L6/7- Option Pricing

Question 1

What are 2 types of options

Answer 1

–Puts
–Calls

Question 2

Define Option

Answer 2

An option is a financial contract giving the buyer the right, but not the obligation, to buy or sell an asset at a specific price on or
before a certain date.

Question 3

Define Call Option

Answer 3

gives its owner the right to buy stock at a
specified exercise or strike price on or before a specified maturity date.

Question 4

Suppose you believe an asset will
increase in value. You purchase a call option to buy the asset at $900 in a month. What happens if the value rises to $950

Answer 4

you exercise your option, buy it for $900, and gain $50 in value.

Question 5

What is the formula for a call option payoff?

Answer 5

𝐶𝑎𝑙𝑙 𝑝𝑎𝑦𝑜𝑓𝑓 = 𝑚𝑎𝑥(𝑆 − 𝑋, 0)

S - the current price of the underlying asset
X - exercise price- buy one unit of stock at X exercise price

Question 6

True or False for Call Options: For every pound, the stock price is higher than the exercise Price, you will get a pound profit.

Answer 6

True

Question 7

How do you interpret the payoff of a call option when the stock price is higher or lower than the exercise price?

Answer 7

When the stock price (S) is higher than the exercise price (X), the call option will have a profit:
You can buy the stock at the lower exercise price and sell it at the market price.
Profit = S−X.
When the stock price (S) is lower than the exercise price (X), the call option expires worthless (because you’d buy at a lower price on the open market).
Payoff = 0.

Question 8

What is the difference between European and American call options?

Answer 8

–European Call Option: Can only be exercised at maturity (the specified expiration date).
–American Call Option: Can be exercised at any time before or at maturity

Question 9

Define Put Options

Answer 9

A put gives you the right to sell the share

Question 10

Suppose the asset might lose value soon.
You buy a put option to sell it at $900.
* If the assets price drops to $850, you use your option to sell at $900… what do you gain?

Answer 10

, gaining $50 compared to the lower market price.

Question 11

What’s the formula for Put Payoff

Answer 11

𝑃𝑢𝑡 𝑝𝑎𝑦𝑜𝑓𝑓 = max (𝑋 − 𝑆, 0)

–S - the current price of the underlying asset
–X - exercise price- buy one unit of stock at X exercise price

Question 12

What is the payoff of buying one call option and investing in the present value of the strike price at the risk-free rate?

Answer 12

Payoff=max(S−X,0)+X=max(S,X)

Question 13

What is the payoff of buying one put option and investing in one unit of stock?

Answer 13

Payoff=max(X−S,0)+S=max(X,S)

Question 14

What is the Put-Call Parity equation?

Answer 14

C+PV(X) = 𝑺𝟎+P

C=price of call option, P= price of put option, S0= current price of underlying asset, X= strike price of options, PV(X) = Present value of the strike price discounted at the risk-free rate

Question 15

What is a synthetic risk-free investment?

Answer 15

is a combination of financial instruments that replicates the payoff of a risk-free bond by using a mix of the underlying asset, a call option, and a put option

Question 16

Synthetic risk- free investment equation

Answer 16

𝑷𝑽 (𝑿) = 𝑺𝟎 + 𝑷 − C

PV(X) is the present value of the strike price discounted at the risk-free rate
➢ C is the price of the call option
➢ P is the price of the put option
➢ S is the current price of the underlying asset
➢ X is the strike price of the options

Question 17

In a Binomial world, what are the possible outcomes for an asset’s price?

Answer 17

–Prices go up by a certain percentage
–Prices go down by a certain percentage

Question 18

CAPM Formula

Answer 18

ERi = Rfr + βi(ERm – Rf)

ERi= Expected return of investment
Rfr= risk free rate
(ERm – Rf)= market Risk premium

Question 19

REVISE BINOMAL VALUATION

Question 20

What is Option pricing theory about

Answer 20

risk-neutral valuation

Question 21

What is Risk-neutral valuation used for in option pricing theory?

Answer 21

Risk-neutral valuation is used to calculate the value of an option by assuming that all assets are priced in such a way that the expected return on any asset is the risk-free rate, regardless of the asset’s risk.

Question 22

What does the CAPM model tell us about the price of an asset?

Answer 22

Price= Expected CF/(1+risk adjusted DR)

Question 23

How does option pricing theory differ from the CAPM model in valuing assets?

Answer 23

Price= (Expected CF * 𝑟𝑖𝑠𝑘−𝑛𝑒𝑢𝑡𝑟𝑎𝑙 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑒𝑠) / (1 + Rfr)

Question 24

Are the valuation methods of CAPM and option pricing theory equivalent?

Answer 24

Yes, the valuation methods of CAPM and option pricing theory are equivalent.

–CAPM requires information about the asset’s beta.
–Option pricing theory requires information about the risk-neutral probabilities.

Question 25

REVISE BLACK SCHOLES FORMULA