In the binomial model,if the stock moves up by a factor $\mathcal { U }$ 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 $\mathcal { U }$ 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) $u < R < d$
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 borrowing or lending at the risk-free rate cannot be exploited for riskless profit. This is expressed as $d < R < u$.

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