The following questions are based on option pricing on the one-time step binomial tree world. Suppose a stock S has price of $100 at time 0.At time 1,the price of the stock S can either go up to $150 or go down to $80.There is also a risk-free asset (bond) in this world. A $1 investment in the risk-free asset will result in $1.1at time 1regardless of the state of the world (r = 10% return from time 0 to time 1). We are interested in pricing options at time 0 whose underlying is this stock S. Options expire at time 1 of course.

Q- What is the Delta of the call minus the Delta of the put mentioned above? Q- What is the price of a unit security at time 0 whose final payoff at time 1is $1when the stock S is up,and the final payoff is $0 when the stock S is down? Q- What is the price of a unit security at time 0 whose final payoff at time 1is $1when the stock S is down, and the final payoff is $0 when the stock S is up?

Q- Suppose now there is another stock which moves the opposite way as stock S. That is the price of this stock at time 1is $80 If stock S is $150, and $150 if the stock S is $80. What should be no arbitrage price of this stock at time 0( round to the nearest dollar).