ch. 10 - options
price of a call option
(1 + r )( HS − C ) = uHS − Cu
CDS benefits
(1) a CDS allows parties to buy and sell credit risk, and (2) the mechanism is not like the standard swap described in the previous chapter in which two parties exchange payments periodically.
intrinsic value
-The intrinsic value of an option is the economic value of the option if it is exercised immediately. -iv = current asset price - strike price (zero if neg) -If no positive economic value will result from exercising immedi-ately, then the intrinsic value is zero -The intrinsic value of a call option is the difference between the current price of the underlying asset and the strike price if positive -example, if the strike price for a call option is $100 and the current asset price is $105, the intrinsic value is $5.
risk/return
-The maximum amount that an option buyer can lose is the option price. -The maximum pro t that the option writer can realize is the option price. -The option buyer has substantial upside return potential, while the option writer has substantial downside risk.
in the money/out of money
-When an option holds intrinsic value, it is said to be " in the money." -When the strike price of a call option exceeds the current asset price, the call option is said to be " out of the money " ; it has no intrinsic value -at the money: strike price = current asset price, zero intrinsic value
alternative option
-also called an either-or option , provides a payoff that is the best independent payoff of two distinct assets. -Donna will buy the asset with the larger payoff.
interpretation of cap/floor
-cap = call option -floor = put option
hedge ratio
-how much of the asset to purchase -H=Cu-Cd/(u-d)S =iv if asset price rises-iv if asset price declines/(1+%change in asset price if price rises-1+%change in asset price if price declines)*current asset price
(time) premium
-option price minus intrinsic value. -if the price of a call option with a strike price of $100 is $9 when the current asset price is $105, the time premium of this option is $4 ($9 minus its intrinsic value of $5). -A current asset price of $90 instead of $105 means that the time premium of this option would be the entire $9 because the option has no intrinsic value. -other things being equal, the time premium of an option increases with the amount of time remaining to expiration -can sell the call option for $9. In the rst example, selling the call is preferable because the exercise of an option realizes a gain of only $5 — it causes the immediate loss of any time premium
Expected Price Volatility of the Underlying Asset over the Life of the Option
All other fac-tors being equal, the greater the expected volatility of the price of the underlying asset, the more an investor will be willing to pay for the option, and the more an option writer will demand for it. -The greater the volatility, the greater is the probability that the price of the underlying asset will move in favor of the option buyer at some time before expiration.
Anticipated Cash Payments on the Underlying Asset
Cash pay-ments on the underlying asset tend to decrease the price of a call option because the cash payments make it more attractive to hold the underlying asset than to hold the option. For put options, cash payments on the underlying asset tend to increase their price.
outperformance option
for people who want to speculate how two industries/companies will relate in terms of price--e.g. By how much will financial services beat industrial -is an option whose payoff is based on the relative payoff of two assets at the expiration date. -At the expiration date, if the market value of portfolio A is greater than the market value of portfolio B, then this option expires worthless. -The option is exercised if the market value of portfolio B exceeds the market value of portfolio A at the expiration date..
writer/seller
grants this right to the buyer in exchange for a certain sum of money, which is called the option price or option premium
short call position
writing/selling call option -Consequently, the maximum pro t that the short call position can produce is the option price. The maximum loss is not limited because it is the highest price reached by asset-the option price
speculative appeal
if buy option: -Suppose an investor has strong expectations that asset XYZ ' s price will rise in one month. -At an option price of $3, the speculator can purchase 33.33 call options for each $100 invested. -If asset XYZ ' s price rises, the investor realizes the price appreciation associ-ated with 33.33 units of asset XYZ, underlying asset: with the same $100, the investor could buy only one unit of asset XYZ selling at $100, realizing the appreciation associated with one unit if asset XYZ ' s price increases.
outcome of hedged portfolio
if exercised: strike price - (1-hedge ratio)*final asset price + call price if no exercised: hedge ratio * final asset price + call price outcome value is same in both either scenario --> hedge portfolio is riskless
option price
intrinsic value + premium
American option
may be exercised at any time up to and including the expiration date. *American and any → both start with A
European option
may be exercised only at the expiration date. *European and expiration → both start with E
strike price
price at which the asset may be bought or sold
Time to expiration
the longer the time to expiration of the option, the greater the option price, because as the time to expiration decreases, less time remains for the underlying asset ' s price to rise (for a call buyer) or fall (for a put buyer) and therefore the probability of a favorable price movement decreases.
vs. strike price
the lower the strike price, the higher the price of a call option. For put options, the higher the strike price, the higher the price of a put option
option
the option the right, but not the obligation o purchase from or sell to the writer something at a speci ed price within a speci ed period of time.
hedged portfolio
the portfolio consisting of the long position in the asset and the short position in the call option will produce the risk-free interest rate.
option price vs. current asset price
For a call option, as the price of the underlying asset increases, the option price increases. The opposite holds for a put option.
cost of hedged portfolio
HS - C =(hedge ratio*current asset price) - current call price
binomial pricing model
construct a portfolio: (1) a long position in a certain amount of the asset and (2) a short call position in the underlying asset. *amount of asset purchased will be hedged portfolio
spot price
current asset price
example
current asset price = $100. option price = $3 1. asset price at exp. date <100 --> do not exercise. 2. asset price at exp. date =100 --> do not exercise. 3. asset price at exp. date >100,<103 --> exercise. investor can sell the asset and gain to offset the $3 option price. 4. breakeven - if asset price = 100+option price 5. asset price >103, exercise
cap and floors
*do example from notes -speculating on movements in rates/indices -Agreements are available in the nancial market in which one party, for a fee (premium), agrees to compensate the other if a designated reference is different from a predetermined level. - cap: When the seller agrees to pay the buyer if the designated reference exceeds a predeter-mined level, -floor is when the seller agrees to pay the buyer if a designated reference falls below a predeter-mined level. -The predetermined level is called the strike -For a cap, If the reference is greater than the strike, then the seller pays the buyer the following: Notional amount × (Actual value of designated reference − Strike). -floor: Notional amount × (Actual value of designated reference − Strike).
long call vs. long position in underlying asset
- An investor who takes a long position in asset XYZ realizes a pro t of $1 for every $1 increase in asset XYZ ' s price. As asset XYZ ' s price falls, however, the investor loses dollar for dollar. -If the price drops by more than $3, the long position in asset XYZ results in a loss of more than $3.The long call strategy, in contrast, limits the loss to only the option price of $3 but retains the upside potential, which is $3 less than for the long position in asset XYZ
econ role of nonlinear payoff
- protection against an adverse price movement while maintaining the opportunity to bene t from a favorable price movement. -benefits: 1. more ef cient vehicle to create the hedged positions. 2. ef -cient way to expand the range of return characteristics available. -Investors can use options to " mold " a return distribution for a portfolio to fit particular investment objectives
credit default swaps
-A credit default swap (CDS) is a derivative that can be used to buy or sell protection against particular types of events that can adversely affect the credit quality of a debt obli-gation, such as the default or bankruptcy of the borrower. -If a credit event does occur, the protection buyer makes a payment only up to the credit event date and makes no further payment At this time, the protection buyer is obligated to perform. -The contract will call for the protection seller to compensate for the loss in the value of the debt obligation.
margin
-Because the option price is the maximum amount the investor can lose, no matter how adverse the price movement of the underlying asset, margin is not necessary. -Because the writer of an option agrees to accept all of the risk (and none of the reward) of the posi-tion in the underlying asset, the writer is generally required to put up the option price received as margin.
Asset/Liability Management
-Buckingham Bank's objective is to lock in an interest rate spread over its cost of funds. -Yet because it borrows short term, its cost of funds is uncertain. Buckingham Bank may be able to purchase a cap such that the cap rate plus the cost of purchasing the cap is less than the rate it earns on its fixed-rate commercial loans. -If short-term rates decline, Buckingham Bank does not bene t from the cap, but its cost of funds declines. -The cap therefore allows the bank to impose a ceiling on its cost of funds while retaining the opportunity to bene t from a decline in rates.
Short-Term Risk-Free Interest Rate
-Buying the underlying asset ties up an investor ' s funds. -Buying an option on the same quantity of the underlying asset makes the difference between the asset price and the option price available for investment at (at least) the risk-free rate. i.e. money saved from not buying asset and just buying option can be used to invest -the higher the short-term risk-free interest rate, the greater the cost of buying the underlying asset and carrying it to the expiration date of the call option -the higher the short-term risk-free interest rate, the greater is the price of a call option.
time value of money
-the buyer of an option must pay the seller the option price at the time the option is purchased. -Thus, the buyer must nance the pur-chase price of the option, or, assuming the purchase price does not have to be borrowed, the buyer loses the income that can be earned by investing the amount of the option price until the option is sold or exercised. -In contrast, assuming that the seller does not have to use the option price amount as margin for the short position or can use an interest-earning asset as security, the seller has the opportunity to earn income from the proceeds of the option sale. -The time value of money changes the pro t and loss pro le of the option position, as just discussed. -The breakeven price for the underlying asset at the expiration date is higher (lower) for the buyer (seller) of a call option. The reverse is true for a put option. -We did not consider the fact that the underlying asset may generate interim cash ows (dividends in the case of common stock, interest in the case of bonds). The buyer of a call option is not entitled to any interim cash ows generated by the underlying asset. -The buyer of the underlying asset, however, would receive any interim cash ows and would have the opportunity to reinvest them
otc (hc, l)
1. higher cost - reflects the cost of customizing the option for the nstitutional investor because the standardized exchange-traded option does not satisfy its investment objectives. 2. less liquid
options vs futures
1. obligation -buyer does is not obligated to act -writer is obligated -for futures, both parties are obligated -futures buyer does not pay seller to accept obligation, whereas option buyer pays option price 2. symmetry -for futures, buyer gets dollar-for-dllar gain when futures price increases and vice versa. -options are asymmetric -The most that the buyer of an option can lose is the option price. The buyer of an option retains all the potential ben-e ts, but the gain is always reduced by the amount of the option price. The maximum pro t that the writer may realize is the option price, and this potential is offset by substantial downside risk
exchange-traded (s,cpr,tc)
1. standardized exercise price and expiration date 2. the direct link between buyer and seller is severed after order execution because of the interchangeability of exchange-traded options. -The clearinghouse associ-ated with the exchange where the option trades performs the same function in the options market that it does in the futures market. Hence, counterparty risk is minimal with exchange-traded options. 3. Lower transaction costs than OTC
put-call parity
Put option price − Call option price = Present value of strike price + Present value of cash distribution − Price of underlying asset. -If this relationship does not hold, arbitrage opportunities exist. That is, portfolios that consist of long and short positions in the asset and related options will provide an extra return with (practical) certainty.
summary
To summarize, buying calls or selling puts allows the investor to gain if the price of the underlying asset rises. Selling calls or buying puts allows the investor to gain if the price of the underlying asset falls
call option
When an option grants the buyer the right to purchase the designated instrument from the writer
Put option
When the option buyer has the right to sell the designated instrument to the writer,
