You have purchased a 40-strike call with 91 days to expiration. You wish to deltahedge, but you are also concerned about changes in volatility; thus, you want to vega-hedge your position as well.
a. Compute and graph the 1-day holding period profit if you delta- and vegahedge this position using the stock and a 40-strike call with 180 days to expiration.
b. Compute and graph the 1-day holding period profit if you delta-, gamma-, and vega-hedge this position using the stock, a 40-strike call with 180 days to expiration, and a 45-strike put with 365 days to expiration.