Individual Assignment This assignment is worth 25% of the final mark for FIN201 Financial Mathematics. The cut-off date for this assignment is 31 October 2016, 2359hrs. In this assignment, you are expected to: • Use a computing tool (e.g. Excel/Google Spreadsheets or Python) for financial calculations. • Use a financial information system (e.g. Reuters Eikon, or the Internet) for obtaining market data and information as well as harnessing well-documented API/library/models to make inferencing more expedient. ___________________________________________________________________________ Question 1 The term structure is a basic device that provides a snapshot of the interest rate environment in terms of borrowing costs across terms. (a) Describe how the term structure of zero coupon yields is constructed starting from a set of yields of par bonds across terms. (10 marks) (b) Be sure to express your answers clearly in your own words, based on your own understanding, with Python as an aid in your calculations and reasoning. (10 marks) (i) Calculate the 2-year, 3-year and 4-year zero-coupon yields and discount factors consistent with the following bonds. The 1-year yield is 10.00%. Maturity Coupon Price 2 Years 9.0% (Annual) 97.70 3 Years 7.0% (Annual) 90.90 4 Years 11.0% (Annual) 99.40 What are the 1-year v 2-year, 2-year v 3-year and 3-year v 4-year forward-forward yields? (ii) The forward-forward curve is as follows: 1-year yield: 8.00% 1-year v 2-year 8.24% 2-year v 3-year 9.00% 3-year v 4-year 9.50% (1) Calculate the 2-year, 3-year and 4-year zero-coupon yields and par yields. (2) What is the yield to maturity of a 4-year 12% annual coupon bond, consistent with the rates above?   Question 2 The interest rate parity is a fundamental notion that is applied to relate exchange rates with interest rates. (a) Describe the relationship between exchange rates and interest rates in the interest rate parity. (10 marks) (b) Be sure to express your answers clearly in your own words, based on your own understanding, with Excel as an aid in your calculations and reasoning. (10 marks) (i) The EuroSterling interest rate for 1 year (exactly 365 days) is 6%. The EuroSwiss Franc interest rate for the same period is 3%. The spot rate today is GBP/CHF 1.3580 / 90. What would you expect the GBP/CHF swap price to be for 1 year forward? (Ignore the buy-sell spread and calculate the middle price only.) (ii) Spot 3-month forward swap USD / SGD 1.2340 / 45 29 / 32 USD / CAD 0.9720 / 40 46 / 59 GBP / USD 1.6490 / 00 268 / 265 Based on the prices above, what are the two-way prices for: 1) CAD / SGD spot? Which side does the customer buy SGD? 2) GBP / CAD spot? Which side does the customer sell GBP? 3) USD / CAD 3 months forward outright? 4) GBP / USD 3 months forward outright? 5) GBP / CAD 3 months forward outright? Which currency has higher interest rates? 6) CAD / SGD 3 months forward outright? Which currency has higher interest rates? 7) CAD / SGD 3 months forward swap?   Question 3 The equity option market is closely linked to the stock market but at the same time it is structurally different from the latter. (a) Describe three (3) significant features of the option market that distinguish it from the stock market and two (2) ways that the two markets are closely linked. (10 marks) (b) Be sure to express your answers clearly in your own words, based on your own understanding, with Python as an aid in your calculations and reasoning. (10 marks) (i) What is the estimated annualised volatility of the GBP / USD exchange rate, based on the following daily data, assuming the usual lognormal probability distribution for relative price changes and 252 days in a year? Day 1 1.6320 Day 2 1.6410 Day 3 1.6350 Day 4 1.6390 Day 5 1.6280 Day 6 1.6300 Day 7 1.6250 Day 8 1.6200 Day 9 1.6280 Day 10 1.6200 (ii) Construct a three-step binomial tree to calculate a price for a 3-month put option on as asset at a strike of 101. The current price is 100. At each step, the price either rise or falls by a factor of 2% (that is, either multiplied by 1.02 or divided by 1.02). The risk-free interest rate is 12% per annum.   Question 4 Augustin manages bonds in the fixed income arm of a private equity company. He holds a portfolio of the following bonds: Bond Coupon rate Maturity Number of bonds a 4.5% 0.5 year 500 b 5.5% 1 year 750 c 6.5% 1.5 years 1000 d 5% 2 years 600 Augustine collects the following data on government bonds: Maturity Coupon rate Yield 0.5 year 0% 3% 1 year 0% 3% 1.5 years 3% 2 years 5% Assume that every bond in question has a face value of SGD 1000 and pays coupons semi-annually, and the 1.5y and 2y government bonds are issued at par. (a) Compute all the zero coupon discount factors from the information given. (10 marks) (b) Calculate the current value of Richard's bond portfolio. (10 marks) Show your workings clearly with calculations performed with Excel.   Question 5 Answer the following questions on option pricing. (a) Suppose that a call option and a put option have the same characteristics (i.e. same underlying, strike price and time-to-maturity) and are European. Describe, using a graph, the payoff of the position in which the call option is long and the put option is short. (6 marks) (b) Suppose that the stock price of a company X is currently USD 200, has a volatility of 30% and the prevailing risk-free rate is 2%. Find, by applying the Black-Scholes formula, the price of an at-the-money put option that matures in 3 months. Who in the financial market would quote an option price this way? (7 marks) (c) Suppose that the stock price of a company Y is currently USD 250, has a volatility of 25% and the prevailing risk-free rate is 2.5%. What is the hedging position in the stock for an option writer who has sold an at-the-money 6-month call option 3 months ago? (7 marks) Show your workings clearly with calculations performed with Python. ---- END OF ASSIGNMENT ----