To create a delta-neutral portfolio, the SIT fund has sold 10,000 at-the-money (ATM) put options on Epsilon stock with when the shares were trading at $100. The risk manager from SIT uses the Black-Scholes model to value all option exposures. The current price of the shares is $90. The annualized standard deviation of Epsilon stock returns is 40% and the option expires in six months. If the risk-free rate is 2%, approximately, what is the likelihood that this option will be exercised? (a) 0.7975 (b) 0.6839 (c) 0.3161 (d) 0.2025

A portfolio manager has asked his analyst to use Monte Carlo simulation to price an Asian option on a stock. The derivative expires in 6 months and the risk-free rate is 1% per year compounded continuously. The analysts generate a total of 10,000 paths using a geometric Brownian motion model, record the payoff for each path, and report that the average payoff per path (USD) is 44. What is the estimated price of the derivative? (a) 44.0 (b) 44.8 (c) 43.8 (d) 41.8