Derivative Products

Options: Contract Terms & Conditions

Terminology & Definitions

Options are the right but not the obligation to buy (call) or sell (put) the underlying asset. The buyer of an option pays a premium for these rights to the seller of the contract.  The seller of the contract is obligated to perform if the buyer exercises.

For purposes of this module, terms and conditions will relate to equity options.

CALLS

The buyer of a call has the right, but not the obligation to buy the underlying asset at the strike price prior to or on the expiration date (depending on the expiration type). The buyer of the call pays a premium for the right.

The seller of a call receives the premium in exchange for taking on the obligation of selling the underlying asset (at the strike price) if the buyer of the call exercises. The call buyer is likely to exercise their right if the asset is ABOVE the strike price.

PUTS

The buyer of a put has the right, but not the obligation to sell the underlying asset at the strike price prior to or on the expiration date (depending on the expiration terms of the option). The buyer of the put pays a premium for the right.

The seller of the put receives the premium in exchange for taking on the obligation of buying the underlying asset (at the strike price) if the buyer of the put exercises. The put buyer is likely to exercise their right if the asset is BELOW the strike price.

THE INPUTS TO PRICE AN OPTION

To price a call or put on the common stock of a public company, the following variables are known:

Asset price – the current price of the common stock (currency units per share)

Strike price – the price at which the option holder can buy (sell) the underlying asset upon exercising the call (put)

• Exchange-traded options have fixed strike prices
• Exchanges also offer FLEX options, which allows buyers and sellers to agree to customized terms but still have the protection of the Options Clearing Corporation and a central marketplace for pricing.
• OTC options are customized contracts between two counterparties.

Expiration date – calculate the fraction of a year to expiration.  i.e., 60 days to expiration = 60/365 = .16438

Expiration type – There are different types of exercise features:

• American style options can be exercised any business day
• European style options can be exercised only on the expiration date
• Bermudan style options can be exercised based on a schedule agreed to by the buyer & seller

Dividends – Any dividends which will be paid during the life of the option

Interest rate – The interest rate charged to borrow money from today to expiration day.

Implied Volatility – The market’s expectation of the magnitude of price change (up or down) at expiration.

OPTION PREMIUMS

The price of an option is broken down into two components: the intrinsic value and the time value.

Intrinsic Value is the amount the option is In-The-Money

Time Value is the amount above the Intrinsic Value

EXAMPLE:

• Asset at $65
• $60 call at $6.50
• Intrinsic Value = $5
• Time Value = $1.50

THEORETICAL VALUE

The diagram below shows the Theoretical Value & the Greeks for the option described.

• To the left of the word CALL or PUT are the inputs defined above.
• To the right of the word CALL or PUT are the outputs of the Black-Scholes Option Model (BSOM).

OPTIONS RISK-REWARD & BREAKEVEN POINTS

The table below

PAYOFF PROFILES – SINGLE OPTION POSITIONS

Three questions to ask for any option strategy

• Is the risk limited or unlimited?
  • If the risk is limited, what’s the limited amount?
• Is the reward limited or unlimited?
  • If the reward is limited, what’s the limited amount?
• What is (are) the breakeven point(s)?
  • Call = Strike + premium; Put = Strike – premium

The diagrams below show the payoff profiles (a.k.a. Hockeysticks) at expiration.  The graphs show:

• Long $65 call; Short $65 call;
• Long $65 put; Short $65 put;

INTRINSIC TABLES

Viewing each of the four illustrations above, on the left is an intrinsic value table. Intrinsic tables show the intrinsic value of the option on the expiration day.

• Long option positions show the intrinsic value in black (because we’re making money) and in
• Short option positions show the intrinsic values are red (because we’re losing money)

Intrinsic Tables make it easier to draw the “hockeysticks” or payoff profile graphs.  Especially with spreads, straddles, etc.

PUT-CALL PARITY

Put-Call Parity defines the “arbitrage-free” price of the options.

• “No-arbitrage” theory states the price of the derivative must equal the price of the underlying asset under the same terms and conditions.
  • We use the term “synthetic” when referring to the derivatives position.
  • We use the term “actual” when referring to the underlying asset.
• In other words, “no-arbitrage” theory states the synthetic asset must equal the “actual asset” (or forward)

ACTUAL LONG STOCK

The asset is purchased for $65.00.

• The spreadsheet above shows an Interest for 60 days of 3.50%.
  • The interest or Cost to Carry = $65 * .035 / (365 * 60) = $.38 . (rounded up)
  • The total cost basis for ACTUAL LONG STOCK is $65.38 (rounded up)

SYNTHETIC LONG STOCK

To create a SYNTHETIC LONG position in the underlying asset: BUY CALL & SELL PUT (same strike & expiration date).

• The $65 call is @ $3.44 and
• The $65 put is @ $3.06.
• In 60 days, if the stock is above $65, the call will be exercised. If the stock is below $65, the put will be assigned

The table below shows the SYNTHETIC LONG and the ACTUAL LONG

Notice the Synthetic Long Stock and Actual Long Stock provide the same result. This tells us the options are correctly priced with “no-arbitrage”.

PUT-CALL PARITY EQUATION

Call Price (C) + Present value of Strike Price (Ke-rt)  = Spot price of Asset (S) + put price (p)

MEMORY TIP: ClicK = SoaP 

SYNTHETIC OPTIONS

Just as we can create synthetic stock using options, we can create synthetic options using a combination of options and the underlying asset. The table below illustrates each possible single option position.

MEMORY ASSIST

• a long option can never be synthetically made using short options
• a short option can never be synthetically made using a long option

• SYNTHETIC LONG CALL = BUY a put AND BUY the underlying asset (1:1)
• SYNTHETIC LONG PUT = BUY a call and S
• • This is accomplished by purchasing a call and shorting the underlying asset.
• Review the rest of the matrix below and bear this memory tool in mind as your further your studies.