Question

A call option on a particular stock with a six-month maturity is currently priced at $9.96. The stock price is $62 and the call’s exercise price is $60. The risk-free-rate is 6%/year and is compounded continuously. Using the information above, answer the following questions.

a)What is the value of a put option written on the same stock having the same maturity and exercise price?

b)What is the intrinsic value of the call and the put options? c)What is the time (speculative) value of the call and the put options?

d)Suppose you are forming a portfolio consisting of a call and a put option as stated above. Such a portfolio is called a straddle. Is this portfolio risk free (hedged)? Show you results graphically or numerically.

Answer 1

a]

As per the put-call parity equation, C + (K/ert) = P + S,

where C = price of call option,

P = price of put option,

S = current stock price

K = exercise price of option

r = risk free rate

t = time to expiration in years

We plug in the values to find the price of the put option :

C + (K/ert) = P + S

9.96 + (60/e0.06*(6/12)) = P + 62

9.96 + 58.23 = P + 62

P = 6.19

value of a put option is $6.19

b]

For an in-the-money call option, intrinsic value = stock price - option exercise price

Intrinsic value of call option = $62 - $60 = $2

For an out-of-the-money put option, intrinsic value = zero

Intrinsic value of put option = $0

c]

Value of option = intrinsic value + time value

time value = Value of option - intrinsic value

time value of call option = $9.96 - $2 = $7.96

time value of put option = $6.19 - $0 = $6.19

d]

Profit of a long call option = Max[S-X, 0] - P

Profit of a long put option = Max[X-S, 0] - P

S = underlying price at expiry,

X = exercise price

P = premium paid

The profit of the portfolio at different levels of stock price at maturity is as below :

Yes, the portfolio is hedged because the maximum loss is limited.