1. What is the fair value for a two-year American put option with a strike price of $75 over a stock which is trading at $76.15 which has a volatility of 27% when the risk free rate is 0.75% using the two step binomial tree? a) What is the delta of this option? b) What is the probability of a down movement in this stock? c) What is the probability of an up movement in this stock? d) What is the proportional move up for this stock e) What is the proportional move down for this stock f) What would be the value of the call option with the same strike price?

2.What is the fair value for a six-month European call option with a strike price of $35 over a stock which is trading at $35.15 and has a volatility of 38% when the risk free rate is 0.85% using the two step binomial tree? a) What is the delta of this option? b) What is the probability of an up movement in this stock? c) What is the probability of a down movement in this stock? d) What is the proportional move up for this stock e) What is the proportional move down for this stock f) What would be the value of the put option with the same strike price?

3.. Determine the price of a two-year EUROPEAN put option with a strike price of $52 on a stock that is currently priced at $50 if the risk free rate was 2.2%? Each year there are only two outcomes for this stock, either: A 15% move up, or A 15% move down After the first year the stock pays a dividend of $2 and after the second year the stock is expected to pay a dividend of $2.10.

4.What is the fair value for the call option with the same strike price? a) What is the delta of this option b) What is the probability of a move up for this stock? c) What is the probability of a move down for this stock? d) What is the proportional move up in price for this stock? e) What is the proportional move down for this stock?

5.Determine the price of a two-year AMERICAN put option with a strike price of $52 on a stock that is currently priced at $48.50 which has a volatility of 45%pa if the risk free rate was 2.2%. After the first year the stock pays a dividend of $2 and after the second year the stock is expected to pay a dividend of $2.10. a) What is the delta of this option? b) What is the probability of a move up for this stock? c) What is the probability of a move down for this stock? d) What is the fair value for the call option with the same strike price? e) What is the delta of the call option? f) What is the proportional move up for this stock g) What is the proportional move down for this stock