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4) Using daily returns for the period from January 3, 2012 to January 1, 2013, create an Excel spreadsheet for volatility monitoring of NAB stock returns.
1. Provide a plot of the daily returns and squared returns.
1. Using the exponentially weighted moving average (EWMA) model, provide a plot of the estimated daily volatilities for λ=0.75, λ=0.85 and λ=0.95. To start the EWMA calculations, set the variance forecast at the end of the first day (January 3, 2012) equal to the square of the return on that day. Interpret the results with respect to the choice of λ in the EWMA model.
1. Using the Solver tool in Excel to estimate the value of λ in the EWMA model that minimizes the value of 2 for the period from January 4, 2012 to July 2, 2012. Hereby, vi is the variance forecast made at the end of day i-1 from your EWMA model and βi is the variance calculated from data between day i and day i+9 as . As in part b), to start the EWMA calculations, set the variance forecast at the end of the first day (January 3, 2012) equal to the square of the return on that day. Provide a plot of your results for the estimated value of λ. Interpret your results in comparison to your results in part b).
Now suppose that the estimated parameters in a GARCH(1,1) model that is used to monitor the volatility of NAB stock returns are ω= 0.000002, α= 0.92 and β= 0.062.
(use new spreadsheet for the following tasks of this question)
1. What is the long-run average volatility?
1. Assume that the current volatility estimate of the model is 1.122% per day. Using Excel calculate the volatility estimates in t=1, 2,…, 60 trading days. Provide a graph showing your results.
1. On July 2, 2012, what volatility should be used to price a European call option on NAB with strike price K=23 that expires on November 1, 2012 (count the number of trading days left until November 1, 2012). Using the DerivaGem software and assuming that the risk-free rate is 4%, calculate the price of the option. Further, calculate the delta, gamma and vega of the option. Using DerivaGem also provide a graph of delta, gamma and vega with respect to the price of the underlying.
