Financial engineering

1. Bond and Yield curve
   Each group should collect daily information on bonds issued by the Government of Canada from a source such
   as database Datastream, center for research in security prices, newspaper for two weeks. Calculate the yield
   curve for each day using bootstrap method. The yield curves should present for the next 20 years, using at
   least 5 bonds. If necessary, you can also round the day counting to nearest month.
   Code or source file, detailed explanation, and calculation for the construction of, at least, ONE yield curve have
   to be presented in the report in order to get full marks. The behavior of each curve should be explained clearly.
   Similarly, you pick a company and its published bond information to calculate the yield curve for that company.
   Follow the same procedure as you did for the Government of Canada bond.
2. Portfolio
   Collect daily share price data for four companies for a year and calculate daily return. Present the daily return
   data using a distribution. Assume market is determined by S&P 500. Calculate of each company using
   different methods that you learnt in this course, and discuss about the values that you obtained for . Establish
   the efficient frontier for the portfolio of the four companies and determine the efficient portfolio.
3. Fitting geometric Brownian motion and mean-reverting process
   Each group need to collect daily foreign exchange rates between Canada and another country (each group
   should have different exchange rates) for at least 2 years. Fit the exchange data into geometric Brownian
   motion and mean-reverting processes. Justify the results you obtained.
   1
   Code or source file, detailed explanation, and calculation for the processes should be provided.
4. Option pricing
   Collect daily price of a stock for year 2019 and fit the data into a geometric Brownian motion (GMB). Then,
   using Mote Carlo simulation for 1000 sample paths, calculate at the money European call and put options.
   Repeat the process with 2000, 4000, 6000, 8000, 10000, and 12,000 sample paths. Plot the call and put
   options prices against the number of sample paths. Now, determine the values of the call and put options
   applying the Black-Scholes model. Compare and explain the results you obtaine

Sample Solution