A stock price is currently 50. It is known that at the end of 2 months it will be either 53 or 48. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a 2-month European call option with a strike price of 49?

  • 1
    $\begingroup$ You might start by pretending that the interest rate is zero. What would be the value then? $\endgroup$ – Ross Millikan Sep 19 '13 at 4:40

Hint: If you buy $1$ stock and put $b$ in interest free bonds, at the end of two months, your value would be either $53 + e^{1/60} b$ or $48 + e^{1/60}b$ depending on the market.

Now if instead you had invested the $50+b$ of money in options at a price $p$, you would either have $\dfrac{50+b}{p}\cdot 4$ or $0$ as the respective values.

If you can find values of $b, p$ to so that these situations are identical, then that $p$ must be your option price.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.