• April 12th, 2016

Finance Derivatives and Future Contracts

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Question 1

 

Consider the UK production company Ascot, producing laptop screens, that in a half a year expects a supply of an important element in its production process. The supplier is a German company so the company will have to pay to the supplier 175,000.00EUR in half a year. Current exchange rate is 0.83GBP/EUR and Ascot expects the Euro will appreciate so it will turn unprofitable for the company to produce laptop screens. Ascot considers hedging the exchange rate risk with derivatives. The following derivatives are available for them on the market:

Type of derivative Size of contract Maturity of the derivative (time from now) Strike price (in GBP) Futures price (in GBP) Current price of derivative (in GBP)
futures contract 1,000 Euros 3 months 834.160
futures contract 1,000 Euros 6 months ?
futures contract 1,000 Euros 9 months 842.544
European call option 1,000 Euros 6 months 840 35.580
European call option 1,000 Euros 6 months 830 ?
European put option 1,000 Euros 6 months 840 ?
European put option 1,000 Euros 6 months 830 32.289
American call option 1,000 Euros 6 months 830 44.210
American put option 1,000 Euros 6 months 830 35.332?
American futures call option 1,000 Euros 6 months (the same as futures maturity) 830 ? 47.500
American futures put option 1,000 Euros 6 months (the same as futures maturity) 830 ? 33.466

 

Assume that the GBP/EUR exchange rate volatility is 16% and interest rates for UK and Euro area (annualized, continuously compounded) are the following:

  3-month rate 6-month rate 9-month rate
UK 7% 8% 9%
Euro area 5% 6% 7%

 

  1. a) Some elements of the table are denoted as questions marks “?”. Find these values, i.e. specifically find the following:
  • (i)  futures price of a 6-month futures contract (size of contract is 1,000 Euros)
  • (ii)  price of a 6-month European call option with a strike price of 830 Pounds (size 
of contract is 1,000 Euros)
  • (iii)  price of a 6-month European put option with a strike price of 840 Pounds (size 
of contract is 1,000 Euros)
  • (iv)  current futures prices underlying the American call and put futures options for 
which futures mature in 6 months (size of each contract is 1,000 Euros)
  • b)  Using a two-step binomial pricing model, find the current value of the 6-month American put option with strike price of 830 Pounds. Compare it with the price from the table and comment on this comparison.
  • c)  Explain how the company can hedge their exchange rate risk with the derivatives available to them as specified in the table. In your explanations be specific about the quantities of the derivatives that the company needs to buy/sell (individually or as a portfolio) as well as the benefits and costs of that.
  • d)  Explain why futures options might be preferred to the spot options for the same asset underlying option and futures contract.

 

Question 2

Consider the following borrowing rates offered to company X and company Y for a £100 million loan:

  Fixed rate per annum (compounded semianually) Floating rate
Company X 5.0% 6-month LIBOR
Company Y 6.1% 6-month LIBOR+0.4%
  1. a) If company X requires a floating rate loan and company Y requires a fixed rate loan, should the two companies enter a swap? Explain the reason.
  2. b) Suppose you represent a bank, which acts as an intermediary in swap deals. Design a swap that is equally attractive for company X and Y that will give your bank 0.1% per annum. Demonstrate your answer with appropriate diagrams and calculations.
  3. c) Since the swap you proposed is a fair deal, company X and Y entered the swap contract in January 2015 for 3 years. Given the following data obtained from the bond market on January 2015:
Bond principal (£) Time to maturity (years) Annual coupon (£) Bond price (£)
100 0.25 0 97.5
100 0.5 0 94.9
100 1 0 90
100 1.5 8 96

 

100 2 14 105

 

Coupon bonds pay coupon semi-annually. What is the value of the swap contract at January 2016 just right after the coupon payment? Does company X gain or lose from the swap contract at this point in time?

 

Question 3

On 01-May-2014, a bank made a loan to company X. The loan has a principal of £10 million and should be paid back after 2 years. For simplicity, assume that the term structure of interest rates is flat. The risk-free rate is currently 5% per annum, continuously compounding. Credit rating of company X is currently B, and the rating can change each year. The yearly risk-neutral probability is given below:

Rating at the beginning of the year

 

Rating at the end of the year
A B C Default
A 0.9 0.05 0.04 0.01
B 0.04 0.85 0.06 0.05
C 0.00 0.04 0.80 0.16

 

In case of default, the recovery-rates for an A-rated, B-rated and C-rated firm are 65%, 40% and 30% of the promised payment respectively. If company X defaults before the loan matures, the bank will receive the present value of the recovery.

  • a)  Plot the tree diagram of how the credit rating of company X evolves in year 1 and year 2. Use the information from the tree to compute the total probability that the firm will survive until the loan matures.
  • b)  Find the current value of the loan per year. What is the present value of expected loss on 
the loan?

 

Question 4

  • a)  You are considering buying an oil futures contracts traded at NYMEX (NYMEX Brent 
Crude Oil Futures). You are interested in the following two contracts:

Contract 1: for 1000 barrels of oil and delivery in one year exactly

Contract 2: for 1000 barrels of oil and delivery in two years exactly

The prevailing interest rates (continuously compounded) are the following: 6-month rate 0.05%, 12-month rate 0.10%, 18-month rate 0.18%, 24-month rate 0.30%, per annum and we can assume that they will be held constant for at least next two years. There is a fixed cost of $3 per barrel related to storing oil (paid at the end of each half a year, with the next payment in 6 months). Current price of oil is equal to $68 per barrel.

Compute the futures price for the two contracts. Assuming that the price of oil will be constant over the next half a year, do you expect the futures prices to increase or decrease over that period? Give reasons in your answer; it is suggested you use relevant computations to justify your answer.

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