1
Q
Moneyness of an option
A
Refers to the relationship between the price of the underlying and the exercice price
2
Q
Option premium
A
Sometimes used instead of option price
3
Q
Long-term equity anticipatory securities (LEAPS)
A
Options with expiration of several years
4
Q
Options Clearing Corporation (OCC)
A
A clearinghouse that manages options
5
Q
Interest rate option settlement
A
The settlement is done at the end of the period covered by the option and not at expiration
6
Q
Interest rate cap
A
- An interest rate cap is a series of European interest call options (called caplets), with a particular interest rate, each of which expires on the date the floating loan rate will be reset
- In an interest rate cap, the seller agrees to compensate the buyer for the amount by which an underlying short-term rate exceeds a specified rate on a series of dates during the life of the contract
7
Q
Interest rate floor
A
- An interest rate floor is a series of European interest floor options (called floorlets), with a particular interest rate, each of which expires on the date the floating loan rate will be reset
- In an interest rate floor, the seller agrees to compensate the buyer for a rate falling below the specified rate during the contract period
8
Q
Interest rate collar
A
A collar is a combination of a long (short) cap and short (long) floor, struck at different rates
9
Q
Zero-cost collar
A
When the price received for going short either the floor or the cap is precisely the price required to go long the other one
10
Q
Options notation - European vs American
A
- c0, cT = price of European call today and at expiration
- C0, CT = price of American call today and at expiration
- p0, pT = price of European put today and at expiration
- P0, PT = price of American put today and at expiration
11
Q
Options value vocabulary
A
- Intrinsic value = exercise value
- Time value = speculative value
12
Q
Options minimum and maximum value
A
- c0 ≥ Max [0, S0 − X / (1+r)T]
- C0 ≥ Max [0, S0 − X / (1+r)T]
- p0 ≥ Max [0, X / (1+r)T − S0]
- P0 ≥ Max (0, X − S0)
13
Q
A lower bound combination for European Calls
A
14
Q
A lower bound combination for European Puts
A
15
Q
Fiduciary call and protective put values
A
16
Q
Put-call parity equation
A
17
Q
Fiduciary Call
A
A combination of a European call and a risk-free bond that matures on the option expiration day and has a face value equal to the exercise price of the call
18
Q
Protective Put
A
An option strategy in which a long position in an asset is combined with a long position in a put
19
Q
Synthetic put
A
20
Q
Synthetic call
A
21
Q
Synthetic call values
A
22
Q
Synthetic put values
A
23
Q
Lower bounds for European options considering cash flows
A
24
Q
Put-call parity considering cash flows
A
25
The hedge ratio
26
Value of c and pi in a hedged portfolio
27
Value of c+ and c- in a two-period binomial hedged portfolio
28
The hedge ratio in a two-period binomial portfolio
29
Black-Scholes-Merton formula
30
Black-Scholes-Merton d1 & d2 formula
31
American versus European option values considering cash flows
When the underlying makes no cash payments, C0 = c0
When the underlying makes cash payments during the life of the option, early exercise can be worthwhile and C0 can thus be higher than c0
The American put is nearly always worth more than the European put: P0 \> p0
32
Lower bounds for European options of futures
33
Lower bounds for American options of futures
34
Put-call-forward parity
35
Put-call-forward parity formula
36
Synthetic forward contract
37
Black-Scholes-Merton for futures formula
38
Black-Scholes-Merton for futures d1 & d2 formula
39
Price of call and put options relative to interest rate
* When rates are higher:
* Call prices are higher
* Put prices are lower
* When rates are lower:
* Call prices are lower
* Put prices are higher
40
Effect of volatility on put and call option prices
* Increases the prices of both of them
* The upside effect increases the call price and does not hurt the put
* The downside effect increases the put price and does not hurt the call
41
The different measures of option price sensitivity
* Delta is the sensitivity of the option price to a change in the price of the underlying
* Gamma is a measure of how well the delta sensitivity measure will approximate the option price’s response to a change in the price of the underlying
* Rho is the sensitivity of the option price to the risk-free rate
* Theta is the rate at which the time value decays as the option approaches expiration
* Vega is the sensitivity of the option price to volatility
42
European put option prices can be either higher or lower the longer the time to expiration
American put option prices are always higher the longer the time ot expiration
43
Option delta
* Change in the option price / Change in the underlying price
* Approximately N(d1) for calls and N(d1) - 1 for puts
44
Hedging with delta (dynamic hedging)
* To hedge options → buy delta \* (number of options)
* To hedge an underlying position → buy [1 / delta] \* (number of unit of the underlying)
45
Option delta as the price moves
* The delta of a call will move towards 1.0 as the underlying moves up and towards 0 as it moves down
* The delta of a put will move towards -1.0 as the underlying moves down and towards 0 as it moves up
46
Option delta when the underlying price does not move and the option gets closer to maturity
* The delta of a call will move towards 1.0 if the call is in-the-money or 0 if it is not
* The delta of a put will move towards - 1.0 if the call is in-the-money or 0 if it is not
47
We can treat European options on futures the same way as options on forwards
American options on futures will differ from American options on forwards
48
Black-Scholes-Merton assumptions
* The Underlying Price Follows a Geometric Lognormal Diffusion Process
* The Risk-Free Rate Is Known and Constant
* The Volatility of the Underlying Asset Is Known and Constant
* There Are No Taxes or Transaction Costs
* There Are No Cash Flows on the Underlying
* The Options Are European
49
Black-Scholes-Merton notation
* S0 is the price of the underlying
* X is the exercise price
* rc is the continuously compounded risk-free rate
* T is the time to expiration
* σ is the annualized standard deviation of the continuously compounded return on the stock
* N(d1) and N(d2) represent normal probabilities based on the values of d1 and d2
50
A hedged portfolio should grow in value at the risk-free rate (H+ & H-)
* H+ = H (1+ r), or
* H– = H (1 + r)
51
Gamma characteristics
* Gamma is larger when there is more uncertainty about whether the option will expire in- or out-of-the-money
* Gamma will tend to be large when the option is at-the-money and close to expiration
* Delta will be a poor approximation for the option’s price sensitivity when it is at-the-money and close to the expiration day
52
Interest rate put or call option in relation to floors and caps
* A 2-year floor equals the value of a comparable 1-year European put option (1-year floorlet) plus the value of a comparable 2-year European put option (2-year floorlet)
* The value of the 1-year put option is equal to the value of a comparable 1-year European put option (1-year floorlet)
* Vice-versa for calls and caps
CFA Level 2
flashcards
Decks in class (13)
# Cards
-
Quantitative Methods99
-
Economics83
-
Ethics27
-
Financial Reporting and Analysis106
-
Corporate Finance90
-
Equity131
-
Alternative Investments56
-
Futures and Forwards58
-
Swaps, Credit default swaps and Interest Rate Derivatives39
-
Portfolio Management68
-
Options52
-
Economics and Investment Markets16
-
Fixed Income105
