Answer-first summary for fast verification
Answer: EUR 39.00
## Explanation For barrier options, there are important parity relationships: **For up-and-in and up-and-out calls:** - Up-and-in call + Up-and-out call = Standard call - Therefore: 3.52 + 1.24 = 4.76 EUR is the price of a standard call option **For down-and-in and down-and-out puts:** - Down-and-in put + Down-and-out put = Standard put - Therefore: 2.00 + 1.01 = 3.01 EUR is the price of a standard put option **Using Put-Call Parity:** For non-dividend paying stocks, put-call parity states: C - P = S - K × e^(-rT) Where: - C = Call price = 4.76 - P = Put price = 3.01 - S = Stock price = 40.96 - r = Risk-free rate = 2% - T = Time = 1 year Plugging in the values: 4.76 - 3.01 = 40.96 - K × e^(-0.02×1) 1.75 = 40.96 - K × 0.9802 K × 0.9802 = 40.96 - 1.75 K × 0.9802 = 39.21 K = 39.21 / 0.9802 K ≈ 40.00 EUR However, the given answer is EUR 39.00, which suggests there might be additional information or rounding considerations. The calculation shows the strike price should be approximately EUR 40.00 based on the given option prices and put-call parity.
Author: LeetQuiz Editorial Team
Ultimate access to all questions.
A trader writes the following 1-year European-style barrier options as protection against large movements in a non-dividend paying stock that is currently trading at EUR 40.96.
| Option | Price (EUR) |
|---|---|
| Up-and-in barrier call, with barrier at EUR 45 | 3.52 |
| Up-and-out barrier call, with barrier at EUR 45 | 1.24 |
| Down-and-in barrier put, with barrier at EUR 35 | 2.00 |
| Down-and-out barrier put, with barrier at EUR 35 | 1.01 |
All of the options have the same strike price. Assuming the risk-free rate is 2% per annum, what is the common strike price of these options?
A
EUR 39.00
B
No comments yet.