Chapter 13 - The Binomial Model

Question 1

Binomial model assumptions (5)

Answer 1

1. There are no trading costs
2. No taxes
3. No min or max units of trading
4. Stocks and bonds can only be bought and sold at discrete times
5. Principle of no arbitrage applies (d< e^r

Therefore, the model seems to be unrealistic. It simply provides a great computational tool for derivative pricing.

Question 2

Cash process

Answer 2

B_t = e^rt

Assumed to be risk free and predictable throughout the process.

Question 3

Replicating portfolio

Answer 3

A replicating portfolio will always precisely reproduce the relevant payoff or cashflow.
A replicating portfolio is only a hedging portfolio if the position taken in it is opposite to that of the payoff or cashfloe which it aims to reproduce.

Question 4

Hedging portfolio

Answer 4

A hedging portfolio aims to reduce the amount of risk relating to a derivative strategy, but is not guaranteed to reproduce the payoff or cashflow precisely.

Question 5

Equivalent measures

Answer 5

Two measures P and Q which apply to the same sigma-algebra F are said to be equivalent if for any event E in F:
P(E)>0 iff Q(E)>0
Where P(E) and Q(E) are the probabilities of E under P and Q respectively.

Question 6

Other names for state price deflator

Answer 6

1. Deflator
2. State price density
3. Pricing kernel
4. Stochastic discount factor

Question 7

Define Hedging strategy

Answer 7

An investment strategy which reduces the amount of risk carried by the issuer of the contract.

A replicating portfolio is only a hedging strategy if the position taken in is the opposite to that of the payoff or cashflow which it aims to reproduce.

Question 8

In the recombining model, how many states do we have at time n?

Answer 8

Instead of 2ⁿ we have n+1 possible states

Question 9

Calibrating binomial models: Cox, Ross and Rubenstein (1979)

Answer 9

u = exp(sigma*sqrt(delta t))

d = exp(- sigma*sqrt(delta t))

Add v delta t in the end of the exponential if dividend rate is v