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.

(4 marks)

3. As part of the presentation to junior members of staff your supervisor has asked you to do the following: -

1. 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

(Maximum wordcount:120 words)

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

(Maximum wordcount:120 words)

Answer 1

a) The Formula for Black Scholes model to find out call and put option pricing is :

So Here

First we have to find out d1

d1 = {ln(38/47)+(0.03+0.25^2/2)*1} / (0.25*1)

= -0.15/0.25 = -0.61 (approx) [note. you can find the value of LN thorugh tables or financial calculator or excel]

d2 = -0.61 - 0.25*1 = -0.86 (aprrox.)

C = 38 x N(-0.61) - 47 x e^-0.03*1 x N(-0.86)

= 1.406 approx.

[ note in excel just type {=NORMSDIST(the value of d)} without using curly brackets and enter you find the value of N(d) ]

limitations:

• Assumes constant values for risk free rate of return and volatility over the option duration—none of those may remain constant in the real world
• Assumes continuous and costless trading—ignoring liquidity risk and brokerage charges
• Assumes stock prices to follow lognormal pattern, e.g., a random walk (or geometric Brownian motion pattern)—ignoring large price swings that are observed more frequently in the real world
• Assumes no dividend payout—ignoring its impact on the change in valuations

b) Put option valuation:

Formula :

P = 1.4061 + 47 x e^-0.03*1 - 38

= 9.017 (approx.)

c)

Differences:

Call option and Put option: A call option is the right to buy an asset at an agreed-upon exercise price.

Put option: A put option is the right to sell an asset at a given exercise price

European option: in this the buyer of option cannot exercise the option before the maturity date

American option : in this the buyer of either of the option can exercise the option before the maturity date also

Long Position : it refers to the buying of the option ( in the context of buyer)

short postion: basically means writing the option ( in the context of seller)

d) another method of calculating option prices is Binomial Distribution method.

thanks

plz rate the answer and give feedback