Consider an option on a stock when the stock price is $41, the strike price is $
ID: 2672239 • Letter: C
Question
Consider an option on a stock when the stock price is $41, the strike price is $40, the risk-free rate is 6%, the volatility is 35%, and the time to maturity is 1 year. Assume that a dividend of $0.50 is expected after 6 months.
a) Use DerivaGem to value the option assuming it is a European call.
b) Use DerivaGem to value the option assuming it is a European put.
c) Verify that put-call parity holds.
d) Explore using DerivaGem what happens to the price of the options as the time to maturity becomes very large. For this purpose, assume there are no dividends.
Explain the results you get.
Explanation / Answer
DerivaGem shows that the price of the call option is 6.9686 and the price of the put
option is 4.1244.in this case
c+D Ke-rT = 6.9686 0.5e-0.06x0.5 + 40e-0.06x1 = 45.1244
Also p + S = 4.1244 + 41 = 45.1244
As the time to maturity becomes very large and there are no dividends, the price of the
call option approaches the stock price of 41.(For example when T = 100 it is 40.94.).This
is because the call option can be regarded as a position in the stock where the price does
not have to be paid for a very long time. The present value of what has to be paid is close
to zero.
As the time to maturity becomes very large the price of the European put option
becomes close to zero. (For example when T = 100 it is 0.04.) This is because the present
value of what might be received from the put option becomes close to zero.