Explanation:
To hedge Gamma and Vega, the sum of the Greeks from the position and the hedging instruments must equal zero. Let be the number of Call Option 1 contracts and be the number of Call Option 2 contracts.
We set up the following system of equations based on the Greeks:
Gamma: $100 + 0.25w_1 + 0.1w_2 = 0100` + 30w_1 + 10w_2 = 0$
From the Vega equation:
$10w_2 = -100 - 30w_1 \Rightarrow w_2 = -10 - 3w_1$
Substitute into the Gamma equation:
$100 + 0.25w_1 + 0.1(-10 - 3w_1) = 0100+ 0.25w_1 - 1 - 0.3w_1 = 0$
Substitute back into the equation:
Anna should buy 1,980 contracts of Call Option 1 () and sell 5,950 contracts of Call Option 2 ().
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Q.76 Anna Frost is a junior options trader at an investment bank. She recently finalized a non-standardized options contract with a new client. The option had the following Greeks:
| Delta | 25 |
|---|---|
| Gamma | 100 |
| Vega | 100 |
Although Frost’s supervisor does not mind bearing the risk of the changes in the price of the underlying, he is not comfortable with the Gamma and Vega risk exposures and asks Frost to hedge her position. At the moment, she has the following two options available on the market:
| Call Option 1 | Call Option 2 | |
|---|---|---|
| Delta | 0.55 | 0.85 |
| Gamma | 0.25 | 0.1 |
| Vega | 30 | 10 |
Which trades should Anna undertake to accomplish her supervisor’s task?
A
Buy 2,131 contracts of Call Option 1 and sell 5,639 contracts of Call Option 2
B
Sell 1,980 contracts of Call Option 1 and buy 2,131 contracts of Call Option 2
C
Buy 5,950 contracts of Call Option 1 and buy 1,980 contracts of Call Option 2
D
Buy 1,980 contracts of Call Option 1 and sell 5,950 contracts of Call Option 2