FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A European call and a European put on the same non-dividend-paying stock have the same strike and maturity. The call has a vega of 0.18 per one percentage point change in volatility. A trader is long 1,000 calls and long 500 puts, with each contract covering one share. By how much does the portfolio value change if implied volatility rises by 2 percentage points?
The portfolio gains USD 540. Put and call vega are equal for the same strike and maturity, so the 1,500 long options each gain 0.18 per volatility point. Multiplying 1,500 by 0.18 by 2 points gives USD 540.
- AUSD 270
- BUSD 360
- CUSD 540Correct
- DUSD 180
Explanation
By put-call parity, call and put vega are equal at 0.18 per point. Total options = 1,000 + 500 = 1,500. Change = 1,500 x 0.18 x 2 = USD 540. USD 360 counts only the calls; USD 270 uses only one point of volatility.
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