Question

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?

Answer 1

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.