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?
2026-04-03 03:02:08.1775185328
financial calculus call option
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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.