# Question: a using the following data for beta ltd calculate the...

###### Question details

a. Using the following data for Beta Ltd., calculate the value of a call option and a put option

using Black-Scholes formula:

Current share price =$170

Exercise price = $155

Interest rate per annum = 6%

Dividend yield per annum = 2%

Time to expiration = 6 months

Standard deviation = 0.30 per annum.

b. Assume you have purchased 50,000 equity shares of a listed company in Australia and want to

sell these shares after 6 months to buy a house in Sydney. A call option and a put option on these

shares are currently selling at $3 and $2, respectively. The exercise prices of the call and put

options are $110 and $90, respectively. You intend to use either a protective put, a covered call, or

a collar to protect the value of your portfolio. Calculate the value of your portfolio after 6 months

for the following three market prices: $120, $100 and $80. Out of the above three strategies,

which one is the best strategy? Justify your answer based on the calculations you have performed.

10 marks

c. Using the data in a., calculate the value of the put option using the put-call parity relationship.

If the current market value of the put option $5, explain the action you would take.

d. Using your calculations for part a. find out the values of hedge ratios for the call and put

option, respectively? Interpret the values of these hedge ratios.

e. Using your calculations for part a. calculate the elasticity of the call option and interpret its

value.

f. Suppose you consider two portfolios. One holding 1000 calls and 300 shares of Beta company

and the other holding 900 shares of Beta company. Using appropriate calculations explain which

portfolio has greater dollar exposer Beta’s price movements.