Chapter 13 Delta Hedging

Question 1

What is Delta Hedging?

Answer 1

It is buying an offsetting number of stocks (delta of an option) so that we don’t lose much as that option changes value

Question 2

During Delta Hedging what 3 things can change the value of our “portfolio”, hint not GREEK

Answer 2

1. Borrowing Capacity Change due of portfolio
2. purchase or sale of new stock
3. Interest payments

Question 3

what is theta’s effect on delta hedging?

Answer 3

as time goes on, the value of an option decreases as theta decreases so works on market makers side

Question 4

what is gamma’s effect on delta hedging?

Answer 4

Position becomes unhedged, so we lose money on large movements.

Question 5

What is a self-financing portfolio

Answer 5

A portfolio that moves by one standard deviation, so that the market maker always breaks even.

The binomial model comes close to this, very close.

Question 6

What is the formula for delta gamma change in option price approximation, using epsilon as the change in price

Answer 6

average delta is ((delta1 + delta1(epsilongamma))/2)

new Call price =
old Call price + epsilon * average delta

Question 7

What is the formula for delta gamma and theta change in option price approximation, using epsilon as the change in price and h as change in time

Answer 7

average delta is ((delta1 + delta1(epsilongamma))/2)

new Call price =
old Call price + epsilon * average delta + h*theta

Question 8

mean return on Delta Hedged position is

Answer 8

risk free rate

Question 9

By rehedging more often (hourly vs. daily) you gain what in delta hedging

Answer 9

lower variance, specifically 1/24 for the daily vs. hourly.

Question 10

Can you delta hedge for an american option tat should be exercised

Answer 10

no

Question 11

Black Scholes partial differential equation is on 396

Answer 11

yep

Question 12

What are 4 ways Market makers can avoid large payments when stocks make large moves

Answer 12

1. buy deep out of money options
2. variance swaps (make payement on low hcange , get payment on high change)
3. create interest in offsetting options
4. gamma neutral position

Question 13

How to gamma hedge.

Answer 13

Find option and take raio of gammas to get how many of one to buy in relation of other, then fidn new delta and buy stocks(0 gamma) to ofset delta

Question 14

Greeks for a binomial model

Gamma->

Answer 14

Delta of step up - delta of step down / (up stock price - down stock price) doesn’t work at time 0

Question 15

Greeks for a binomial model

Theta->

Answer 15

use epsilon = uds - s and use delta gamma theta approximation.