You are interested to value a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it either increases to $120 or decreases to $80. The risk-free rate of interest is 10%. Calculate the call option's value using the binomial pricing model, presenting your calculations and explanations as follows:

a. Draw tree-diagrams to show the possible paths of the share price and call payoffs over one year period. (Note: Show the numbers that are known and use letter(s) for what is unknown in your diagrams.)

b. Compute the hedge ratio.

c. Find the call option price. Explain your calculations clearly.

d. Use put-call parity, find the price of a put option with the same exercise price and the same expiration date.

Subject : Portfolio and fund management