Topic 14 Option Pricing

Question 1

Put-Call Parity

Answer 1

Allows to price call IF know value of put and vice versa

Question 2

Binomial Option Pricing

Answer 2

-Arbitrage Model: uses only interest rate and value of underlying asset

Question 3

Binomial Option Pricing Assumptions

Answer 3

1) Single Period with 2 dates, t=0, t=1
2) Stock price can go up or down ->two possible values of stock at t=1
3) Perfect Markets with no transaction costs
4) Risk free rate, Rf

Question 4

Value a call in Binomial pricing

Answer 4

1) Determine payoff option at time 1
2) Create a portfolio at time 0 by combining N shares of stock and B dollars in the Rf bond
3) Choose N and B such that payoffs to portfolio exactly replicate the payoff at time 1 equal to the call option at t=0
-payoff of replicating portfolio and option are the same->C=(S)(N)+B
4) Solve for system of equations for B which will allow you to sub back into C to find Call price
*In multiple periods just work backwards

Question 5

What is hedging and When hedge

Answer 5

What = Wish to protect the payoff of a position from adverse changes
When = The losses in the protected position are compensated by the gains in the hedged position -> decreases risk and gains

Question 6

Perfect Hedge

Answer 6

-A hedge where all the changes in the protected position are perfectly compensated by changes in the hedged position
*Binomial model creates a portfolio of stock and risk free bond that can perfectly “hedge” the payoff of the option
-thus through no arbitrage rep portfolio must equal the value of the option at t = 0

Question 7

Hedge Ratio

Answer 7

-number of shares needed to replicate the value of a call
N=(Cu-Cd)/(Su-Sd)
call up - down / stock up - down

Question 8

Pseudo probability

Answer 8

p and 1-p
derived as probabilities of the stock price moving up or down

Question 9

Black-Scholes Pricing Model

Answer 9

-Easier formula to use and extend periods over binomial
->extension of binomial pricing model for infinite number of small periods

Question 10

Black Scholes Assumptions

Answer 10

1) Stock pays constant dividend yield
2) Constant interest rate, r, and stock volatility, o^2
3) Stock prices are continuous (no discrete jumps)

Question 11

N(d) term

Answer 11

-value that comes from standard normal dist
-probability between 0 and 1
-probability that the option will expire in the money

Question 12

e^(-rT) term

Answer 12

present value factor based on continuously compounded returns for T period (time to maturity in years)

Question 13

Value of call is higher when:

Answer 13

Ex Price (X) is lower
So is higher
Dividends are lower
Interest rate is higher
Time to maturity is greater
stock volatility is greater

Question 14

Value of Put is higher when:

Answer 14

Different than Call:
Ex price (X) is higher
Stock price lower
Dividends are greater
Interest rate is lower
Same as Call:
Time to maturity is greater
stock volatility is greater

Question 15

Implied Volatility

Answer 15

-The standard deviation necessary for the option price to be consistent with the Black Scholes formula
->if you believe actual volatility > implied volatility that option FV > price thus is Cheap

Question 16

Delta

Answer 16

-Same as value of hedge ratio aka option’s delta
->Delta value option/Delta value stock
-call option has positive hedge ratio <1
-put option has negative hedge ratio <1
*cannot be less than one bc options values cant more more than the dollar increase in stock value

Question 17

Option’s delta value?

Answer 17

-Slope of option pricing curve
*assumes no dividends
*Hedge ratio changes with stock price and time
——————————-
For Call: H = N(d1)
For Put: H = N(d1) -1
———————————–

Question 18

Delta Neutral Hedge

Answer 18

-Use options to protect portfolio from small changes in underlying portfolio prices
*bc hedge ratio changes with large changes in price only protects small price changes
->therefore have to rebalance over time or constantly (delta hedging or dynamic hedging)