In the 3-period binomial model, define the random variables (Yo, Y, Y, Y3) by setting Yk...

Transcribed Image Text:

In the 3-period binomial model, define the random variables (Yo, Y₁, Y₂, Y3) by setting Yk (₁) to be the number of times H occurs in the sequence Yk (₁,..., wk) not adjacent to another H. Examples: Y₁(H) = 1, Y₂(HH) = 0, and Y3(HTH) = 2. The coin flips are iid with P(H) = P(T) = 1/2. (a) Write out the values that this process takes on in each period on a 3-period tree. (b) Determine whether or not this process is Martingale, and prove your assertion. (c) Determine whether or not this process is Markov, and prove your assertion. In the 3-period binomial model, define the random variables (Yo, Y₁, Y₂, Y3) by setting Yk (₁) to be the number of times H occurs in the sequence Yk (₁,..., wk) not adjacent to another H. Examples: Y₁(H) = 1, Y₂(HH) = 0, and Y3(HTH) = 2. The coin flips are iid with P(H) = P(T) = 1/2. (a) Write out the values that this process takes on in each period on a 3-period tree. (b) Determine whether or not this process is Martingale, and prove your assertion. (c) Determine whether or not this process is Markov, and prove your assertion.