# Binomial Trees

## 5 important questions on Binomial Trees

### Real-world vs. Risk-neutral world

Risk-neutral valuation solves this as the discount rate and expected return are the same for all assets.

### WHat about a two-step model?

value of option (today) = e^(-2*r*t)*(p^2*value(uu) +p*(1-p)*value(ud) + (1-p)^2*value(dd)).

If we add more steps, the risk-neutral valuation principle continues to hold. THe option price is always equal to its expected payoff in a risk-neutral world discounted at the risk-free rate.

### How about american option?

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### WHat about volatility to calculate u and d?

Match volatility in the risk-neutral world! For real-world formulas will be the same. This links to Girsanov's theorem: when we move from the risk-neutral world, the expected return from the stock price changes, but the volatility remains the same!! Switching risk-preference only changes the measure (p is real and q is neutral)

### What if we increase the number of steps?

The question on the page originate from the summary of the following study material:

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