Question

a) A stock currently sells for $33.75. A 6-month call option with a strike price of $33 has a premium of $5.3. Let the continuously compounded risk-free rate be 6%.

What is the price of the associated 6-month put option with the same strike (to the nearest penny)?
   Price = $ -------------------


b) A stock currently sells for $34.3. A 6-month call option with a strike price of $30.9 has a premium of $2.11, and a 6-month put with the same strike has a premium of $1.26. Let the continuously compounded risk-free rate be 5%.

What is the present value of dividends payable over the next 6 months (to the nearest penny)?
   Value = $ ----------------

Answer 1

(a) Current Stock Price = S = $ 33.75, Call Price = C = $ 5.3 and Strike Price = K = $ 33, Risk-Free Rate = 6% compounded continuously and let the put price be $P

Using put-call parity, we have:

C + PV of K = S + P

5.3 + [33 / EXP(0.06 x 0.5)] = 33.75 + P

P = 5.3 + 32.0247 - 33.75 = $ 3.5747 ~ $ 3.57

NOTE: Please raise a separate query for the solution to the remaining unrelated question, as one query is restricted to the solution of only one complete question with a maximum of four sub-parts.