ABC stock is currently trading at 100. In the next period, the price will either go up by 10% or down by 10%. The risk-free rate of interest over the period is 5%. 

(a) Construct a replicating portfolio to value a call option written today with a strike price of 100. What is the hedge ratio?

(b) Calculate the risk-neutral probabilities in the model. Value the same call option using the risk-neutral probabilities. Check that you get the same answer as in part (a). 

(c) Using the risk-neutral probabilities, find the value of a put option written today, lasting one period and with an exercise price of 100. 

(d) Verify that the same price for the put results from put-call parity.