’s delta and gamma are 0.56 and 1.4 respectively. There are two options available for hedging with following information: delta gamma Option A (call) 0.48 0.96 Option B (put) -0.66 1.20 How many options of each to hold in order to make your portfolio both delta- and gamma-neutral?
OPTION GREEK: VEGA J. Wei, Department of Management, U of T 7 MGTD78 change of option’s or portfolio’s value w.r.t. change of volatility vega is the highest at S = X, and goes to zero as S → 0 or S → ∞ (similar to gamma, see Figure 6.6 in book) vega neutral:

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## This note was uploaded on 05/10/2011 for the course MGT D78 taught by Professor Wei during the Spring '11 term at University of Toronto- Toronto.

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2_option_greeks - OPTION GREEKS, HEDGING AND INTEREST RATE...

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