Question: 1. = a O = = = a. (10 pts) Consider a stock S with initial value S(0) = $50, in a market where the

1. = a O = = = a. (10 pts) Consider

1. = a O = = = a. (10 pts) Consider a stock S with initial value S(0) = $50, in a market where the continuously , compounded interest rate is rc = 8%. Find an arbitrage opportunity for the given one-year 8. European call options with following properties A six-month European put option with strike price X = $55 is priced pE = $5 A seven-month American call option with strike price X = $55 is priced CA = $2. $. b. (10 pts) Consider three European call options, written on the same stock S, with the same matu- rity date T, and with the strike prices: $100, $145, and $160. Assume also that CE(100) = $80, CE(145) = $36, and CE (160) = $20, where CE(X) is the price of the option at time 0. The ) interest is some given r > 0, compounded continuously. Find an arbitrage opportunity. Provide all the transactions at time 0 and all the transactions at time T. You may assume that there are no dividend payments. eta = > = = SSBALL 1. = a O = = = a. (10 pts) Consider a stock S with initial value S(0) = $50, in a market where the continuously , compounded interest rate is rc = 8%. Find an arbitrage opportunity for the given one-year 8. European call options with following properties A six-month European put option with strike price X = $55 is priced pE = $5 A seven-month American call option with strike price X = $55 is priced CA = $2. $. b. (10 pts) Consider three European call options, written on the same stock S, with the same matu- rity date T, and with the strike prices: $100, $145, and $160. Assume also that CE(100) = $80, CE(145) = $36, and CE (160) = $20, where CE(X) is the price of the option at time 0. The ) interest is some given r > 0, compounded continuously. Find an arbitrage opportunity. Provide all the transactions at time 0 and all the transactions at time T. You may assume that there are no dividend payments. eta = > = = SSBALL

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