Stock-A has current price, S_A = $90 and stock-B has current price, S_B = $80.

Put options on A and B have 30 (trading) days to maturity and are currently both at-the

money. The risk-free rate is r = 2% pa (continuously compounded).

You do not have closed form solutions (e.g. Black-Scholes) for these option

prices but the portfolio deltas and gammas for long positions in these put options

are

Delta of a = -400, Delta of b = -200 and gamma of a = 30, gamma of be = 20

The mean growth rate and volatility for stock-A are 5% pa and 15% pa, respectively

and for stock-B the figures are 10% pa and 20% pa, and the correlation between the

two stock returns is 0.7.

a). Carefully, outline the steps you would take to simulate stock prices A and B over

10 trading days using Monte Carlo Simulation (MCS), and how you would calculate

the possible outcomes for the change in value of your options portfolio (over 10 trading

days).

b). Assume you only hold options-A. Using your own formulas in Excel, perform a

MCS (for m=1000 simulations) over 10 trading days. Show the possible changes in the

options premium and present the results in a histogram.

Now, calculate the change in value of your options position at the 5^th percentile.

Briefly comment and interpret your results.

c). Use MCS (in Excel) to price option-A and measure the error in your estimate.

Set out the steps in your analysis and briefly comment on your results by noting any

changes in your MCS analysis between b). and c).

Provide the Excel file with the above illustrative simulations.