Given the following portfolio

One unit of stock S with initial value $50

$50 in a money market (MM) account (Risk-free)

Other assumptions

Risk free rate term structure of 3% flat

o Model as a Hull-White process with a=0.10 and sigma = 0.01

Stock Real World (RW) growth rate of 8%

Stock RW volatility of 15%

Implied volatility of 20%

Simulate 100 RW scenarios and calculate the following.

a) What is the VaR and Expected Shortfall of this portfolio in 1

year?

b) What is the VaR and Expected Shortfall of the same

portfolio if you rebalance each month to the original

50%/50% split between S and MM?