FIN 338 Lecture 5

What types of options are there?

1) American, European, and Bermuda Options 2) Naked -vs- Covered Options 3) Exchange Traded -vs- OTC Traded Options

What are the factors impacting option valuations?

1) Call options 2) Put options

What are the call and put option factors impacting option valuation?

1. Stock Price (Positive Relationship) 2. Exercise price (Inverse Relationship) 3. Time to Expiration (Positive Relationship) 4. Interest Rate (Positive Relationship) 5. Volatility of the Underlying Asset (Positive Relationship).

What is the most important risk a speculator/hedger faces in dealing with commodity prices?

Basis risk

When is a cash and carry arbitrage possible?

Cash-and-carry arbitrage is possible if the spot price is too low relative to the futures price (i.e., when the futures contract is overvalued relative to its cost-of-carry valuation).

What would happen to an option at an "in-the-money" position upon expiration?

It would be exercised

What is the relationship of options and their intrinsic value in the market?

Options may sell for more than their intrinsic value in the market, but should never sell for less than their intrinsic value.

What is the procedure for cash and cary arbitrage when the spot price is too low relative to the futures price (i.e., the futures contract is overvalued relative to cost-of-carry valuation)?

Procedure: NOW at present: 1. Borrow necessary funds at the risk-free rate to purchase the underpriced commodity/item in the spot market; 2. Purchase commodity/item in the spot market; 3. Go short the futures contract in agreement to sell the commodity/item at settlement. At SETTLEMENT: 1. Sell the commodity/item under the previous short futures contract position; 2. Payoff the loan (with interest due at risk-free rate) originally taken out to make the spot market purchase; 3. The remaining difference is the arbitrage profit.

What would an investor do in a reverse cash and carry arbitrage?

- Sell short the commodity in the spot market (by borrowing the commodity and selling it at the spot price) - Lend the funds obtained from the short sale at the risk- free rate; - Go long (buy) the futures contract. - At settlement, the investor buys the commodity at the futures price with the funds lent at the risk-free rate and returns the commodity borrowed to the lender.

What are the characteristics of delta for option valuation terminology?

1) Identifies the sensitivity of an option's price to the price of the underlying security. 2) Delta values will be positive for calls and negative for puts.

What are the characteristics of theta for option valuation terminology?

1) Measures how the option premium changes as expiration approaches. 2) Theta values are positive for both calls and puts.

What are the characteristics of rho for option valuation terminology?

1) Measures the sensitivity of the option premium to changes in interest rates. 2) Rho values are positive for calls and negative for puts.

What are the characteristics of vega for option valuation terminology?

1) Measures the sensitivity of the option premium to the price volatility of the underlying security. 2) Vega values are positive for both calls and puts.

What are the characteristics of an exchange traded options?

1) Most option contracts are traded on exchanges, and are standardized as to size (normally 100 options/contract), maturity date, and exercise (strike) price for the contract. 2) In April 1973, standardized options began trading on the Chicago Board Option Exchange (CBOE). 3) The Options Clearing Corporation (OCC) acts as guarantor of each CBOE traded option contract

What are the characteristics of an Over-the-counter options?

1) Some options are traded OTC (Over-the-Counter), and offer the advantage that terms of the contract (exercise price/maturity date/number of shares committed) can be tailored to the needs of the traders (cf., forward contracts). 2) The costs (premium) of such contracts though are normally far higher than exchange traded options.

What are the variable functions of time premium?

1) The amount of time before expiration of the option; 2) The volatility of the underlying asset; 3) The time value of money (usually identified with the risk-free rate); 4) The yield (if any) on cash payments of the underlying asset (e.g., dividends).

What are the characteristics of exchange traded options?

1. Exchange traded options expire on the 3rd Saturday of the expiration month. 2. Normally, options are set up on a 3-month cycle (called the January/February/March cycle). As such, options usually go out 1 month, 2 months, 3 months, 6 months, and 9 months. (The Wall Street Journal normally lists 1 to 3 month option prices only.) 3. Some option exchanges (e.g., CBOE and AMEX) also offer LEAPS (Long-Term Equity Anticipation Securities) which are option contracts on securities and indexes that can run up to 2 years in maturity.

What are the option relationships?

1. Generally, because the buyer of a option is never obligated to exercise the option, the contract should always be worth at least the option's intrinsic value. (The payment of cash flows [e.g., dividends] on the underlying asset though can impact this value.) 2. Neither a call nor a put option can be worth less than zero. 3. For call options having the same maturity and based upon the same underlying asset, the lower the exercise price, the higher will be the contract's intrinsic value and, hence, the greater the contract's premium. 4. On the other hand, for put options having the same maturity and based upon the same underlying asset, the higher the exercise price, the higher will be the contract's intrinsic value and, hence, the greater the contract's premium. 5. Increasing the amount of time until an option expires will increase the contract's time premium as it allows the price of the underlying security more opportunity to move in the direction anticipated by the investor (i.e., up for a call option; down for a put option). 6. Because they provide investors with more choices about exercising the agreement, American-style options are at least as valuable as otherwise comparable European or similar type option contracts

What is the relationship between spot and futures price movements?

1. Over time, the spot and futures prices converge, and basis becomes zero at expiration. 2. Between time t and expiration (T), basis can change as the difference between spot and futures prices vary (known as basis risk). If one buys a commodity now for cash and stores it until delivery, the price one wants under a forward contract would have to cover: a) The cost of buying the commodity now; b) The cost of storing the commodity until the contract matures; c) The cost of financing the initial purchase. 4. When a disparity occurs between the futures contract price (F0) and the spot market price (S0), this disparity can be classified as one of the following contango and normal backwardation

What are the key concepts of the put/call parity?

1. Premiums for puts and calls are not completely independent otherwise arbitrage opportunities would exist. 2. Two investments with equally risky payoffs should have similar costs. 3. Parity relationships exist between options, options and futures, options and spot prices, and futures and spot prices.

What are the characteristics of stock cash dividends in an option contract?

1. Stock cash dividends do NOT affect an option contract. But because cash dividends do tend to reduce a stock's price by the amount of the paid dividend, all other things being equal, a. Call option values (premiums) are lower for high dividend paying stocks because such payouts slow the rate of increase of the stock's price; b. Put values (premiums) are higher for high dividend paying stocks because such payouts tend to increase the drop in the stock's price. On the day a dividend is paid, all else being equal, the stock's price will drop by the value of the dividend.

What are the characteristics of published option listings?

1. The exchanges offer options on stocks with exercise prices that bracket the stock's current price. 2. Exercise prices are generally set at 5-point (i.e., $5) intervals for stocks selling below $100/share, with larger intervals possible on stocks selling over $100/share. 3. If the stock's price moves outside the range of exercise prices of the existing set of options, new options with appropriate exercise (strike) prices will be offered. (As such, at any time both "in-the-money" and "out- of-the-money" options will be listed.)

What are the problems with the Black-Scholes Model?

1. The model assumes continuous rather than discrete changes for stocks. In fact, some stock prices do not change continuously. 2. The formula assumes that the risk-free rate and volatility levels remain constant until the expiration date. Again, this is an unrealistic assumption. 3. The formula can only be used with European style options, whereas, the American style option is more popular. 4. Academic findings have shown that market imperfections (due to brokerage fees, bid-ask spreads, and inflexible position sizes, etc.) can produce arbitrageable differences between option values and prices, a fact Black-Scholes ignores. 5. Empirical studies have also showed that the Black-Scholes model undervalues out-of-the-money options. 6. In addition, Black-Scholes can not be used to price long-term options (LEAPS). 7. Therefore, any violation of the assumptions upon which the Black- Scholes model is based can lead to a misevaluation of the option contract. 8. Thus, it is best to view the formula's results as only approximations producing a band or range of possible option prices rather than a specific single value. As such, Black-Scholes is perhaps best suited for comparing prices of different option contracts rather than determining specific contract prices.

How does an interest rate of a call option impact option valuation?

A call option resembles buying on margin yet without the traditional interest charged for borrowed funds. As interest rates go higher the savings implied by the use of a call option (i.e., less funds invested; lower opportunity costs) increases and thus too the implied value of the option contract. This creates a positive relationship between the market interest rate and the value of the call option.

What is a call option?

A contract giving the holder the right to buy an item at a predetermined price (strike price).

What is a put option?

A contract giving the holder the right to sell an item at a predetermined price (strike price).

What happens in an option?

An Option does not require the option holder to exercise the option. If the market value of the underlying asset hits the strike (exercise) price and/or goes above (call) or below (put) the strike price, the option holder can exercise his/her right to buy/sell the asset to the holder's profit. When the market price does go above/below the exercise price, the option holder can either sell the option to another investor or can "CALL AWAY" the option (i.e., either purchase the underlying security/asset [in the case of a call] or sell the asset/security to the option writer [in the case of a put] and reap the profits on the transaction.

What is the difference between option contracts and options?

An option contract is entered; options are exercised.

What is a Bermuda (Atlantic or Modified American) Option?

An option that allows for exercise of the option before expiration, but only on specific dates as set forth in the contract

What is a European Option?

An option that allows for exercise of the option only on the expiration date

What is an American Option?

An option that allows the holder of the option to exercise the right to purchase (call) or sell (put) the underlying asset on or before the expiration date

What is a naked (uncovered) option?

An option where the writer of the option contract does not have nor has made provisions for the acquisition of, the asset (security) in the case where the contract is exercised. As such, the writer has not limited the extent risk of risk involved in the option contract written.

What is a covered option?

An option where the writer of the option contract either owns the underlying security (asset) or has limited risk with the purchase of an offsetting contract

What are the characteristics of an out-of-the-money" option?

An out-of-the-money option has no intrinsic value and normally would not be exercised if expiring. If not expiring though, the contract could still have value in the open market as it may later become "in-the-money" for the holder.

What is the use of the black-scholes model?

Black-Scholes (and Black-Scholes-Merton) models can only be used for determining the value of European style options.

How does a stock price of a call option impact option valuation?

For a given exercise price, the higher the stock price, the greater the intrinsic value of the call option (or the closer the option will be to being in-the-money).

How does a stock price of a put option impact option valuation?

For a given exercise price, the lower the stock price, the greater the intrinsic value of the put option (or the closer the option will be to being in-the-money).

What are the option pricing relationships for exercise prices?

For call options its a negative (inverse) relationship and for put options its a positive relationship

What are the option pricing relationships for interest rate options?

For call options its a positive relationship and for put options its a negative (inverse) relationship

What are the option pricing relationships for stock prices?

For call options its a positive relationship and for put options its a negative (inverse) relationship

What are the option pricing relationships for time to expiration options?

For call options its a positive relationship and for put options its a positive relationship

What are the option pricing relationships for volatility of underlying stock price?

For call options its a positive relationship and for put options its a positive relationship

What is the concept of cost of carry?

Futures prices and spot market prices must be related to one another in order for there to be no arbitrage opportunities for investors. When inconsistencies appear in this relationship, potential arbitrage opportunities can occur.

What would an investor do in a cash and carry arbitrage?

In such a case the investor would: - Buy the commodity in the spot market with funds borrowed at the risk-free rate (implied repo rate); - Go short (sell) the futures contract. - At settlement, the investor sells the previously purchased item in delivery of the short position and repays the borrowed funds.

What does cost of carry incorporate?

Incorporates storage and insurance costs as a percentage of contract value

What are the components of the option premium?

Intrinsic Value and Time premium

What does an option have at an "in-the-money" position?

Intrinsic value

Who is the buyer under the option agreement said to be?

Long or long position

What are the characteristics of gamma for option valuation terminology?

Measures the sensitivity of delta to changes in the underlying security price.

What is the characteristic for time premium component of an option premium?

Normally, the longer the time to expiration of the option, the larger the time premium. The reduction of this time premium as time to expiration draws nearer is termed time decay and is usually measured by an option's theta value.

Which of the inputs in the Black-Scholes model is not observable and must be estimated (calculated) by the investor?

Of the above inputs, only the last (standard deviation of stock price) is not observable and must be estimated (calculated) by the investor.

What happens after the Black-Scholes model is used to compute the value of a call option?

One can then determine the value of a put option by using the put/call parity formula

What are the requirements of option writers?

Option writers are required to post margin amounts to guarantee that they can fulfill their obligations under the option contract.

What are the similarities of options and futures contracts?

Options and Futures contracts are sometimes called derivative securities, as their value is derived from the value of the underlying primary asset or security. (For this reason, options and futures are also termed contingent claims, as their payoff is contingent on prices of other (underlying) securities/assets).

Who developed the Black-Scholes/Black-Scholes-Merton Model?

Originally developed by Fischer Black and Myron Scholes, the model led to their being awarded the Nobel Prize in Economics in 1997.

What is the procedure for reverse cash and cary arbitrage when the spot price is too low relative to the futures price (i.e., the futures contract is overvalued relative to cost-of-carry valuation)?

Procedure: NOW at present: 1. Borrow the overpriced commodity/item and sell short the commodity/item in the spot market; 2. Place the short sale funds in risk-free securities earning the risk-free rate of return; 3. Go long the futures contract in agreement to buy the commodity/item at settlement. At SETTLEMENT: 1. Buy the commodity/item under the previous long futures contract position with the funds earlier placed in risk-free securities; 2. Replace the previously borrowed commodity/item used in the short sale in the spot market; 3. The remaining difference is arbitrage profit.

When is a reverse cash and carry arbitrage possible?

Reverse cash-and-carry arbitrage is possible if the spot price is too high relative to the futures price (i.e., when the futures contract is undervalued relative to its cost-of-carry valuation).

When is reverse cash and carry arbitrage possible?

Reverse cash-and-carry arbitrage is possible if the spot price is too high relative to the futures price.

What position does the seller (writer) take in the option contract?

Short position (short)

What can the cost of carry integrate?

The Cost-of-Carry Model can integrate ownership benefits lost with a futures position, especially such cash flows as dividends

Who is the person in the long (long position)?

The buyer under the option agreement

What happens under a futures contract?

The contract holder MUST carry out delivery of the underlying asset at the agreed price on the specified date. (This will hold true unless the contract is offset by a reverse trade.)

How are time premiums of an option identified?

The difference between the actual price of an option and its intrinsic value is identified with the option's time premium (or time value component) in the option's overall price structure.

What is the time premium component of an option premium?

The difference between the option premium charged in the open market for the option and the intrinsic value component of that premium.

What is a basis?

The difference between the spot price and futures contract price for a commodity.

How does volatility of the underlying asset of a call option impact option valuation?

The greater the volatility of the underlying stock, the more likely that the option position will be valuable and the investor's expectations about the asset's movement will be correct.

How does volatility of the underlying asset of a put option impact option valuation?

The greater the volatility of the underlying stock, the more likely that the option position will be valuable and the investor's expectations about the asset's movement will be correct.

How does an exercise price of a put option impact option valuation?

The higher the exercise price at which one can purchase the put option, the more value the put option will have to the investor.

How does an interest rate of a put option impact option valuation?

The interest rate effect on the value of a put option is negative (inverse) because buying a put option is like deferring the sale of a security to a future date (i.e., you receive the proceeds of the sale of the security in the future when the put option is exercised). As such, one is dealing with the present value of these future proceeds. Thus, the higher the interest rate (i.e., the discount rate) used to discount these future proceeds to today, the lower the present value realized for these future sale proceeds.

How does time to expiration of a call option impact option valuation?

The longer the time to expiration, the more likely the call option will be valuable. (That is, the longer the investor has to be correct about the direction of the movement of the underlying asset.)

How does time to expiration of a put option impact option valuation?

The longer the time to expiration, the more likely the put option will be valuable. (That is, the longer the investor has to be correct about the direction of the movement of the underlying asset.)

How does an exercise price of a call option impact option valuation?

The lower the exercise price at which one can purchase the call option, the more value the call option will have to the investor.

How is the margin required determined by the option writers?

The margin required is determined in part by the amount by which the option is "in-the-money," as that value is an indication of the potential obligation of the option writer upon exercise of the option.

What is the intrinsic value of an option premium?

The positive difference between the strike (exercise) price and the market value (price) of the underlying asset/security. (It is the value of the option to the investor or what the option holder could financially extract from the option if exercised immediately.)

What does the premium represent?

The premium represents the compensation the purchaser of the option must pay the seller (writer) of the option for the ability to exercise the option if it becomes profitable. The seller (writer) of the option keeps the premium regardless of whether the option is ever exercised.

What is a premium?

The price a put/call buyer must pay to a put/call seller (writer) for an option contract. (The premium is determined by market supply/demand.)

What is the strike (exercise) price?

The price at which an asset (e.g., stock or commodity) underlying a call or put option can be purchased (call) or sold (put) over the specified period of the life of the option.

What is an option?

The right (but not the obligation) to enter into a contract to buy/sell an item at a predetermined price (strike price) until some future date.

What is basis risk?

The risk to an investor arising from the uncertainty about the basis at a given future date.

What is a characteristic of time premium?

The time premium is a function of the probability that the option could change in value by the time of expiration.

What is cost of carry?

The total amount of all storage and financing costs incurred in obtaining and holding an asset, less any income earned on the asset during the period the asset is held.

What is the effect of gains/losses on futures contracts?

They are potentially unlimited; the holder of an option on the other hand, can lose at most the premium paid to acquire the option contract.

What are the requirements of option buyers (holders)?

They need not post margin, as the holder will exercise the option only if it is profitable to do so. After the purchase of the option, no further money is at risk on the part of the option buyer.

What is cash and carry arbitrage?

This occurs when the futures contract is overvalued relative to its cost-of-carry valuation.

When does a reverse carry and cash arbitrage occur?

This occurs when the futures contract is undervalued relative to its cost-of-carry valuation.

How to account for stock dividends in an options?

To account for stock dividends, both the value in shares each option represents and the exercise price (strike price) of the option will be adjusted to accommodate the stock dividend.

How to account for stock splits in an option?

To account for stock splits, the exercise price of an option contract on the impacted security is reduced by the factor of the split, and the number of options held by the option buyer under the contract is increased by that factor.

What is the formula for time premium component of an option premium?

Total Option Premium - Intrinsic Value

When would an exercise produce a profit for its holder?

When an option is "in-the-money"

When may an arbitrage may be possible to investor?

When discrepancies occur between the cost-of-carry futures price and the actual contract price

When is an option said to be "in-the-money"?

When its exercise would produce a profit for its holder

What is weakening of basis?

When the basis narrows over some period of time (i.e., the spot price increases by less than the futures price during some period of time).

What is strengthening of basis?

When the basis widens over some period of time (i.e., the spot price increases by more than the futures price during some period of time).

When is the option said to be "out-of-the-money"?

When the exercise of the option would be unprofitable for its holder

When is an option said to be "at-the-money"?

When the exercise of the option would produce neither a profit nor a loss for its holder (This normally means the current price of the underlying asset is equal to the contract's strike price. An "at-the-money" option has no intrinsic value)

When will the time premium be at its maximum value?

When the option is "at the money."

When does an option writer receive a margin call?

When the required margin exceeds the posted margin

When is a put option "in-the-money"?

When the strike (exercise) price exceeds (i.e., is above) the security/asset's market value because delivery of the lower-valued asset in exchange for the exercise price would be profitable

When is a call option "in-the-money"?

When the strike (exercise) price is below the security/asset's value (i.e. market price) because purchase of the asset at the exercise price would be profitable

What are the mathematical values of the Black-Scholes model?

• Current stock price (Ps) • Exercise price (X) • Market interest rate (risk-free rate) (r) • Time to expiration (T) • Standard deviation (volatility) of the underlying stock price (σ)