Assume r = 8%, σ = 30%, δ = 0. In doing the following calculations, use a stock price range of $60-$140, stock price increments of $5, and two different times to expiration: 1 year and 1 day. Consider purchasing a 100-strike straddle, i.e., buying one 100-strike put and one 100-strike call.
a. Compute delta, vega, theta, and rho of the call and put separately, for the different stock prices and times to expiration.
b. Compute delta, vega, theta, and rho of the purchased straddle (do this by adding the Greeks of the individual options). As best you can, explain intuitively the signs of the straddle Greeks.
c. Graph delta, vega, theta, and rho of the straddle with 1 year to expiration as a function of the stock price. In each case explain why the graph looks as it does.