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As always I recommend reading Rennie and Baxter for an introduction to option pricing that's not too technical and gives intuition about how it all works.


You would like to have a payoff of £40m in year 5. If you buy the 5y annuity you will get £40m in year 5 and each year before ... so you can sell a 4y annuity that pays £40m each year. And you have the information on the prices.


I read the question as follows: You have one stock $S_0$ and after one period it either goes up to $S^+$ where the option takes the value $f^+$ or it goes down to $S^-$ where the option takes the value $f^-$. The bond grows from $B_0$ to $B_1 = B_0 \exp(r)$. Then you need to solve $$ a S^+ + b B_1 = f^+ \\ a S^- + b B_1 = f^- $$ for $a,b$ which are $2$ ...

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