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In the CRR model, describe the strategy replicating the payoff $X=(S_T-K)^{ +} +a(K-S_{T-2})^{+ }$ for $a \neq 0$

$X$ consists of two parts:

  1. European call option with strike price $K$ and expiration date $T$
  2. $a$ European put options with strike price $K$ and expiration date $T-2$

So I think I should replicate these two parts separately, but I don't know how to do that.

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Do you know how to use the CRR model for a standard Call and a Put? If not, you can learn that from a textbook or this site. If you know how to:

  1. Find the replicating portfolio for the Call
  2. Find the replication portfolio for the Put
  3. Add the weights together, multiplying the weights of the put by $\alpha$. For the final two days, set the weight of the Put-replicating portfolio to 0.
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  • $\begingroup$ Yes, I know how to use the CRR model for a standard call and put option. Moreover I know how to find the replicating portfolio for the call and put, but only for $T=1$. I have problem how to do it for bigger $T$, because for every $T$ we have $2^T$ possibility of payout options and I don't know how to consider it in general case. $\endgroup$ Apr 16, 2023 at 15:58
  • $\begingroup$ The general case can be found in textbooks or on this site as well. What does your source say about the general case? $\endgroup$
    – Bob Jansen
    Apr 16, 2023 at 16:51

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