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For the solution: Just wanted to ask for $V_{3}(HTH)$ I get $S_{1}(H)$ and $S_{3}(HTH)$ to give me the same maximum value of $16$ so would it also be right if I used $S_{1}(H)$ nstead of $S_{3}(HTH)$? Same applies for $V_{3}(THT)$ for which I get $S_{0}$ and $S_{2}(TH)$ which both give me a maximum value of $8$ so could I have used $S_{3}(TH)$ instead of $S_{0}$?

Any help would be much appreciated.


1 Answer 1


First, you have to compute the value of the payoff of your lookback option.

For example consider path $THT$. You have:

$S_{0}=8$, $S_{1}=4$, $S_{2}=8$ and $S_{3}=4$

It means that


So the payoff is of the form

$$V_{3}(THT)=\max_{0\leq n\leq 3}S_{n}-S_{3}=8-4=4$$

It doesn't matter if you choose $S_{0}$ or $S_{2}$ to compute the maximum.

If you compute all $8$ payoffs you have two methods for pricing: replication and risk-neutral pricing method.

In the case of risk-neutral pricing method the martingale measure is of the form $Q(p^{*},1-p^{*})$, where


And you have to compute the following steps:

First step:





Second step:



Last step:


The price of the lookback option is equal to $C(0)$.


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