### Task:

**Bonds and Yield Curve**

Download the data for the term structure of the US risk-free interest rates. Explain your choice.

a) Calculate the prices of Treasury bonds with 5, 15, and 25 years until maturity. In each case, assume the face value of $100 and the coupon rate of 6% per annum and that coupons are paid annually. Assume continuous compounding. In case your interest rates dataset does not include a required maturity, apply an average of the rates corresponding to the closest maturities. Discuss the results.

b) Calculate the yield of each bond with the use of the bisection technique. Discuss your findings. Are they consistent with the theoretical predictions?

c) Calculate the prices of Treasury bonds with 5, 15, and 25 years until maturity. In each case, assume the face value of $100 and the coupon rate of 6% per annum and that coupons are paid quarterly. Assume quarterly compounding. In case your interest rates dataset does not

include a required maturity, apply an average of the rates corresponding to the closest maturities. Discuss the results.

d) How would your results obtained in a) change in each of the following four cases (consider each of the points below separately)? Explain.

a. Quarterly compounding

b. Annual compounding

c. Simple compounding

d. Coupons being paid out semi-annually

e. Coupons being paid out annually

e) If the three bonds from a) were currently trading in the market at $110, $130, and $200, respectively, would there exist any arbitrage opportunities? Explain and provide an example.

**Futures**

Download the daily stock price data of Netflix over the period from 1 October 2020 to 30

September 2021.

a) Construct a system of monitoring the margin account for a long and short positions in the same futures contract, which has a one-year maturity and is entered into at the start of the period. Assume the following: initial margin of 30% of the futures value, maintenance margin of 80% of the value of the initial margin, continuous compounding, no withdrawals of the excess margin. Provide your own assumption for a flat risk-free interest rate and explain your choice.

b) Show graphically the evolution of the margin account over the analysed period. Clearly indicate the days on which an investor holding a long/short position in the contract would have received a margin call.

c) Discuss the implications of your findings, particularly with regards to the counterparty risk.

d) How would the outcome of the settlement change if the two parties had used a forward contract with the same maturity and price instead?

**Futures Contracts**

Download the daily data on Intel stock over the period 1 October 2020 to 30 September 2021.

Download the data for the UK risk-free rate and explain your choice of the data. Also, use the data series of the six-month futures prices provided on Moodle (assume the Intel stock as the underlying).

a) Prepare your dataset of the daily stock prices, risk-free interest rates, and the six-month futures prices to cover all the calendar days during the analysed period.

b) Calculate the theoretical six-month forward price for the stock on each day during the analysed period.

c) Compare the theoretical six-month forward price to the six-month futures price observed in the market (from the time series provided). Analyse graphically the difference between the two over time and discuss your findings.

d) Based on your analysis, can you conclude what the market’s expectations regarding the likely behaviour of the Intel stock prices and/or interest rates in the future are? Explain.

Download the data for the UK risk-free rate and explain your choice of the data. Also, use the data series of the six-month futures prices provided on Moodle (assume the Intel stock as the underlying).

a) Prepare your dataset of the daily stock prices, risk-free interest rates, and the six-month futures prices to cover all the calendar days during the analysed period.

b) Calculate the theoretical six-month forward price for the stock on each day during the analysed period.

c) Compare the theoretical six-month forward price to the six-month futures price observed in the market (from the time series provided). Analyse graphically the difference between the two over time and discuss your findings.

d) Based on your analysis, can you conclude what the market’s expectations regarding the likely behaviour of the Intel stock prices and/or interest rates in the future are? Explain.

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