Financial risk management 2 | Business & Finance homework help

1.

Suppose the spot exchange rate between the US dollar and Canadian dollar is US$0.75/C$. The Canadian dollar and US dollar risk-free rates are 2.5% and 1.5% per annum, respectively, compounded annually. The price of a two-year European call option with an exercise price of US$0.76/C$ is US$0.03. What is the price of the option in US dollars if it is a put?

(6 marks)

2.

In a quote, the spot US dollar/Canadian dollar exchange rate is C$1.30/US$, and the six-month forward exchange is C$1.32/US$. The interest rates of the Canadian dollar and US dollar are 2.5% and 1.5% per year, respectively. Assume that you can lend or borrow at those rates in both currencies. Is there any “free lunch” in this market?

(8 marks)

3.

Suppose that the US dollar interest rate is 2% per annum and Canadian dollar interest rate is 3% per annum for all maturities, annually compounded. The current exchange rate is US$0.75/ C$. Under the terms of a swap agreement, a bank receives 4% per annum in Canadian dollars and pays 5% per annum in US dollars. Payments are exchanged every year, with one exchange having just taken place. The principal amounts are C$14 million and US$10 million. The swap will last two more years.

a.

Determine the cash flows to the bank.

(4 marks)

b.

What is the value of the swap to the bank in terms of Canadian dollars?

(6 marks)

4.

CP Financial owns a $10 million 10-year maturity, non-callable corporate bond with a 6.8% coupon paid annually. The company pays annual LIBOR minus 1% on its three-year term time deposits.

VG Corporation owns an annual pay LIBOR floater and wants to swap this variable rate for a fixed rate.

CP and VG enter into a $10-million plain vanilla interest rate for three years in which CP receives annual LIBOR.

The spot term structure of LIBOR is as follows:

Years to maturity

LIBOR rate (c.c.)

1

5.0%

2

5.2%

3

5.5%

   

a.

Determine the swap rate.

(8 marks)

b.

Diagram the cash flows between CP, VG, CP’s depositors, and CP’s corporate bond. Label the following items:

  • CP, VG, CP’s depositors, and VG’s corporate bond
  • the applicable interest rate at each line, specifying whether it is floating or fixed
  • the direction of each of the cash flows.

(6 marks)

c.

Calculate the first net swap payment between CP and VG, and indicate the direction of the net payment amount.

(4 marks)

5.

Linda longs a FRA on three-month LIBOR with a fixed rate of 8.75% and a notional principal of $20 million. If the market LIBOR rate is 9% at expiration, what would be the payoff of the FRA to Linda?

(5 marks)

6.

Are a long cap and a short floor with the exercise price set at the swap rate equivalent to a swap? Explain.

(10 marks)

7.

A portfolio consists of 100,000 shares of stock A and 500,000 of stock B. Currently, the price of stock A is $80, and the price of stock B is 40. Stock A has an expected return of 15% per annum and a volatility of 20% per annum; stock B has an expected return of 20% per annum and volatility of 30% per annum. The correlation coefficient between the two stocks is 0.6. What is the daily 95% VAR?

(12 marks)

8.

Consider three calls—Call 1, Call 2, and Call 3—all written on the same underlying stock, with the following information:

Current price of the underlying stock: S = $80
Volatility of the stock: sigma equals zero point 2
Risk-free interest rate: r = 0.07

Option

Strike price

Days to maturity

Option price

Delta

Gamma

Call 1

70

90

11.40

0.94

0.015

Call 2

75

90

7.16

0.81

0.034

Call 3

80

120

 

4.60

 

0.60

0.042

 

             

a.

If the stock price rises to $80.10, what is your “best” estimate of what the Call 1 price will be?

(5 marks)

b.

Using Call 1 and Call 2, create a delta-neutral portfolio assuming that the position is long one Call 1.

(5 marks)

c.

Use all three calls to form a portfolio that is delta-neutral and gamma-neutral, assuming the portfolio is long one Call 1.

(5 marks)

9.

A portfolio consists of 400 shares of stock and 200 calls on that stock. If the delta for the call is 0.6, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

(6 marks)

10.

Explain the difference between centralized and enterprise risk management.

(10 marks)

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