State the conditions under which binomial tree model is arbitrage free.

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Answer-

The conditions for the binomial tree model to be arbirage free are

1) The Q measure is the risk neutral measure with no interpretation. There has to be a risk neutral measure Q for the binomial measure to be arbitrage free.

2) The abinomial model is free of arbitrage if there exists a risk neutral measure 'Q' and complete if the risk neutral measure is unique.

3) The binomial tree is free of arbitrage on the condition that

u > e(r x T) > d.

u - the increase in rate of stock in up movement
d - the decrease in rate of stock in ddown movement
T - maturity period
r - risk free rate
e - 2.7183

4) The binomial tree model is arbitrage -free and complete if it satisfies the condition
d < 1+r < u
u - increased rate of the stock in up movement
d - decreased rate of the stock in down movement
r - risk free rate

5) The simplest random binomial tree model with two possible environments (u1, d1) and (u2, d2) is arbitrage-free and complete if the given condition is satisfied

max (d1,d2) < 1+r < min ( u1,u2)

u1, d1 - The conditional values in one case
u2, d2 - The conditional values in other case
r - risk-free rate

jeff jeffy answered 1 year ago

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