Chapter 13: The Binomial Model

Question 1

4 Assumptions of the binomial model

Answer 1

• Assets may be bought and sold at integer times t = 0,1,2,3,…
• Assets may be held in any amount
• There are no taxes or transaction costs
• There are no arbitrage opportunities

Question 2

q, under the risk-neutral probability measure

Answer 2

q = (e^r - d) / (u - d)

Question 3

State the condition under which the market is arbitrage free

Answer 3

The market is arbitrage free if and only if there exists a probability measure under which discounted asset prices are martingales.

Question 4

Recombining binomial tree (lattice)

Answer 4

A binomial tree in which values of u and d, and consequently the risk-neutral probabilities are the same in all states.

With such models:

• the volume of computation required is reduced
• Nt, the number of up-steps up to time t, has a binomial distribution with parameters t and q.