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

Question

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.

Answer 1

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.