A stock follows the three period binomial model with u = 1.2, d = 0.9, r = 0.05, S_0 = 100. We wish to compute the value of an American straddle option with strike price 100. At each time t at which you may exercise the option, the exercised value of the option is |S_t - 100|. In other words, if you choose to exercise the option, your profit will be the difference between the stock price and the strike price of 100, regardless of whether the stock is up or down. Example: If the stock price is currently 120, you could exercise the option and profit 20. If the stock price is currently 90, you could exercise the option and profit 10. A straddle allows you to bet on high volatility. A straddle is good when you are sure the stock price is going to move, you just aren't sure whether it will go up or go down. Find the theoretical probability p* necessary for no arbitrage. Find the value of an American straddle option with strike price 100. Find the hedging strategy necessary to replicate the option. Describe when you should exercise the option early. Show that the hedging strategy allows you to break even in the case the stock goes up, then down, then down. (HTT). Describe at each time, how much stock you should hold, how much cash you have (either invested in the bank or borrowed from the bank), and what transactions you need to make. A stock follows the three period binomial model with u = 1.2, d = 0.9, r = 0.05, S_0 = 100. We wish to compute the value of an American straddle option with strike price 100. At each time t at which you may exercise the option, the exercised value of the option is |S_t - 100|. In other words, if you choose to exercise the option, your profit will be the difference between the stock price and the strike price of 100, regardless of whether the stock is up or down. Example: If the stock price is currently 120, you could exercise the option and profit 20. If the stock price is currently 90, you could exercise the option and profit 10. A straddle allows you to bet on high volatility. A straddle is good when you are sure the stock price is going to move, you just aren't sure whether it will go up or go down. Find the theoretical probability p* necessary for no arbitrage. Find the value of an American straddle option with strike price 100. Find the hedging strategy necessary to replicate the option. Describe when you should exercise the option early. Show that the hedging strategy allows you to break even in the case the stock goes up, then down, then down. (HTT). Describe at each time, how much stock you should hold, how much cash you have (either invested in the bank or borrowed from the bank), and what transactions you need to make
