1. (a) In a one-period binomial model a share price starts at S and after one time step it becomes Sa where a is a constant and interest rate r = 0. For a call option with strike = S, show that the number of shares held in the replicating portfolio is 1/2. (b) Consider the following filtration (P+)}=, where r = 0: W1 S(0,w) S(1,w) S(2,w) 30 40 60 30 40 30 30 20 30 30 20 10 (i) Define the conditional probability and the conditional expectation associated with Pt. (ii) Calculate the conditional probabilities for each edge of the tree. (iii) Deduce the probability associated with each path wi (iv) Show that for all paths wi: E [S(2)|P1] (Wi) = Si (wi) (v) Also show that E [S(2)|Po](Wi) = Sowi). (vi) Hence, or otherwise, calculate the value of a european put option with strike K = 42. 1. (a) In a one-period binomial model a share price starts at S and after one time step it becomes Sa where a is a constant and interest rate r = 0. For a call option with strike = S, show that the number of shares held in the replicating portfolio is 1/2. (b) Consider the following filtration (P+)}=, where r = 0: W1 S(0,w) S(1,w) S(2,w) 30 40 60 30 40 30 30 20 30 30 20 10 (i) Define the conditional probability and the conditional expectation associated with Pt. (ii) Calculate the conditional probabilities for each edge of the tree. (iii) Deduce the probability associated with each path wi (iv) Show that for all paths wi: E [S(2)|P1] (Wi) = Si (wi) (v) Also show that E [S(2)|Po](Wi) = Sowi). (vi) Hence, or otherwise, calculate the value of a european put option with strike K = 42