Topic: options answer with detailed steps please

1.You are provided with the following information on put and call options on a stock:

Call price, c_o = $6.64

Put price, p_o = $2.75

Exercise price, X = $30

Days to option expiration = 219

Current stock price, S_o = $33.19

Put-call parity shows the equivalence of a call/bond portfolio (fiduciary call) and a put/underlying portfolio (protective put).

Illustrate put-call parity assuming stock prices at expiration (S_T) of $20 and of $40. Assume that the risk-free rate, r, is 4 percent.

2.Consider the following information on put and call options on a stock:

Call price, co = $4.50

Put price, po = $6.80

Exercise price, X = $70

Days to option expiration = 139

Current stock price, So = $67.32

Risk-free rate, r = 5 percent

a.Use put-call parity to calculate prices of the following:

i.Synthetic call option

ii.Synthetic put option

iii.Synthetic bond

iv.Synthetic underlying stock

b.For each of the synthetic instruments in Part A, identify any mispricing by comparing the actual price with the synthetic price.

3.A stock price is currently $100. Over each of the next two 6-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a 1-year European call option with a strike price of $100?

3.

4.For the situation considered in Problem 3, what is the value of a 1-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put-call parity.

4.

5.A stock price is currently $50. Over each of the next two 3-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a 6-month European call option with a strike price of $51?

6.For the situation considered in Problem 5, what is the value of a 6-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy put-call parity. If the put option were American, would it ever be optimal to exercise it early at any of the nodes on the tree?