Question

You are working for an investment firm in the City of London and have been asked to perform some analysis of the European-style call options of a company called Elevation Matters Plc (EM).

The most recent closing share price for EM was £38. The risk-free rate is 3%. The time to expiry for the options is one year. The volatility (standard deviation) of EM’s shares is 25% and the company has decided not to pay any dividends this year.

On the basis of these forecasts, you been asked to estimate the option premiums for a strike price of £47.

Once the relevant premium has been estimated, your firm are planning to promote and sell the financial products to all prospective clients and to use this analysis as a tool for explaining share options to junior members of staff.

Required:

1. Using the Black-Scholes option pricing model, calculate the call premium price for the shares of EM

State four limitations of the model.

Note: that d1and d2 should be estimated to two decimal places

2. Calculate, using the call-put parity theory, the put premium at the strike prices for the shares of EM.
3. As part of the presentation to junior members of staff your supervisor has asked you to do the following: -
4. Briefly explain each of these differences:

• The difference between a Call and a Put option
• The difference between a European and a US option
• The difference between the Long and the Short position

2. Explain another method of calculating the premium for a share option using any numerical example you think would assist your explanation.

Answer 1

(a)

So current stock price = 38

K strike price = 47

r risk free rate = 3% = 0.03

s: standard deviation = 25% = 0.25

t: time to maturity = 1 year

d1 = -0.61

d2 = -0.86

N(d1) = normsdist(d1) = 0.273

N(d2) = normsdist(d2) = 0.196

C: value of call option

e: natural exponent

c = 1.406 (price of call option)

(b) Limitations of the Black-Scholes model

1) It assumes that the option is an European style option
2) It assumes zero dividend
3) It assumes a Normal or Log Normal distribution of prices.
4) It assumes constant volatility across different option strike prices.

(c) Price of put option using put call parity

p = 9.02 (price of put option)

Difference between call & put: call option is exercised when stock price is above strike price while put option is exercised when stock price is below strike price)

Difference between European & US option: European option can be exercised only at maturity. US option can be exercised any time between issue and maturity, depending when it comes in money

Difference between long and short position: in long position the option (or an asset) is purchased. In short position the option (or an asset) is sold