# Strike Price Determination

Suppose you know the following: there are 2-month European call and put options on an index-like instrument with no dividends, the calculations show that the call option price is USD 10.1150, the spot index price is USD 120, the risk-free rate is 3% and the volatility is 35%. You happen to know that the put option price is USD 2.5664. What is then the strike price?

Now my questions:

1. Is there a rule holding that the strike price should be the same regardless of whether it is derived from the Black-Scholes model or the put-call parity equation?
2. Given the above information, I compute that the strike price is USD 113.02 using the put-call parity equation. However, when I go back to the Black-Scholes equation and compute the call option price with a strike price of USD 113.02, I end up with a call option price of USD 11.07 rather than USD 10.1150. Am I right to assume that an arbitrage opportunity exists? How can I determine what is the mispriced asset?
• What about time to maturity? May 31, 2021 at 21:26
• Yeah, I forgot it. It is 2 months. I am going to edit it. May 31, 2021 at 21:28

If by volatility you mean the implied volatility then yes, an arbitrage oppurtunity exists. Buy the portfolio $$(C-P)$$ for 7.5486. In the future this will pay off a discounted value of 7.5536 with certainty due to call put parity.