Question16 The price of a European call that expires in 6 months and has a strike price of $30 is $2. The underlying stock price is $29. The term structure is flat, with all risk-free interest rates being 10% (continuously compounded). What should be the price of a European put option that also expires in 6 months and has also a strike price of $30? Select one alternative: A. The put should cost $2 as well because it has the same strike price as the call B. The put should cost $1.54 C. The put should cost $1.60 D. The put should cost $1.57 ResetMaximum marks: 2 Flag question undefinedSingle choice
A
A. The put should cost $2 as well because it has the same strike price as the call
B
B. The put should cost $1.54
C
C. The put should cost $1.60
D
D. The put should cost $1.57

Question

Question16 The price of a European call that expires in 6 months and has a strike price of $30 is $2. The underlying stock price is $29. The term structure is flat, with all risk-free interest rates being 10% (continuously compounded). What should be the price of a European put option that also expires in 6 months and has also a strike price of $30? Select one alternative: A. The put should cost $2 as well because it has the same strike price as the call B. The put should cost $1.54 C. The put should cost $1.60 D. The put should cost $1.57 ResetMaximum marks: 2 Flag question undefinedSingle choice

A

A. The put should cost $2 as well because it has the same strike price as the call

B

B. The put should cost $1.54

C

C. The put should cost $1.60

D

D. The put should cost $1.57

BlackTom AI · Accepted Answer

Put-call parity for European options gives the key relationship: C + K e^{-rT} = P + S. This links the call price C, put price P, current stock price S, strike K, continuous risk-free rate r, and time to expiration T.

1) Relevant knowledge points and concepts
- Put-call parity applies to European options on non-dividend-paying stocks.
- With continuous compounding, the present value of the strike is K e^{-rT}.
- Rearranging put-call parity yields P = C + K e^{-rT} - S.

2) Complete reasoning process step by step
- Identify given values: C = $2, S = $29, K = $30, r = 10% = 0.10 (continuous), T = 0.5 years.
- Compute the present value of the strike: K e^{-rT} = 30 * e^{-0.10 * 0.5}.

3) Calculations with intermediate steps
- rT = 0.10 * 0.5 = 0.05.
- e^{-rT} = e^{-0.05} ≈ 0.9512294245.
- K e^{-rT} = 30 * 0.9512294245 ≈ 28.536882735.
- Now compute P: P = C + K e^{-rT} - S = 2 + 28.536882735 - 29 = 1.536882735.
- Rounded to two decimal places gives P ≈ $1.54.

4) Why the correct answer is correct
- Put-call parity enforces no-arbitrage pricing. Given the call price, stock price, and discounted strike, the put price must equal about $1.5369 to prevent arbitrage. Rounding to cents yields $1.54.

5) Why the other options are incorrect
- A ($2) is wrong because a put need not equal the call price; the relationship involves S and the discounted strike.
- C ($1.60) and D ($1.57) are slightly off due to rounding; they do not match the precise parity calculation (1.5369 → $1.54).

6) Conclusion confirming the final answer
- Using put-call parity with continuous compounding yields P ≈ $1.5369, rounded to $1.54, which matches option B.