Problem:

Call options gives the possessor of the option the right to buy shares of a stock at a pre-determined strike price at some time in the future. Recall that a call option would only be exercised if the stock price was above the strike at the time of expiration, otherwise the call option expired worthless. In this question we consider a similar object, referred to as a put option, which allows the possessor the right to sell shares of a stock at a pre-determined strike price at some time in the future. Notice in this way that a put option would only be exercised if the stock price was below the strike at the time of expiration, otherwise the put option expires worthless.

1. A stock currently at $100 can be at either $150 or $75 at time 1 (present value). An option to sell y shares (i.e., a put option) of the stock at time 1 at a strike price of $125 can be purchased now at a cost of cy. Determine the value of c for which there is no sure win.
2. If c = 30, describe a strategy for guaranteeing a sure win.