Chapter 24 Finance

american/european options

An American option may be exercised anytime up to and including the expiration date. A European option may be exercised only on the expiration date.

call option pricing at expiry

At expiry, an American call option is worth the same as a European option with the same characteristics. - If the call is in-the-money, it is worth ST-E. - If the call is out-of-the-money, it is worthless Where ST is the value of the stock at expiry (time T) E is the exercise price.

put option at expiry

At expiry, an American put option is worth the same as a European option with the same characteristics. If the put is in-the-money, it is worth E - ST. If the put is out-of-the-money, it is worthless. P= Max[E - ST, 0]

investors in options

Buyer (holder) - pays the premium Seller (writer) - receives the premium

formula for call option value

Call option value = Stock value − Present value of the exercise price = S0 − E/(1 + Rf)t

out-of-the-money

Exercising the option would result in a negative payoff

in-the-money

Exercising the option would result in a positive payoff.

at-the-money

Exercising the option would result in a zero payoff (i.e., exercise price equal to spot price).

Call option trends

Higher the stock price the more the call is worth higher the exercise price the less the call is worth longer the time to expiration the more the call is worth higher the risk free rate the more the call is worth because - exercise price is a cash outflow, a liability. The current value of the liability goes down as the discount rate goes up.

strike price/exercise price

The fixed price specified in the option contract at which the holder can buy or sell the underlying asset is called the strike price or exercise price. The strike price is often called the striking price.

option

an arrangement that gives its owner the right to buy or sell an asset at a fixed price anytime on or before a given date.

seller of a put option

an investor who sells a put option receives cash up front and is then obligated to buy the asset at the exercise price if the option holder demands it

expiration date

an option usually has a limited life. The option is said to expire at the end of its life. The last day on which the option may be exercised is called the expiration date.

upper bound on call option

call option will sell for no more than underlying asset

call option

gives the owner the right to buy an asset at a fixed price during a particular time period. - has a long position in the contract It may help you to remember that a call option gives you the right to "call in" an asset.

put option

it gives the holder the right to sell that asset for a fixed exercise price. - If you buy a put option, you can force the seller of the option to buy the asset from you for a fixed price and thereby "put it to them."

lower bound on call option

lower bound is 0 or stock price - exercise price, whichever is bigger. lower bound = intrinsic value - what call is worth if it expires

special option features

options give buyer the right, but not the obligation, to do something. The buyer uses the option only if it is profitable to do so; otherwise, the option can be thrown away.

seller of a call option

seller receives money up front and has the obligation to sell the asset at the exercise price if the option holder wants it. -short position in the contract

exercising the option

the act of buying or selling the underlying asset via the option contract

selling options

the seller or writer always has the obligation the seller receives the option premium in exchange. The Seller hopes the option will never be exercised.

stock price compared to exercise price for calls

want stock price higher than exercise price