In the binomial model, if the stock moves up by a factor $u$ and down by a factor $d$ , and a $1 investment in a risk-free bond returns an amount $R$ per time step, which of the following statements is true in a market that is free from arbitrage?
A) $d

Question

In the binomial model, if the stock moves up by a factor $u$ and down by a factor $d$ , and a $1 investment in a risk-free bond returns an amount $R$ per time step, which of the following statements is true in a market that is free from arbitrage?
A) $d < u < R$
B) $\mathcal { U } < R < d$
C) $d < R < u$
D) $R < d < u$

Quizplus · Accepted Answer

For a market to be free from arbitrage in the context of the binomial model, the risk-free rate $R$ must be between the down factor $d$ and the up factor $u$, ensuring that investing in the stock is neither a guaranteed win nor a guaranteed loss compared to the risk-free asset. This condition is necessary to prevent arbitrage opportunities, where one could make a riskless profit.

In the Binomial Model, If the Stock Moves Up by a Factor