ACCA Strategic Professional · Advanced Financial Management · Application of option pricing theory in investment decisions
A European call has share price 100, exercise price 100, risk-free rate 5% per year (continuously compounded), volatility 20% per year and one year to expiry. What is the value of d2 in the Black-Scholes model?
d2 is 0.15. First compute d1 as (0 + 0.05 + 0.02) divided by 0.20, which gives 0.35. Then subtract volatility times the square root of time, 0.20, to get d2 of 0.15.
- A0.15Correct
- B0.35
- C0.05
- D0.55
Explanation
d1 = [ln(100/100) + (0.05 + 0.5 × 0.2²) × 1] / (0.2 × 1) = 0.07/0.20 = 0.35. d2 = d1 − σ√T = 0.35 − 0.20 = 0.15. The figure 0.35 is d1 itself. The figure 0.05 comes from omitting the σ²/2 term in d1 (0.25) and then subtracting 0.20. The figure 0.55 comes from adding σ√T instead of subtracting it.
Did you get it right without looking?
One question tells you little. A timed set on Application of option pricing theory in investment decisions shows your real accuracy, how long you take and where you lose marks.
More Application of option pricing theory in investment decisions questions
- Zeta Co has assets worth $100m and a single zero-coupon debt issue with a face value of $80m due in one year. Using option pricing, equity i…
- The monthly standard deviation of continuously compounded returns on a comparator company's shares is 4.0%. Assuming returns are independent…
- A company values a project's option to delay using the Black-Scholes model. Which of the following is a recognised limitation of applying th…
- Daily share price returns of a proxy company have a standard deviation of 1.5%. Assuming 250 trading days in a year and independent returns,…
- A share is priced at $80 and will pay a dividend before the options expire, with a present value of $3. A European put with an exercise pric…
- A European call on a non-dividend-paying share is priced at 9. The share price is 98 and the exercise price is 100, with one year to expiry.…