4.
Download the time series for S&P500 from Yahoo finance for the period of Jan.
3, 1975 - March 4, 2016 with daily, weekly and monthly sampling.
a)
For each sampling frequency, provide summary statistics for S&P500
returns, which include mean, median, maximum, standard deviation,
skewness and kurtosis. Compare the annualized mean and standard
deviation among different sampling frequency. What are your
observations?
4
b)
Divide the time series into 4 sub-sample periods: 1975-1986, 1987 –
1999, 2000-2016, and 2015 - 2016. Use the daily return time series to
compute annualized summary statistics for these sub sample periods and
summarize your observations in comparison to the summary statistics
obtained for the entire sample period.
c)
In the morning on March 30, 2016, S&P 500 was traded at 2063. There
were call options written on S&P500 with a strike price of K=2050 and
maturity of June 2016. The annualized continuous compounded interest
rate is 2% and the annualized dividend yield is 0.2%. Use the estimated
return volatilities from parts (a) and (b) to compute the Black-Scholes
option values. What are your observations on the calculated call values?