Question 1 Assume that the stock price of the Socceros, a publicly traded sports team in Brazil, follows the Black-Scholes model. Its stock price today (time t = 0) is $55, it has a volatility of 25%, and a 10% expected rate of return (compounded continuously, under the physical probability measure). The stock does not pay dividends. The risk-free force of interest in the market is 4%. After 6 months, you observe a stock price of $48, and after one year the stock price is $51 (of course, you won't know these two values until times 0.5 and 1, respectively). Gaby is a market maker who at time 0 sells 100 put options that have a strike of $60 and that mature in one year. (a) Compute the no-arbitrage price of one such option. (b) What will be Gaby's profit/loss after one year if she did not hedge her position? (c) If Gaby wants to Delta-hedge her option position, what should her hedging portfolio look like at time 0? (d) If she then maintains this hedging position for the entire year, what will be her profit/loss when the options mature? Question 1 Assume that the stock price of the Socceros, a publicly traded sports team in Brazil, follows the Black-Scholes model. Its stock price today (time t = 0) is $55, it has a volatility of 25%, and a 10% expected rate of return (compounded continuously, under the physical probability measure). The stock does not pay dividends. The risk-free force of interest in the market is 4%. After 6 months, you observe a stock price of $48, and after one year the stock price is $51 (of course, you won't know these two values until times 0.5 and 1, respectively). Gaby is a market maker who at time 0 sells 100 put options that have a strike of $60 and that mature in one year. (a) Compute the no-arbitrage price of one such option. (b) What will be Gaby's profit/loss after one year if she did not hedge her position? (c) If Gaby wants to Delta-hedge her option position, what should her hedging portfolio look like at time 0? (d) If she then maintains this hedging position for the entire year, what will be her profit/loss when the options mature