Compute the Profit/Loss of the FI for Each Price Trajectory - Accounting & Finance Assignment Help

Assignment Task

"Suppose a FI has written and sold an option to a client on 10,000 shares of a listed stock. The current share price S0 = 24, expected return μ = 0.02, volatility σ = 0.80. Moreover, the put option has a strike price of K = 24 and a maturity of 1 year. The FI has decided to charge the client 10% more than theoretical no-arbitrage price of the option, and then delta-hedge its risk exposure on a daily basis by trading the underlying stock and the risk-free asset. For simplicity, assume the risk-free interest rate r = 0. The FI wants to be informed about the potential profit and loss of this trade. As a result, you are required to perform the following tasks.

a. Assume the stock price follows a geometric Brownian motion, 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 the two price trajectories together in a graph. Label x-axis as t (number of years) and y-axis as St (stock price at time t).

b. Suppose the option is a call option. For each of the price trajectories simulated in Part (a), perform a dynamic delta-hedging strategy. Compute the profit/loss of the FI for each price trajectory.

c. Suppose the option is a put option. Repeat the exercise in Part (b).

d. Does the profit/loss in Part (b) and Part (c) depend on the difference between the two price trajectories? Why or why not?"

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