FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
A market maker is short options with portfolio delta of 0 and portfolio gamma of -4,000. The underlying then moves by $3 in either direction, with no time passing and no change in volatility. Using the delta-gamma approximation, what is the estimated change in portfolio value?
The portfolio loses about $18,000. With delta zero only the gamma term matters: 0.5 x (-4,000) x 3^2 = -$18,000. Negative gamma means losses for a large move in either direction, regardless of its sign.
- A+$18,000
- B-$6,000
- C+$6,000
- D-$18,000Correct
Explanation
With zero delta, dV = 0.5 x gamma x dS^2 = 0.5 x (-4,000) x 9 = -$18,000. The loss occurs for moves in either direction because gamma is negative. A positive sign would wrongly treat the position as long gamma.
Did you get it right without looking?
One question tells you little. A timed set on Option Sensitivity Measures: The "Greeks" shows your real accuracy, how long you take and where you lose marks.
More Option Sensitivity Measures: The "Greeks" questions
- A trader holds a European call option on a non-dividend-paying stock with a delta of 0.60. The stock price rises by USD 1.00, and no other i…
- A European call has a rho of 36.0 per 1.00 (100%) change in the continuously compounded risk-free rate. If the rate rises from 3.00% to 3.50…
- A European put and call have the same strike and expiry on a non-dividend-paying stock. Using put-call parity, which expression correctly li…
- A portfolio manager combines three option positions on the same underlying. Position A has delta 1,500 and gamma 300; position B has delta -…
- A European call and a European put on the same non-dividend-paying stock share strike K = 80 and maturity T = 2 years. The continuously comp…
- Which factor would cause the absolute value of theta of an at-the-money European call option to increase most sharply, holding other inputs …