– the right to buy the underlying security

call option

the right to sell the same asset.

put option

Option contract terms

Two prices are important in evaluating an option position.

• The exercise price or strike price is the price the call buyer will pay to – or the put buyer will receive from – the option seller if the option is exercised.
• The exercise price (X) is to an option what the contract price (F_0,T) is to a forward agreement.
• The second price (option premium) is what the option buyer must pay to the seller at Date 0 to acquire the contract itself.

Two prices are important in evaluating an option position.

1. exercise price or strike price .
2. second price (option premium)

• The ______ is the price the call buyer will pay to – or the put buyer will receive from – the option seller if the option is exercised.
• The _____ is to an option what the contract price (F_0,T) is to a forward agreement.

exercise price (X) or strike price

• The second price _____ is what the option buyer must pay to the seller at Date 0 to acquire the contract itself.

(option premium)

OPTION CONTRACT TERM 1.1

• A basic difference between options and forwards is that an option requires this upfront premium payment from buyer to seller while the forward ordinarily does not.
• It is because forward contract allowed both the long and the short positions to WIN at Date T (depends on where S_T settled relative to F_0’T ) but the option agreement will only be exercised in the buyer’s favor; hence the seller must be compesated at Date 0, or he/she would never agree to the deal.
• Althoug both puts and calls require premium payments it is quite likely that these two prices will differ.
• As a definition, the Date 0 premium to acquire an option expiring at Date T as C_0’T for a call and P_0’T for a put .

Example: instead of a long position in a bond forward contract, the investor could have paid 20 (=C_0’T) at Date 0 for a call option that would have given him the right to buy the bond for 1,000 (=X) at Date T, but would not require him to do so if S_T is less than 1,000.

Option Valuation basics

• The Date 0 option premium can be divided into two components: intrinsic value and time premium.
• Intrinsic value represents the value that the buyer could extract from the option if they exercised it immediately.
• For a call, it is the greater of either zero or the difference between the price of underlying asset and the exercise price (max[0,S₀ – X]).
• For a put, intrinsic value would be max[0,X – S₀], as X would now represent the proceeds generated from the asset’s sale.
• An option with positive intrinsic value is to be in the money, while one with zero intrinsic value is out of the money.
• For the special case where S₀=X, the option is at the money.
• The time premium component then is the difference between the whole option premium and the intrinsic components:
• (C_0’T - max[0,S₀ – X]) for a call and
• (P_0’T - max[0,X – S₀ ]) for a put.

• The Date 0 option premium can be divided into two components:

1. intrinsic value
2. time premium.

• _____ represents the value that the buyer could extract from the option if they exercised it immediately.
• For a call, it is the greater of either zero or the difference between the price of underlying asset and the exercise price (max[0,S₀ – X]).
• For a put, _____ would be max[0,X – S₀], as X would now represent the proceeds generated from the asset’s sale.
• An option with positive intrinsic value is to be in the money,
• while one with zero intrinsic value is out of the money.
• For the special case where S₀=X, the option is at the money.

Intrinsic Value

• For a _____, it is the greater of either zero or the difference between the price of underlying asset and the exercise price (max[0,S₀ – X]).

call

• For a _____, intrinsic value would be max[0,X – S₀], as X would now represent the proceeds generated from the asset’s sale.

put

An option with positive intrinsic value is to be ___ the money,

in

• while one with zero intrinsic value is ____ of the money.

out

• For the special case where S₀=X, the option is ___ the money.

at

• The ____ component then is the difference between the whole option premium and the intrinsic components:
• (C_0’T - max[0,S₀ – X]) for a call and
• (P _0’T - max[0,X – S₀ ]) for a put.
• The buyer is willing to pay this amount in excess of the option’s immediate exercise value because of his/her ability to complete the transactions at a price of X that will remain in force until Date T.
• Thus the _____ is connected to the likelihood that the underlying asset’s price will move in the anticipated direction by the contract’s maturity.

time premium

Option Valuation basics 1.1

• Basic relationship of valuing options premiums:
• (1) the buyer of a call option is never obligated to exercise, the contract should always at least be worth its intrinsic value.
• In any event, neither a call or a put option can be worth less than zero.

• (2) For a call options having the same maturity and the same underlying asset, the lower the exercise price (X), the higher will be the contract’s intrinsic value and hence the greater its overall premium.
• Coversely, put options with higher exercise prices are more valuable than those with lower exercise prices.

• (3) increasing the amount of time until any option expires will increase the contract’s time premium because it allows the price of the underlyig security more opportunity to move in the direction anticipated by the investor (that is, up for a call option, down for a put option)

Option trading markets

• Like forwards and futures, options trade both in over-the-counter markets and on exchanges.
• When exchanged-traded, just the seller of the contract is required to post a margin account because he is the only one obligated to perform on the contract on the later date.
• Options can be based on a wide variety of underlying assets, including futures contracts or other options.

Investing with derivative securities

The ultimate difference betweeen forward and option lies in the way investor must pay to acquire those benefits of the two derivatives.

The primary nature of derivative investing

• Assuming investor A decides at Date 0 to purchase shares in BAB corp. six months from now, coinciding with an anticipated receipt of funds.
• Assuming that both BAB share forward contracts and call options are available with the market prices of F_0’T and C_0’T (where T =0.50 year) and that
• the exercise price (X) of the call option is equal to F _0’T.
• Thus , if the investor wants to lock in the price now at which the share purchase will eventually take place, he has two choices:
• a long position in the forward or the
• purchase of the call option.

The primary nature of derivative investing 1.1

• The clear difference between these strategies is that the forward position requires no initial payment or receipt by either party to the transaction,
• whereas the investor (call buyer) must pay a cash premium to the seller of the option.
• This front-end option payment releases the investor from the obligation to purchase BAB shares at Date T if the terms of the contract turn out to be unfavorable (S_T less than X).
• When the expiration date price of BAB shares exceeds the exercise price, the investor will exercise the call and purchase the shares.
• However, this leads to exactly the same exchange as the long forward contract.
• It is only when the share price falls below X (F_0’T) on Date T that there is a difference between the two positions; under this condition, the right provided by the option not to purchase BAB shares is valuable since the investor in the forward contract will be required to execute that position at a loss.
• Thus the call option can be viewed as the good half of the long forward position because it allows for the future acquisition of BAB shares at a fixed price but does not require the transaction to take place.

The primary nature of derivative investing 1.2

• It is the critical distinction between forward and option contracts.
• Both the long forward and the long call positions provide the investor with exactly the same amount of insurance against the price of BAB shares rising over the next six months.
• Both contract provide a payoff of [S_T – X] = S_{T –} F_0,T] whenever S_T exceeds X,
• which reduces the effective purchase price for the share back to X.
• The difference show the investor is required to pay for that price insurance.
• With a forward contract , no money is paid up front , but the investor will have to complete the purchase at the expiration date, even if the share price falls below F_0’T.
• Conversely, the call option will never require a future setllement payment, but the investor will have to pay the premium at origination.
• Thus for the same Date T benefit , the investor’s decision between these two insurance policies comes down to choosing the certainty of a present premium payment (long call) versus the possiblity of a future payment (long forward) that could potentially be much bigger.

The primary nature of derivative investing 1.3

• For a clearer distinction, suppose the investor A plans to buy BAB shares in six months when some of the bonds in his portfolio mature.
• He is concerned that share values could rise substantially between now and the time he receives his investment funds, and so to hedge that risk he considers two insurance strategies to lock in the eventual purchase:
• (1) pay nothing now to take the long position in a six month BAB share forward contract with a contract price of F_0,T = 45, or
• (2)pay a premium C_0,T = 3.24 for a six-month.
• European -style Call option with an exercise price of X= 45.
• If at the time of his decision the price of BAB shares is S₀ = 40,
• the call option is out of money, meaning that its intrinsic value is zero and the entire 3.24 is time premium.

The primary nature of derivative investing 1.4

• An obvious difference between the two strategies is that the option entails a front-end expense while the forward position does not.
• The other difference occur at the expiration date , depending on whether the BAB share price is above or below 45.
• If, for instance, S_T = 51, both the long forward position and the call option will worth 6 (51-45) to the investor, reducing his net purchas price for BAB shares to 45 (51-6).
• That is, when the shares settled above 45( the common value for F_0’T and X) both long forward and long call positions provided the same protection agains the rising prices.
• On the other hand , if S_T = 40.75, the forward contract will require the investor to pay 4.25 (=40.75 -45) to his counterparty raising once again the net cost of his shares to 45.
• With the call option , however, he could have let the contract expire with out exercising it and purchased his BAB shares in the market for only 40.75.
• Thus the exchange for the option’s front-end expense of 3.24, the investor retains the possiblity of paying less than 45 for his eventual share purchase.

The primary nature of derivative investing 1.5

• The connection between forward contracts and put options can be made in a similar fashion .
• Suppose a different investor – let us say investor B, has decided to liquidate shares of BAB for her portfolio in six month’s time.
• Rather than risk a falling share price over that period,
• she could arrange now to sell the share at that future date for a predetermined fixed price in one of two ways:
• as short forward position or the purchase of put option.
• For the same insurance against BAB share price declines,
• the choice comes down to the certainty of paying the put option premium versus the possibility of making a potentially larger payment with the forward contract by having to sell his/her share for X=F_0’T when that value is considerably less than the share’s Date T market price.
• The put option allows the investor to walk away from her obligation under the short forward position to sell her share on the expiration date under disadvantageous conditions.
• Thus, in exchange for a front-end premium payment, the put option enables the investor to acquire the good half of the short position in a forward contract.