In the one-period binomial model, let d be the down factor and let r be the risk-free rate. What will be the arbitrage opportunity if d > 1 + r?
If d > (1 + r) we can create an arbitrage opportunity by borrowing an amount equal to the current stock pirce, S and buying one unit of stock.
Since d > (1 + r); hence, d - (1 + r) > 0
|Action at time 0||t = 0||t = T|
|Borrow @ risk free rate||S||- (1 + r) x S|
|Buy stock||- S||d x S|
|Total||0||d x S - (1 + r) S = [d - (1 + r)] x S >0|
Thus you end up making a riskfree and riskless profit of [d - (1 + r)] x S at t = 1 without any initial investment. This is the arbitrage profit.
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