Chapter 12 - The Binomial Model

Question 1

What is the Binominal Model used for?

Answer 1

Value/Price Derivatives

Question 2

What are the 5 assumptions of the Binomial Model?

Answer 2

• The principle of no arbitrage apply
• No trading costs
• No taxes
• No minimum or maximum units of trading
• Stocks and bonds can only be sold at discrete times

Question 3

What is the Expected Return of the underlying stock under the risk-neutral probability Q at time 1? (stock price at t=0 is S0)

Answer 3

E_Q[S1] = S0Uq + S0D(1-q)

q=(exp(r)-d)/(u-d)

E_Q[S1] = S0*exp(r)

Question 4

What is the value of q (the risk-neutral probability)?

Answer 4

q= (exp(r)-d)/(u-d)

Question 5

Why is Q called the risk-neutral probability?

Answer 5

E_Q[S1] = S0Uq + S0D(1-q) = S0*exp(r)

Question 6

How many states in the n-binomial tree at time n?

Answer 6

2^n

Question 7

How does the binomial model allow for different level of volatility in different states?

Answer 7

By allowing different values for u and p in different states.

u & p are price factors.

Question 8

What is the downfall to allowing for different levels of volatility in each state?

Answer 8

the model is limited by the number of states which exists even for relatively low numbers i.e. 2^n.

Question 9

What does the Recombining Binomial tree assume?

Answer 9

That u & d and the same in every states.

Question 10

How many different states do we have for the recombining binomial tree?

Answer 10

N+1

Question 11

What is the formula for the price of a derivative at time t using the recombining binomial tree?

Answer 11

Vt = exp(-r(n-t)) sun[0, n-t] f(S_t* u^k *d^(n-t-k)) * (n-t)Ck * q^k * (1-q)^(n-t-k)