ABC Ltd. Is currently trading at $27.00 per share. A one-year European put option on ABC with a strike price of $30.00 is currently trading for $2.60. If the risk-free interest rate is 6.00% per year, then the price of a one-year call option on ABC with a strike price of $30.00 will be closest to:

Question

BlackTom AI · Accepted Answer

We start by identifying the key inputs: current stock price S0 = 27, strike price K = 30, one-year maturity T = 1 year, risk-free rate r = 6% per year, and the observed price of a one-year European put with strike 30 is P = 2.60.

To value the corresponding call using put-call parity for European options on a non-dividend-paying stock, we use the relationship:
C + K e^{-rT} = P + S0  (continuous compounding), or equivalently C = P + S0 − K e^{-rT}.

We compute K e^{-rT} first. If we assume continuous compounding, e^{-rT} = e^{-0.06} ≈ 0.941764, so K e^{-rT} ≈ 30 × 0.941764 ≈ 28.25.

Plugging into the parity formula: C ≈ P + S0 − K e^{-rT} ≈ 2.60 + 27 − 28.25 ≈ 1.35.

If instead we use annual (discrete) compounding, K/(1 + r)^T = 30 / 1.06 ≈ 28.30, and C ≈ 2.60 + 27 − 28.30 ≈ 1.30.

Both methods yield a call price in the vicinity of 1.30–1.35. Since the question asks for the price closest to the call, the result typically rounded to two decimals would be about $1.30. The slight difference between the two compounding conventions explains why the parity calculation can land near 1.30 rather than exactly 1.35 in the continuous- vs discrete-compounding interpretations.

In summary, applying put-call parity with the given data leads to a call price around $1.30 to $1.35, with $1.30 being the closest rounded value commonly used in such problems.

MGT232H5 F LEC0101 Quiz 8

ABC Ltd. Is currently trading at $27.00 per share. A one-year European put option on ABC with a strike price of $30.00 is currently trading for $2.60. If the risk-free interest rate is 6.00% per year, then the price of a one-year call option on ABC with a strike price of $30.00 will be closest to:

View Explanation

Log in for full answers

Similar Questions

Which relationship holds with the most precision?

Consider a put and a call on a stock with price S. The stock does not pay dividends. Interest rates are zero. Both options have the same expiration date. Between Monday and Tuesday, S does not change, but the call price falls by $2. What happens to the put price?

Interest rates are 4.5% continuously compounded The December 2026 (1 year) Copper $5 call costs $1.25 The December 2026 (1 year) Copper $5 put costs $2.75 What is spot?

I am long Nasdaq futures because the financial conditions are ridiculously easy given all of the stimulus. However, we are going into earnings to I decide to buy a protective put. This means my synthetic position is

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler