ACCA AFM · Guided practice (Show me how)
Chapter 13: Share Options and Option Pricing
Black-Scholes: valuing a call and building a delta hedge
All options are European. Share and exercise prices are in dollars; calculate option values in cents. Use years in BSOP. For the tutor calls, report each split d1 term to four decimal places before adding; report d2 to four decimal places and use d rounded to two decimals for the table. Round each call-price term to whole cents before subtracting.
(a) Madrid plc shares currently trade at $2.00. Johnson holds a call with strike $1.80 and 3 months to expiry. Consider expiry share prices of $2.50 and $1.50.
(b) Lisbon plc shares are $2.50. A call with strike $2.00 is exercisable immediately.
(c) Current share price $2.90; exercise price $2.60; expiry 6 months; risk-free rate 6% a year; volatility 40%.
(d) Current share price $1.50; exercise price $1.80; expiry 3 months; risk-free rate 10% a year; volatility 40%.
(e) Martin owns 1,000 shares in the company in (d). Use the same call to construct a delta hedge.
The normal-table extract gives the area between zero and the stated positive d.
| d | Table area |
|---|---|
| 0.34 | 0.1331 |
| 0.35 | 0.1368 |
| 0.36 | 0.1406 |
| 0.62 | 0.2324 |
| 0.63 | 0.2357 |
| 0.64 | 0.2389 |
| 0.68 | 0.2517 |
| 0.69 | 0.2549 |
| 0.70 | 0.2580 |
| 0.88 | 0.3106 |
| 0.89 | 0.3133 |
| 0.90 | 0.3159 |
(a) and (b): when an option is used, and its value today
Identify the exercise decisions for Madrid and calculate the immediate value of the Lisbon call.
(c) Black-Scholes value of a call
Calculate d1, d2, the corresponding normal probabilities and the call price in (c).
(d) A call that is out of the money
Calculate d1, d2, the corresponding normal probabilities and the call price in (d).
(e) A delta hedge
Calculate the number of calls for Martin's hedge and identify whether he should buy or sell them.
Opening this exercise…