4. The current price of a certain share is 32 pence and the price evolves according to the standard multi-period Binomial model with u=2 and d=1/2. The one-period interest rate is denoted by R%. A European binary call option with strike price 100 pence and expiry time 2 pays 110 pence if the share price finishes above 100 pence and nothing otherwise. (a) Derive (do not simply state) an expression for the risk-neutral probability p of an upward step in terms of R. (5 marks) (b) Hence, derive the European option pricing formula for the case of the n-period Binomial model. (6 marks) (c) Find an expression for the current value (at t=0 ) of the option for the example stated above. (2 marks) (d) Find the current value (at t=0 ) of the option when the one period interest rate is 5%, that is, R=5. (1 mark) (e) Find the price of an American put option with expiry time n=2 and strike price 100 pence in the example above. 4. The current price of a certain share is 32 pence and the price evolves according to the standard multi-period Binomial model with u=2 and d=1/2. The one-period interest rate is denoted by R%. A European binary call option with strike price 100 pence and expiry time 2 pays 110 pence if the share price finishes above 100 pence and nothing otherwise. (a) Derive (do not simply state) an expression for the risk-neutral probability p of an upward step in terms of R. (5 marks) (b) Hence, derive the European option pricing formula for the case of the n-period Binomial model. (6 marks) (c) Find an expression for the current value (at t=0 ) of the option for the example stated above. (2 marks) (d) Find the current value (at t=0 ) of the option when the one period interest rate is 5%, that is, R=5. (1 mark) (e) Find the price of an American put option with expiry time n=2 and strike price 100 pence in the example above