Lecture 8 - Binomial trees

Question 1

Explain the no-arbitrage and risk-neutral valuation approaches to valuing a European option using a one-step binomial tree.

Answer 1

In the no-arbitrage approach, we set up a riskless portfolio consisting of a position in the option and a position in the stock.
By setting the return on the portfolio equal to the risk-free interest rate, we are able to value the option.
When we use the risk-neutral valuation, we first chose the probabilities for the branches of the tree so that the expected return on the stock equals the risk-free interest rate. We then value the option by calculating its expected payoff and discounting the expected payoff at the risk-free interest rate.

Question 2

What is meant by the delta of a stock option?

Answer 2

The delta of a stock option measures the sensitivity of the option price to the price of the stock when small changes are considered.
Specifically, it is the ratio of the change in the price of stock option to the change in the price of the underlying stock.

Question 3

This strategy involves buying a call option and a put option on the same underlying asset, with the same expiration date and strike price. This strategy is useful when a trader expects a large price movement in the underlying asset but is uncertain about the direction of the movement. This includes bottom and top straddles.

Answer 3

Straddle trading

Question 4

This strategy involves buying a call option with a low strike price, selling two call options with a higher strike price, and buying another call option with an even higher strike price. This creates a profit zone in which the underlying asset’s price is near the middle strike price.

Answer 4

Butterfly trading

Question 5

The trading strategy involves taking a position in two or more options of the same
type (i.e., two or more calls or two or more puts).

Answer 5

Spread

Question 6

This can be created by buying a European call option on a stock with a certain strike price and selling a European call option on the same stock with a higher strike price.

Answer 6

Bull spread

Question 7

This is created by buying a European put with one strike price and
selling a European put with another strike price. The strike price of the option
purchased is greater than the strike price of the option sold

Answer 7

Bear spread

Question 8

This is a combination of a bull call spread with strike prices K1 and K2 and a bear put spread with the same two strike prices.

Answer 8

Box spread

Question 9

This involves positions with three different strike prices. It can be created by buying a European put option with a relatively low strike price 𝐾1=55, buying a European put option with a relatively high strike price 𝐾3=65, and selling two European put options with a strike price 𝐾2=60, halfway between 𝐾1 and 𝐾3.

Answer 9

Butterfly spread

Question 10

This can be created by selling a European call option with a certain strike price and buying a longer-maturity European call option with the same strike price.

Answer 10

Calendar spread

Question 11

In this case, both the expiration date and the strike price of the calls are different.

Answer 11

Diagonal spread

Question 12

This is an options trading strategy that involves taking a position in both calls and puts on the same stock.

Answer 12

Combinations

Question 13

This involves buying a European call and put
with the same strike price and expiration date

Answer 13

Straddle

Question 14

This consists of a long position in one European call and two European puts with the same strike price and expiration date

Answer 14

Strip

Question 15

This consists of a long position in two
European calls and one European put with the same strike price and expiration date.

Answer 15

Strap

Question 16

This is sometimes called a bottom vertical combination, an investor buys a European put and a European call with the same expiration date and different strike prices.

Answer 16

Strangle