C31DE-Sample Exam Paper & Black Scholes Formula - Accounting & Finance Assignment Help

Assignment Task

Task 

SECTION A
 

Question A
Consider a non-dividend paying share with a current price of 420 pence and constant volatility (standard deviation) of 25%. Assume that the annual risk-free rate is constant at 5%.
The Black-Scholes option pricing formula for a European call option on a non-dividend paying share is given by

a) Use the Black-Scholes formula, together with the put-call parity, to calculate fair theoretical prices for a European call option and a European put option on the above share assuming that these options have the same exercise price of 450 pence and time to maturity of six months.

b) If the put option mentioned in part a) is actually selling for 5 pence less than its fair  price calculated in part a), but the call option is selling for the same price as that  calculated in part a), describe in detail a riskless arbitrage strategy, involving both  options, that takes advantage of this mispricing. Assume that the Black-Scholes  equation, together with the put-call parity, is the correct model for pricing options.

c) Briefly describe the terms: implied volatility and option smiles.

d) An investor would like to hedge a portfolio containing 1000 of the shares mentioned in this question, using European call options. How many call options does this investor have to buy or sell, and what is the total cost of this hedging strategy? Assume that.

f) fractions are allowed and indicate whether this investor has to buy the options or sell them.

e) How the investor, mentioned in past d), would hedge the portfolio of WOO shares by using European put options instead? Indicate how many puts this investor has to buy or sell assuming fractions are allowed.

f) Compare and contrast the costs involved in the hedging strategies of parts d) and e), and discuss the issues involved in deciding on one strategy than the other.

SECTION B
Question B1
(Answer either this question or Question 3)
a) Briefly describe the initial margin, maintenance margin, and marking-to-market procedure of futures markets. Why are these margins and procedure necessary?

b) Assume that the spot Yen/Dollar exchange rate is 90. Assume further that annualised interest rates for three-month risk-free deposits are 2.25% in Japan and 5.5% in the US. Answer the following stating your assumptions.

i) What is a fair theoretical forward price of a three-month YenfDollar futures contract?

ii) Why the price calculated in a) is referred to as the theoretical price? (5 marks)
iii) If the contract is quoted in the derivatives market at 85 Yen/dollar, discuss in detail an arbitrage strategy that would exploit any mispricing. Consider the stance of a buyer of Yen.

iv) If according to the evaluation model used in i) the contract is mispriced, briefly discuss the possible reasons for such mispricing?

c) Company Xis based in the United Kingdom and would like to borrow $30 million for 5 years in US funds. Because the company is not very well known in the UnitedStates, this has proved to be impossible. However, it can borrow an equivalent amount in Sterling funds for 5 years at 4% coupon. The spot exchange rate is $1.5 per a pound Sterling. Company Y is based in the United States and would like to borrow £20 million for 5 years. It has been unable to get a quote but has been offered US dollar funds at 7% coupon. Assume a flat term structure and that interest rates (annual yields-to-maturity) for five-year default free bonds are 4% in the UK and 7% in the US. Answer the following:

i) Consider a swap agreement in which the two companies might be interested in entering. What would be the current value of such a swap? Show your calculations.

ii) If at the end of the first year interest rates are 5% in the UK and 8% in the US and the exchange rate is $1.55 to the pound. What is the S and f values of the swap for the party paying S and receiving f?

iii) Following part ii), what is the S and £ values of the swap at the end of the first year for the counter party?

iv) State your assumptions for the above calculations.

Question B2
(Answer gig= this question gr Question 2)
a) Consider the following quoted discounts currently posted for two Treasury Bills and a Futures contract that delivers a 3-month Treasury Bill.

Answer the following.
i) Is the futures contract priced as per the theoretical arbitrage valuation model? Show your calculations.

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