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# P1.T4.819. Theta, gamma and vega for option positions (Hull Ch.19)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
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Learning objectives: Define and describe theta, gamma, vega, and rho for option positions.

Questions:

819.1. At a cost of $43,700.00, Robert enters a long position in 100 at-the-money call option contracts; each contract is for 100 call options. The premium cost is$4.37 per option and the options expire in about three months (60 trading days). The per-option theta is -9.630 per year. There are 250 trading days in a year. He wants to estimate the effect of "time decay" on his position. If twenty trading days (+ 20 days) elapse, but there is no change to the stock price, volatility, or risk-free rate, then what is the expected impact on his position?

a. Loss of about $337.00 b. Loss of about$7,700.00
c. Gain of about $337.00 d. Gain of about$7,700.00

819.2. After Barbara wrote (i.e., sold) 100 put option contracts, the trade's position delta was +7,200. The put options were in-the-money as the stock price was $70.00 while the options' strike price was$100.00. Each contract was for 100 put options. The percentage gamma of each put option was +0.0120. If the stock price subsequently, immediately decreased $10.00 to$60.00, which is nearest to an estimate of the trade's new position delta?

a. -3,500
b. +7,200 (unchanged)
c. +8,400
d. +11,900

819.3. Patricia has a short position in 100 put option contracts where the per-option (aka, percentage) vega is 33.50 and the stock's volatility is 30.0% per annum. The value of each option is $8.77 and each contract is for 100 options. If the volatility jumps by +5.0% to 35.0%, which is nearest to the estimated change in her position's value? a. Loss of$16,750.00
b. Loss of $4,385.00 c. Loss of$1,469.00
d. Gain of \$4,385.00

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