What does it mean that binomial interest rate trees are “lognormal random walk” models?
I was looking to understand the intuition of what does it refers when it says that.
Thanks.
The technical definition of a random walk is, “a random process consisting of a sequence of discrete steps of fixed length.”
In a binomial interest rate tree, the discrete steps go from the interest rate at one time to an interest rate at the next time; the fixed length is the difference in times. In a binomial interest rate tree, the interest rate can take on exactly two possible values at subsequent nodes: the up value and the down value.
A lognormal random walk means that the prices will have a lognormal distribution (which is the case when the (continuously compounded) returns have a normal distribution), and that there is a fixed step (in this case, a fixed amount of time) between one price and the next price.