Question

PLEASE ANSWER ALL QUESTIONS PLEASE.

1A.) What is the forward price (formula) for an asset that provides no income using the parameters of S0 , risk-free rate r (annual rate with continuous compounding), and time to maturity of T? Using this formula, if the spot market price of gold is given as 1715 per ounce, the risk-free rate is 1% per annum with continuous compounding, and two years to maturity, what is the fair price for a two-year forward contract?

b.) What is the forward price (formula) for an index that provides a dividend yield of q, with a current market price of S0 , risk-free rate r (annual rate with continuous compounding), and time to maturity of T? Using this formula, if the current market price of an index is 2868, the risk-free rate is 1% per annum with continuous compounding, a dividend yield of 2% per year, and two years to maturity, what is the fair price for a two-year forward contract?

C.) What is the valid forward price range (formula) for a consumption asset that requires a storage cost of U paid up front, with a current market price of S0 , risk-free rate r (annual rate with continuous compounding), and time to maturity of T? Using this formula, if the current market price of crude oil is $25, the risk-free rate is 1% per annum with continuous compounding, a storage cost of $5 per year, and one year to maturity, what is the fair price range for a one-year forward contract? If the one-year forward contract price is $50 per barrel, is there an arbitrage opportunity? If so, what actions do you want to take

and what’s the associated profit?

2.A.) Describe how an interest rate swap works. In addition, if your company is

concerned that interest rate might go up and wants to take advantage of today’s low interest rate, will you choose a pay-fixed-and-receive-floating-rate swap or a pay-floating-and-receive-fixed-rate swap?

B.) Describe how a currency swap works. In addition, if your company wants to obtain 100 million Euros this year to invest for the coming five years and will end the project after five years, how would you design the swap contract?

C.) Describe how a credit default swap works. In addition, if we bought corporate bonds on TSLA, how can we use a CDS to protect our position?

Answer #1 A-C. Pertaining to options. Please. #2 is about SWAPS. It would be greatly apprciated

Answer 1

1.

A) Using the cost of carry model, the forward price of the asset is simply the Future value of the Asset

F0 = S0*exp(r*T)

Fair price of the 2 year forward contract on gold

F0 = 1715* exp(0.01*2)

= 1749.65

So, Fair price of forward = $1749.65 / ounce

b) Forward price (formula) for an index that provides a dividend yield of q, with a current market price of S0 , risk-free rate r (annual rate with continuous compounding), and time to maturity of T is given as

F0 = S0*exp((r-q)*T) - assuming that yield q is continuously compounded

F0 = S0*exp(r*T)/(1+q)^T - assuming that yield q is annually compounded

So, fair price for a two-year forward contract

F0 = 2868*exp((0.01-0.02)*2) = 2811.21 using continuous compounded yield

F0 = 2868*exp(0.01*2)/(1.02)^2 = 2812.32 using Annually compounded yield

c) The Upper Bound of the Price of a consumption asset is given by

F0 = (S0+U)*exp(r*T) and the lower bound can be taken to be 0 (depending upon the convenience yield of the consumption asset)

So, F0 = (25+5)*exp(0.01*1) = 30.30151 or $30.30/barrel

So, fair price range is $0 < F0 < $30.30151/barrel

Now,

If the one-year forward contract price is $50 per barrel, there is an arbitrage opportunity

Arbitrage steps

1 Buy 1 barrel of Crude oil spot at $25 and pay the storage cost of $5/barrel per year.

Borrow the amount of $30 to do the same. at 1% . Repayment amount = $30.30

2. Simultaneously, sell the forward contract for 1 barrel of crude oil at $50

3. After one year, sell the crude oil barrel using forwards at $50 , repay the loan of $30.30 and take the arbitrage profit of $19.70 per barrel