American option - any time (A = American = Any time)
European option - only at expiration (E = European = Expiration)
At expiration they are identical, but before this they have different values. American option is more valuable than an otherwise equal European option - more flexible
Moneyness - 'in the money' if immediate exercise of the option would result in positive payoff
Call option - in the money if stock price exceeds strike price. Out of money if strike exceeds stock price. You are betting the price will go up (long/bull).
Put option - in the money if stock price is below the strike price. Out of the money if strike price is below the stock price. You are betting the price will go down (short/bear).
If strike = stock price, option is 'at the money'
Exchange traded aka listed options = regulated, standardized options backed by Options Clearing Corp for Chicago Board Options Exchange transactions. LEAPS = long term equity anticipatory securities = longer than a year
OTC - less common, unregulated - mainly for big institutional buyers, similar to forwards mkts.
Financial options - equity options, index options, rates, currencies. Strike can be YTM for bonds, an index level, or exchange rate. Libor based interest rate options have payoffs based on difference between LIBOR at expiration and strike rate on the option.
Bond options - there are relatively few. Mostly related to treasuries and OTC. Can be deliverable or settle in cash. Based on specific face value. Buyer of a call will gain if interest rates FALL and bond prices rise.
Index Options - settles in cash, nothing is delivered, payoff made directly to option holder's account. Amount of change in index level times contract multiplier is the amount paid.
Options on Futures - can have an option to call or put a future, i.e. an option to enter into the contract at a certain price.
Commodity options - options to buy physical assets at a fixed (strike) price.
Real options - capital investment projects can give company the flexibility to change a project's cash flows while in progress. These real options have value. Will be covered in level 2.
Interest rate options - similar to stock options except interest rate is the exercise price. Similar to forward rate agreements in that there is no deliverable asset. Settle in cash. Mostly European options. Amount of settlement is based on notional spread between strike and reference rate. Payoff is one sided. A long interest rate call option plus a short interest rate put option has the same payoff as an FRA (forward rate agreement).
Interest rate cap - a series of interest call options with expirations that correspond to the reset dates of a floating rate loan. Caps place a maximum on the interest pmts of the loan. Each option is called a caplet.
Interest rate floor - series of interest put options to protect a floating rate lender from a decrease in rates. Each option is called a floorlet.
Interest rate collar - combines a cap and a floor. Borrow may buy a cap and sell a floor to defray some of the cost of the cap.
For things quoted in yields, you have to convert asset value to a dollar value and strike price to a dollar strike price. On indexes, you multiply by the multiplier specified in the contract. Payoff on options is cash the option holder receives, and the resulting position is marked to market.
INTEREST RATE OPTIONS ARE DIFFERENT. Call option on 90 day rate for example is based on difference between LIBOR and strike rate, TIMES 90/360. Payment is NOT made at expiration but 90 days later (matches when one would usually have a coupon pmt due).
Intrinsic Value - amount by which an option is in the money. If at or out of money it has no intrinsic. Intrinsic is the amount you would receive if you exercise.
Time Value - the amount by which an option premium exceeds intrinsic value. The 'speculative' value of an option. Total option value = Time Value + Intrinsic Value. When an option reaches expiration there is no 'time' value left. Longer the time value, the greater the premium typically, for American options and USUALLY for European options.
Minimum and Maximum Values of Options
Lower bound for ANY option is zero - will never sell for less than its intrinsic value. Applies to both American and European options.
Max value for either American or European CALL is the time-t share price of the underlying stock - because noone would pay more than the underlying asset price for the option, they would just buy the underlying asset
Upper Bound for PUTS - American: this is the strike price. This is the price in the event the underlying stock goes to 0. For EUROPEAN - you don't get the strike until time t - so you take the strike price and discount the strike price by (1+RFR)^t and this is the upper boundary for the European.
These are all the THEORETICAL bounds - the most permissive. Next we will do more restrictive.
American Style - minimum of call = max[0, S-X]. Minimum of put = max[0, X-S]
European Style call is more complex - figure out by use of a portfolio. Will skip derivation here. Result is that lower bound for European option is c>=max[0, S - X/(1+RFR)^T]
The lower bound on an American call is at least as much as the lower bound on a European call. It is the same formula.
Minimum Bound of European Put: p >= max[0, X / (1+RFR)^T - S]. This lower bound will always be lower than the similar American because the American has the option to call at any time it is in the money and NOT discount the payoff. Therefore the lower bound on an American put is just P >= max[0, X - S].
In general MORE TIME to expiration = good. May have little effect if far out of the money but the longer option will have NO LESS value than the shorter option. BUT you cannot state this necessarily for a European put - no definite relationship there. There is more volatility (value) but also greater discounting. If volatility is really high and discounting is low the value might be higher for a longer option. Low vol and high discounting has the opposite effect.
PUT CALL PARITY FOR EUROPEAN OPTIONS
Fiduciary Call = Bond paying X at maturity + call with exercise price X. It is the same X. Payoff is X when out of the money, and X + (S - X) = S when the call is in the money.
Protective Put = share of stock plus a put option on the stock. Payoff is (X - S) + S = X when put is in money, and S when put is out of the money.
Put Call Parity Formula: c + X/(1+RFR)^T = S + p
You can use this to strip out each part of the formula. The call plus the value of the risk free bond (PV of X) must equal the stock price plus put price. Isolating each variable (X/(1+RFR)^T) is one variable) tells you the 'synthetic equivalent' of that variable.
Key assumptions are that these are European options, and that the put and call must have the same exercise price for these to hold.
Note that the SIGN in front of each position indicates an long or short.
Ex. for S = c - p + X/(1+RFR)^T
you are saying that a long stock position (S) is equivalent to being long a call, short a put, and long a position in a risk free bond.
Put call parity is bad ass. Just wanted to say that.
There is NO REASON to use an American call option early if it is a non-dividend paying stock (you have to subtract the full strike price rather than just the discounted price). On dividend paying stocks this is not necessarily the case - you might want to chuck the stock before a dividend date if the dividend will decrease the price of the stock (remember options are not typically adjusted for dividends).
American Puts - you MIGHT want to use these early if the stock is in bankruptcy - better to get X now than at expiration. Similarly a low stock price might make an American put 'worth more dead than alive.'
If you have additional cash flows over the period of an option this effectively reduces the stock price of the asset. So in the lower bound and put call parity formulas, substitute (S - pvcf) for S.
Effect of Interest Rates:
Interest Rate Increases = Call Increases, Put Decreases (holding price constant)
The put call parity formulas make this relationship obvious - increasing and decreasing RFR shows the relationship. Note that this does not necessarily apply to interest rate or bond/tbill options where change in rate might change price of the underlying asset.
Greater volatility increases the value of both puts and calls due to the one sided nature of options - you get additional upside value for no additional downside value.
European option - only at expiration (E = European = Expiration)
At expiration they are identical, but before this they have different values. American option is more valuable than an otherwise equal European option - more flexible
Moneyness - 'in the money' if immediate exercise of the option would result in positive payoff
Call option - in the money if stock price exceeds strike price. Out of money if strike exceeds stock price. You are betting the price will go up (long/bull).
Put option - in the money if stock price is below the strike price. Out of the money if strike price is below the stock price. You are betting the price will go down (short/bear).
If strike = stock price, option is 'at the money'
Exchange traded aka listed options = regulated, standardized options backed by Options Clearing Corp for Chicago Board Options Exchange transactions. LEAPS = long term equity anticipatory securities = longer than a year
OTC - less common, unregulated - mainly for big institutional buyers, similar to forwards mkts.
Financial options - equity options, index options, rates, currencies. Strike can be YTM for bonds, an index level, or exchange rate. Libor based interest rate options have payoffs based on difference between LIBOR at expiration and strike rate on the option.
Bond options - there are relatively few. Mostly related to treasuries and OTC. Can be deliverable or settle in cash. Based on specific face value. Buyer of a call will gain if interest rates FALL and bond prices rise.
Index Options - settles in cash, nothing is delivered, payoff made directly to option holder's account. Amount of change in index level times contract multiplier is the amount paid.
Options on Futures - can have an option to call or put a future, i.e. an option to enter into the contract at a certain price.
Commodity options - options to buy physical assets at a fixed (strike) price.
Real options - capital investment projects can give company the flexibility to change a project's cash flows while in progress. These real options have value. Will be covered in level 2.
Interest rate options - similar to stock options except interest rate is the exercise price. Similar to forward rate agreements in that there is no deliverable asset. Settle in cash. Mostly European options. Amount of settlement is based on notional spread between strike and reference rate. Payoff is one sided. A long interest rate call option plus a short interest rate put option has the same payoff as an FRA (forward rate agreement).
Interest rate cap - a series of interest call options with expirations that correspond to the reset dates of a floating rate loan. Caps place a maximum on the interest pmts of the loan. Each option is called a caplet.
Interest rate floor - series of interest put options to protect a floating rate lender from a decrease in rates. Each option is called a floorlet.
Interest rate collar - combines a cap and a floor. Borrow may buy a cap and sell a floor to defray some of the cost of the cap.
For things quoted in yields, you have to convert asset value to a dollar value and strike price to a dollar strike price. On indexes, you multiply by the multiplier specified in the contract. Payoff on options is cash the option holder receives, and the resulting position is marked to market.
INTEREST RATE OPTIONS ARE DIFFERENT. Call option on 90 day rate for example is based on difference between LIBOR and strike rate, TIMES 90/360. Payment is NOT made at expiration but 90 days later (matches when one would usually have a coupon pmt due).
Intrinsic Value - amount by which an option is in the money. If at or out of money it has no intrinsic. Intrinsic is the amount you would receive if you exercise.
Time Value - the amount by which an option premium exceeds intrinsic value. The 'speculative' value of an option. Total option value = Time Value + Intrinsic Value. When an option reaches expiration there is no 'time' value left. Longer the time value, the greater the premium typically, for American options and USUALLY for European options.
Minimum and Maximum Values of Options
Lower bound for ANY option is zero - will never sell for less than its intrinsic value. Applies to both American and European options.
Max value for either American or European CALL is the time-t share price of the underlying stock - because noone would pay more than the underlying asset price for the option, they would just buy the underlying asset
Upper Bound for PUTS - American: this is the strike price. This is the price in the event the underlying stock goes to 0. For EUROPEAN - you don't get the strike until time t - so you take the strike price and discount the strike price by (1+RFR)^t and this is the upper boundary for the European.
These are all the THEORETICAL bounds - the most permissive. Next we will do more restrictive.
American Style - minimum of call = max[0, S-X]. Minimum of put = max[0, X-S]
European Style call is more complex - figure out by use of a portfolio. Will skip derivation here. Result is that lower bound for European option is c>=max[0, S - X/(1+RFR)^T]
The lower bound on an American call is at least as much as the lower bound on a European call. It is the same formula.
Minimum Bound of European Put: p >= max[0, X / (1+RFR)^T - S]. This lower bound will always be lower than the similar American because the American has the option to call at any time it is in the money and NOT discount the payoff. Therefore the lower bound on an American put is just P >= max[0, X - S].
Puts: Higher exercise price = good. Put prices are DIRECTLY related to exercise price.
Calls: Lower exercise price = good. Call prices are INVERSELY related to exercise price.
In general MORE TIME to expiration = good. May have little effect if far out of the money but the longer option will have NO LESS value than the shorter option. BUT you cannot state this necessarily for a European put - no definite relationship there. There is more volatility (value) but also greater discounting. If volatility is really high and discounting is low the value might be higher for a longer option. Low vol and high discounting has the opposite effect.
PUT CALL PARITY FOR EUROPEAN OPTIONS
Fiduciary Call = Bond paying X at maturity + call with exercise price X. It is the same X. Payoff is X when out of the money, and X + (S - X) = S when the call is in the money.
Protective Put = share of stock plus a put option on the stock. Payoff is (X - S) + S = X when put is in money, and S when put is out of the money.
Put Call Parity Formula: c + X/(1+RFR)^T = S + p
You can use this to strip out each part of the formula. The call plus the value of the risk free bond (PV of X) must equal the stock price plus put price. Isolating each variable (X/(1+RFR)^T) is one variable) tells you the 'synthetic equivalent' of that variable.
Key assumptions are that these are European options, and that the put and call must have the same exercise price for these to hold.
Note that the SIGN in front of each position indicates an long or short.
Ex. for S = c - p + X/(1+RFR)^T
you are saying that a long stock position (S) is equivalent to being long a call, short a put, and long a position in a risk free bond.
Put call parity is bad ass. Just wanted to say that.
There is NO REASON to use an American call option early if it is a non-dividend paying stock (you have to subtract the full strike price rather than just the discounted price). On dividend paying stocks this is not necessarily the case - you might want to chuck the stock before a dividend date if the dividend will decrease the price of the stock (remember options are not typically adjusted for dividends).
American Puts - you MIGHT want to use these early if the stock is in bankruptcy - better to get X now than at expiration. Similarly a low stock price might make an American put 'worth more dead than alive.'
If you have additional cash flows over the period of an option this effectively reduces the stock price of the asset. So in the lower bound and put call parity formulas, substitute (S - pvcf) for S.
Effect of Interest Rates:
Interest Rate Increases = Call Increases, Put Decreases (holding price constant)
The put call parity formulas make this relationship obvious - increasing and decreasing RFR shows the relationship. Note that this does not necessarily apply to interest rate or bond/tbill options where change in rate might change price of the underlying asset.
Greater volatility increases the value of both puts and calls due to the one sided nature of options - you get additional upside value for no additional downside value.
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