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CFA Level 2 > Options > Flashcards

Options Flashcards

1
Q

Moneyness of an option

A

Refers to the relationship between the price of the underlying and the exercice price

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2
Q

Option premium

A

Sometimes used instead of option price

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3
Q

Long-term equity anticipatory securities (LEAPS)

A

Options with expiration of several years

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4
Q

Options Clearing Corporation (OCC)

A

A clearinghouse that manages options

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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

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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
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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
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8
Q

Interest rate collar

A

A collar is a combination of a long (short) cap and short (long) floor, struck at different rates

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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

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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
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11
Q

Options value vocabulary

A
  • Intrinsic value = exercise value
  • Time value = speculative value
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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)
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13
Q

A lower bound combination for European Calls

A
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14
Q

A lower bound combination for European Puts

A
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15
Q

Fiduciary call and protective put values

A
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16
Q

Put-call parity equation

A
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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

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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

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19
Q

Synthetic put

A
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20
Q

Synthetic call

A
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21
Q

Synthetic call values

22
Q

Synthetic put values

23
Q

Lower bounds for European options considering cash flows

24
Q

Put-call parity considering cash flows

25
Q

The hedge ratio

26
Q

Value of c and pi in a hedged portfolio

27
Q

Value of c+ and c- in a two-period binomial hedged portfolio

28
Q

The hedge ratio in a two-period binomial portfolio

29
Q

Black-Scholes-Merton formula

30
Q

Black-Scholes-Merton d1 & d2 formula

31
Q

American versus European option values considering cash flows

A

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
Q

Lower bounds for European options of futures

33
Q

Lower bounds for American options of futures

34
Q

Put-call-forward parity

35
Q

Put-call-forward parity formula

36
Q

Synthetic forward contract

37
Q

Black-Scholes-Merton for futures formula

38
Q

Black-Scholes-Merton for futures d1 & d2 formula

39
Q

Price of call and put options relative to interest rate

A
  • 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
Q

Effect of volatility on put and call option prices

A
  • 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
Q

The different measures of option price sensitivity

A
  • 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
Q

European put option prices can be either higher or lower the longer the time to expiration

A

American put option prices are always higher the longer the time ot expiration

43
Q

Option delta

A
  • Change in the option price / Change in the underlying price
  • Approximately N(d1) for calls and N(d1) - 1 for puts
44
Q

Hedging with delta (dynamic hedging)

A
  • To hedge options → buy delta * (number of options)
  • To hedge an underlying position → buy [1 / delta] * (number of unit of the underlying)
45
Q

Option delta as the price moves

A
  • 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
Q

Option delta when the underlying price does not move and the option gets closer to maturity

A
  • 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
Q

We can treat European options on futures the same way as options on forwards

A

American options on futures will differ from American options on forwards

48
Q

Black-Scholes-Merton assumptions

A
  • 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
Q

Black-Scholes-Merton notation

A
  • 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
Q

A hedged portfolio should grow in value at the risk-free rate (H+ & H-)

A
  • H+ = H (1+ r), or
  • H– = H (1 + r)
51
Q

Gamma characteristics

A
  • 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
Q

Interest rate put or call option in relation to floors and caps

A
  • 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 (13 decks)

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