Chapter 10 Binomial Pricing

Question 1

Law of one price definition

Answer 1

if two portfolios have the same payoffs then they must have the same price

Question 2

How does leverage relate to options

Answer 2

There is implicit leverage in the stock

Question 3

delta formula for binomial pricing

Answer 3

(e^(-delta * h)) * ((Cu - Cd) / S(u - d))

Question 4

B formula for binomial

Answer 4

e^(-rh) * [ (uCd - d(Cu))/ u - d]

Question 5

What is delta’s interpretation in the binomial pricing method

Answer 5

the amount by which the option changes if the stock moves by 1 dollar

Question 6

what is u in the binomial pricing model

Answer 6

1 + the capital gains rate (Su/S)

Question 7

Formula for risk neutral probability

Answer 7

[e^((r-delta)*h) - d] / [u - d]

Question 8

Binomial Model, Formula for U

Answer 8

e^((r - delta)h) + σsqrt(h)

Question 9

Binomial Model, Formula for D

Answer 9

e^((r - delta)h) + σsqrt(h)

Question 10

Intuition behind U and D in the Binomial Pricing Model

Answer 10

e^((r - delta) * h) represents the risk-free rate, i.e. the rate if returns were certain and then under assumption, we assume it can either move one SD up or down, i.e. e^(σ*sqrt(h))

Question 11

given two prices, the continuously compounded rate can be found by…

Answer 11

taking the natural logarithm of S2/S1

Question 12

if monthly SD’s are σ, then yearly SD is

Answer 12

σ*sqrt(12)

Question 13

Difference in Binomial Tree when Pricing American Options

Answer 13

We check to see if we should exercise, I.e. we get more now than if we sold it and replace it with the higher value

Question 14

Why is the forward contract on currency X0(e^((r - rf)T))

Answer 14

It is for of the foreign currencies. You could be getting rf, but instead you are getting r. Like dividend yield.

Question 15

Difference in Binomial Tree when Currency is your underlying asset

Answer 15

Stock price is replaced with exchange rate and dividend yield is replaced with foreign exchange rate. Rember you subtract off what you aren’t getting now.

Question 16

Difference in Binomial Tree when Futures Contract is your underly asset

Answer 16

Assume risk free rate equals your dividend rate and use Futures Contract

Question 17

Difference in Binomial Tree when a Bond is your underly asset

Answer 17

Dividend rate = yield rate on bonds, returned to in Ch25. Major problems are volatility changes as time to maturaty changes and assuming interest rates are constant means bonds wouldn’t change prices.

Question 18

Value of an option using risk free probability and the binomial pricing model.

Answer 18

C = (e^-rh)*(pCu + (1-p)Cd)

Question 19

Early Exercise is characterized by three things:

Answer 19

1. paying/receiving the strike price
2. receiving/losing the underlying
3. Implicit protection

Question 20

condition for early exercise given that volatility is 0. For a Call Option

Answer 20

deltaS > Kr

Question 21

As time to expiration decreases, the value of the implicit protection…

Answer 21

decreases

Question 22

Risk neutral pricing is true because even if we use real probabilities we get

Answer 22

the same answer.

Question 23

skip if Emily

Answer 23

So basically risk neutral pricing is not useful because more tedious to get same answer, plus you have to estimate alpha the required return on the stock.

But you do it by finding e^-(lambda*h)(pCu + (1-p)Cd) where lambda(required return) is e^(-ah)Sdelta/Sdelta+B + e^(-rh)(b/b+Sdelta) delta is # of shares.

Question 24

as h->0, the binomial price model becomes

Answer 24

a lognormal distribution

Question 25

we can construct u and d in different ways and will get different answers but the same as h goes to 0. ANd u/d = e^(2sigmasqrt(h))

Answer 25

yep that’s right, good job