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

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.

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.
• 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. Apr 16, 2023 at 15:58