Question 1 options:
Consider a one-step binomial tree on stock with a current price of $100 that can go either up to $120 or down to $80 in 1 year. The stock does not pay dividend and interest rates are zero. We want to price the 1-year $90-strike European put option on this tree. (i) What's the put option payoff 1 year later if the stock price ends up at $120?

In a one-step binomial tree model, we are tasked with finding the payoff of a European put option with a strike price of $90. A European put option gives the holder the right to sell the underlying asset at the strike price at maturity (in this case, 1 year).

Given dataIn a one-step binomial tree model, we are tasked with finding the payoff of a European put option with a strike price of $90. A European put option gives the holder the right to sell the underlying asset at the strike price at maturity (in this case, 1 year).

Given 
- Current stock price: $ S_0 = 100 $
- Stock can go up to: $ S_u = 120 $
- Stock can go down to: $ S_d = 80 $
- Strike price of the put option: $ K = 90 $
- Time to maturity: 1 year
- Interest rate: $ r = 0 $ (risk-free interest rate is 0%)

### (i) Payoff of the European put option if the stock price ends up at $120:
The payoff of a put option is given by:

\[
\text{Payoff} = \max(K - S_T, 0)
\]

Where:
- $ K $ is the strike price of the option.
- $ S_T $ is the stock price at maturity.

If the stock price ends up at $ S_u = 120 $, the payoff is:

\[
\text{Payoff} = \max(90 - 120, 0) = \max(-30, 0) = 0
\]

So, the payoff of the put option 1 year later, if the stock price is $120, is **$0**.

Would you like to go further into the pricing model or have any questions?

Here are 5 related questions you could explore:
1. What is the payoff of the put option if the stock price ends up at $80?
2. How do we compute the probability of upward and downward movement in a risk-neutral framework?
3. How would you compute the current price of the European put option using this binomial tree?
4. How does the payoff structure change if the strike price is different?
5. What are the implications of a 0% interest rate on option pricing?

**Tip:** For European options, you only consider the payoff at maturity, unlike American options, which can be exercised at any time before expiry.

Consider a one-step binomial tree on stock with a current price of $100 that can go either up to $120 or down to $80 in 1 year. The stock does not pay dividend and interest rates are zero. We want to price the 1-year $90-strike European put option on this tree. (i) What's the put option payoff 1 year later if the stock price ends up at $120?

Understand how to price a European put option using a one-step binomial tree model. The problem involves a stock with a current price of $100 that can rise to $120 or fall to $80, with a $90 strike price and no dividends or interest. This detailed solution explains the payoff calculation if the stock price reaches $120.

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