Number of shares = 1,000

Current Price = 45

Expected return = 0.03

Volatility = 0.5

Put Option Strike Price = 45 (1 year maturity)

Risk Free Rate = 0

The bank will charge 5% more than the theoretical no-arbitrage price of the option.

The bank will also delta-hedge its exposure daily by trading the underlying stock + the risk-free asset.

________

The stock price follows a geometric Brownian motion. Using excel, simulate two trajectories of daily prices for the next year (assume 252 trading days per year). One of the price trajectories should have ST > S0, and the other should have ST < S0 at maturity.

Plot both price trajectories together in a graph. Label x-axis as t (number of years) and y-axis as St (stock price at time t).