(a) Suppose that on 01-09-2010, the price of stock T could be either €100 or €20
ID: 2734000 • Letter: #
Question
(a) Suppose that on 01-09-2010, the price of stock T could be either €100 or €200. There are no put options available on this stock. Call options are available, with an exercise price of €150. How could you achieve the same payoff as the stock, without buying the stock?
(b) Why does the put-call parity result change when the stock makes a dividend payment before the expiration date of the options? Write the put-call parity theorem in this case.
(c) Suppose the price of stock V is currently €20. In the next six months it will either fall to €10 or rise to €30. The six-month risk-free interest rate is 5% (periodic rate). What is the current value of a put option with an exercise price of €15?
Explanation / Answer
1.(a) There is no sufficient information so we are assuming certain amounts.A call option is nothing but an option which gives buyer of the option a right but not an obligation to ask writer of the option to sell the stock at exercise price.however he used to exercise the call option when the stock price exceeds the actual price.So it was given that Price of stock T could be either 100 or 200.If u can estimate that price of stock could be 100 on 01.09.10 it is better to write a option instead of buying it,So ultimately buyer of the option wont exercise the option since actual price is less than exercise price.So as a writer of the option you will be left with profit in the firm of premium received on writing the option.so in that way you could achieve the samepayoff as the stock.
if in case if u can estimate that stock price could be 200 on 01.09.10 ,it would be better to purchase call option by paying a small amount premium at exercise price of 150,so ultimater you will be left 45(assume call option premium is 5) profit from this option.so in this way also you could earn the same payoff as the stock gives.
(b) Put - Call parity defines a relationship between the priceo of European call option and European put option.
Since the put - call parity based on the stock price at the date of maturity of options.Normally when ever a stock makes a dividend payment then automatically its value will rise depending on the dividend amount.since put - call parity is based on the stock price,if in case the stock pays dividend its price automatically changes so which indireclty leads to change in the put call parity result.
Put call parity theorum with known dividend =
C - P = S - (div)*e-rt - Xe-rt
(c)Calculation of Current value of put option using risk neutral method :
Let probability of attaining minimum price be p
(10-20)p+(30-20)(1-p) = 20*(e0.05 -1)
-10p+10-10p = 20(1.05127-1)
10-20p = 1.0254
20p =10-1.0254
p = 0.44873
The value of put option = 0.4487*(15-10)/1.05127
=2.134
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