Option Pricing

Question 1

What is the Binomial tree ?

Answer 1

-A digram the depicts the different possible paths that the stock price might follow over the life of an option

Question 2

What are some assumptions of the binomial tree ??

Answer 2

1. Stock prices follow a random walk
2. no arbitrage opportunities

Question 3

what is the simple binomial model ?

Answer 3

Question 4

What does the binomial tree look like for a call option

Answer 4

Question 5

Binomial tree for setting up a riskless portfolio

Answer 5

Question 6

What is the value of the portfolios if the stock prices change ?

Answer 6

Question 7

How would you value this option

Answer 7

Question 8

What are the notations of the one-step tree ??

Answer 8

Question 9

using the one step method when is the portfolio riskless ??

Answer 9

Question 10

Write this in words

Answer 10

The portfolio is riskless when the value of stock at time T if the price goes up multiplied by the ratio of the change in the option price to the change in the stock price take away the value of the call option at time T if stock price goes up, is equal to when the value of stock at time T if the price goes down multiplied by the ratio of the change in the option price to the change in the stock price take away the value of the call option at time T if stock price goes down

Question 11

What is delta in option pricing ??

Answer 11

The ratio of the change in the option price to the change in the stock price

Question 12

How do you find delta in option pricing

Answer 12

Question 13

What is the equation to find the option value in the general one-step method ?

Answer 13

Question 14

In option pricing what is the binomial tree looking like with probability included ?

Answer 14

p and 1-p are up and down movements in stock price

Question 15

Using option pricing with probabilities work out the price of this option

Answer 15

Question 16

Why when pricing an option does the risk preferences not matter ??

Answer 16

-The expected return on a stock (or any other investment) is the risk-free rate.
-The discount rate used for the expected payoff on an option (or any other instrument) is the risk-free rate.
-This gives the right price for a derivative in all worlds

Question 17

Show the general two-step model

Answer 17

Question 18

What is the equation for a two-step call option price ?

Answer 18

Question 19

What is the equation for a two-step put option price ?

Answer 19

Question 20

For the two-step option pricing method how do u find P

Answer 20

Question 21

Give an example of a Delta ratio and explain how it hedges risk

Answer 21

-If the delta ratio is 0.25% than 0.25 share of stock must be held in the the portfolio to hedge away risk

Question 21

What is Delta ?

Answer 21

-The ratio of the change in the option price to the change in the price of the underlying asset

-It is also a hedge ratio that provides insurance to the option portfolio value against share price movements

Question 22

What is the differences of delta in a call option and put option ??

Answer 22

Delta in a call is positive, whereas delta in a put is negative

Question 23

Does the value of delta stay the same from node to node ??

Answer 23

No it doesn’t it varies

Question 24

How do you choose the parameters u and d ??

Answer 24

They show be chosen to match the volatility of the stock price

Question 25

Probability for assets other than non-paying dividends

Answer 25