Questions / Quant trading, Option pricing models
A two-step put tree
The stock is 100 and each step moves it up 10% or down 10%. Rates are zero. What is a European put struck at 100 worth after two steps?
Answer it in the app It's free. You get hints, a second try if you miss, and a follow-up question.
Show the answer and worked solution
Answer: 5.25 USD (21/4)
- q = (1 − 0.9)/0.2 = 0.5.
- End prices 121, 99, 81 with probabilities 0.25, 0.5, 0.25.
- Put payoffs 0, 1, 19: 0.5 × 1 + 0.25 × 19 = 5.25.
Interview shortcut. ¼·0 + ½·1 + ¼·19 = 5.25.
Takeaway. Weight terminal nodes by path count.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.