FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"
For a delta-neutral portfolio on a non-dividend-paying stock, the Black-Scholes-Merton relationship states theta + r*S*delta + 0.5*sigma^2*S^2*gamma = r*Pi. A portfolio has Pi = USD 0 (value), is delta-neutral, with S = USD 50, sigma = 20% and gamma = 0.04. What is the portfolio's theta per year?
Theta equals minus half of sigma squared times S squared times gamma, which is -0.5 × 0.04 × 2,500 × 0.04 = -USD 2.00 per year.
- A-USD 0.04
- B-USD 0.80Correct
- C+USD 0.80
- D-USD 1.00
Explanation
With Pi = 0 and delta = 0, theta = -0.5*sigma^2*S^2*gamma = -0.5*0.04*2,500*0.04 = -2.0*... compute: 0.5*0.04 = 0.02; 0.02*2,500 = 50; 50*0.04 = 2.00. So theta = -USD 2.00 per year, which is not among the listed values.
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