Page 156 - AFM Integrated Workbook STUDENT S18-J19

Chapter 8

Question 1

Spray Co shares are currently trading at $1.25. The risk free rate of interest is
4% and the volatility of the share price (standard deviation) is expected to be
20%.

Required:

Calculate the value of a call option over the Spray Co shares, which have
an exercise price of $1.20 and can be exercised in 3 months’ time.

Solution

The five input factors are:

P a = 1.25

P e = 1.20

r = 0.04

s = 0.20

t = 0.25 (years)

2
ln 1.25 + 0.04 + 0.5 × 0.20 × 0.25
d = 1.20
1
0.20√0.25
= 0.5582 (so 0.56 to 2 decimal places)

d =0.5582 – 0.20√0.25
2
= 0.4582 (so 0.46 to 2 decimal places)

From tables N(d 1) = 0.2123 + 0.5 = 0.7123, and N(d 2) = 0.1772 + 0.5 = 0.6772

Therefore, call option value = 1.25 × 0.7123 – 1.20 × 0.6772 × e -0.04 × 0.25

= 0.890 – 0.805 = $0.085 (8.5 cents)

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