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The risk-neutral probability $p$ of the up move is computed using the formula $p = \frac{(1+r)-d}{u-d}$. Given $r = 0.1$, $u = 1.2$, and $d = 0.9$, the calculation is $p = \frac{1.1 - 0.9}{1.2 - 0.9} = \frac{0.2}{0.3} = \frac{2}{3}$.

Conditions: One-period binomial model with up factor $u$, down factor $d$, and interest rate $r$.; $u > 1+r > d$ to ensure $0 < p < 1$.

The risk-neutral probability $p$ of the up move is computed using the formula $p = \frac{(1+r)-d}{u-d}$. Given $r = 0.1$, $u = 1.2$, and $d = 0.9$, the calculation is $p = \frac{1.1 - 0.9}{1.2 - 0.9} = \frac{0.2}{0.3} = \frac{2}{3}$.

Conditions: One-period binomial model with up factor $u$, down factor $d$, and interest rate $r$.; $u > 1+r > d$ to ensure $0 < p < 1$.

Risk-neutral probabilities are defined as the specific set of probabilities chosen precisely to make the discounted price process of any asset a martingale. They are not derived from historical data or investor beliefs, but from the mathematical requirement that discounted prices behave like fair games.

Conditions: Operating within a risk-neutral valuation framework.; Prices are discounted at the risk-free rate.

Risk-neutral probabilities are defined as the specific set of probabilities chosen precisely to make the discounted price process of any asset a martingale. They are not derived from historical data or investor beliefs, but from the mathematical requirement that discounted prices behave like fair games.

Conditions: Operating within a risk-neutral valuation framework.; Prices are discounted at the risk-free rate.