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Actuarial Exams > Exam MFE > Flashcards

Exam MFE Flashcards

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1
Q

PCP for Stock

A
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2
Q

PCP for Exchange Options

A
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3
Q

Exchange Option Duality

A

C(A,B) = P(B,A)

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4
Q

PCP for Currency Exchange

Substitutions:

S ⇒ ?

r ⇒ ?

δ ⇒ ?

A
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5
Q

Bounds for Put Price

Rank the following:

  1. PEur 2. PAmer3. Max(0, Ke^(-rt) - FP(S) ) 4. K
A

K ≥ PAmer≥ PEur ≥ Max(0, Ke^(-rt) - FP(S) )

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6
Q

Bounds for Call Price

Rank the following:

  1. CEur 2. CAmer3. Max(0, FP(S) - Ke^(-rt)) 4. S
A

S ≥ CAmer≥ CEur ≥ Max(0, FP(S) - Ke^(-rt))

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7
Q

Rules for Early Exercise - American Call

Nondividend Stock = ?

Dividend Stock = ?

A

Nondividend Stock

Never Optimal

Dividend Stock

Optimal if PV(Divs) > PV(Int on Strike) + Implicit Put

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8
Q

Rules for Early Exercise - American Put

Nondividend Stock =

Dividend Stock =

A

Early Exercise is optimal if:

PV(Interest on Strike) > PV(Divs) + Implicit Call

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9
Q

Call Options Prices

Given K1 < K2 < K3, what 3 things do you know about call prices?

A
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10
Q

Put Option Prices

Given K1 < K2 < K3, what 3 things do you know about put prices?

A
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11
Q

An option can be replicated by buying ___ shares of the underlying stock and lending ___ at the risk free rate.

A

An option can be replicated by buying Δ shares of the underlying stock and lending B at the risk free rate.

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12
Q

Replicating Portfolio

Δ = ?

A

V = payoff of the option

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13
Q

Replicating Portfolio

B = ?

A

V = payoff of the option

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14
Q

Currency Exchange Duality

A
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15
Q

Replicating Portfolio

For Calls, Δ is (+/-) and **B **is (+/-)?

For Puts, Δ is (+/-) and B is (+/-)?

A

For Calls, Δ is (+) and B ** is (–**)?

For Puts, Δ is (–) and B ** is (+**)?

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16
Q

Risk Neutral Probability Pricing

p* = ?

A
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17
Q

Risk Neutral Probability Pricing - Option Price Formula

Option Price (V) = ?

A
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18
Q

Realistic Probability Pricing

p = ?

A
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19
Q

Realistic Probability Pricing

Option Price (V) = ?

A
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20
Q

Realistic Probability Pricing

A
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21
Q

Forward Tree

If u and d are not given,

u = ?

d = ?

A
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22
Q

Cox-Ross-Rubinstein Tree

u = ?

d = ?

A
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23
Q

Lognormal Tree (Jarrow-Rudd Tree)

u = ?

d = ?

A
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24
Q

In the Binomial model, how can you tell if arbitrage is available?

A

Arbitrage is available if the following inequality is not satisfied:

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25
Futures Contract
26
For options on futures contracts, what two substitutions do you need to make?
27
_Lognormal Stock Price Model_ m = ? v^2 = ?
28
_Lognormal Stock Price Model_
29
_Lognormal Stock Price Model_
30
_Lognormal Stock Price Model_
31
_Lognormal Stock Price Model_ Median = ?
32
_Lognormal Stock Price Model_
33
_Lognormal Stock Price Model_
34
_Lognormal Stock Price Model_
35
_Lognormal Stock Price Model_
36
_Lognormal Stock Price Model_
37
_Conditional Expectation - Lognormal Stock Price Model_
38
_Conditional Expectation - Lognormal Stock Price Model_
39
_Lognormal Stock Price Model_
40
_General Black Scholes_ Call Price = ?
41
_General Black Scholes_ Put Price = ?
42
_General Black Scholes_
43
_General Black Scholes_
44
_Black Scholes - Stock_ Call Price = ?
45
_Black Scholes - Stock_ Put Price = ?
46
_Black Scholes - Stock_
47
_Black Scholes - Stock_
48
_Black Scholes - Currency_ Three Substitutions
49
_Black Scholes - Currency_ Call Price = ?
50
_Black Scholes - Currency_ Put Price = ?
51
_Black Scholes - Currency_
52
_Black Scholes - Currency_
53
_Black Scholes - Currency_
54
_Black Scholes - Futures_
55
_Black Scholes - Futures_
56
_Black Scholes - Futures_ Call Price = ?
57
_Black Scholes - Futures_ Put Price = ?
58
_Black Scholes - Futures_
59
_Black Scholes - Futures_
60
_Option Greeks_ Detla
61
_Option Greeks_ Detla
62
_Option Greeks_ Detla
63
_Option Greeks_ Gamma
64
_Option Greeks_ Gamma of Call Option is (+/-)? Gamma of Put Option is (+/-)? Gamma of Call Option (\<, =, \>) Gamma of Put Option?
Gamma of Call Option is (**+**)? Gamma of Put Option is (**+**)? Gamma of Call Option **=** Gamma of Put Option?
65
_Option Greeks_ Theta
66
_Option Greeks_ Vega
67
_Option Greeks_ Vega of Call Option is (+/-)? Vega of Put Option is (+/-)? Vega of Call Option (\<, =, \>) Vega of Put Option?
Vega of Call Option is (**+**) Vega of Put Option is (**+**) Vega of Call Option **=** Vega of Put Option
68
_Option Greeks_ Rho
69
_Option Greeks_ Rho of Call Option is (+/-)? Rho of Put Option is (+/-)?
Rho of Call Option is (**+**) Rho of Put Option is (**--**)
70
_Option Greeks_ Psi
71
_Option Greeks_ Psi of Call Option is (+/-)? Psi of Put Option is (+/-)?
Psi of Call Option is (**--**) Psi of Put Option is (**+**)
72
_Option Greeks_
73
_Option Elasticity_
74
_Option Volatility_
75
_Option Facts_
76
_Portfolio Elasticity_
77
_Portfolio Return_
78
_Delta Hedgeing_
79
_Delta Hedgeing_
80
_Delta-Gamma-Theta Approximation_
81
82
_Asain Options_
83
_Asain Options_
84
_Asain Options_
85
_Barrier Options_
86
_Barrier Options_
87
_Barrier Options_
88
_Compound Option_
89
_Compound Option_
90
_Compound Option_
91
_Gap Option_
92
_Gap Option_
93
_Gap Option_
94
_Black Scholes - Exchange Options_
95
_Black Scholes - Exchange Options_
96
_Asset Call_ Payoff = ? Time t Price = ?
97
_Asset Put_ Payoff = ? Time t Price = ?
98
_Cash Put_ Payoff = ? Time t Price = ?
99
_Cash Call_ Payoff = ? Time t Price = ?
100
_Working with Max and Min Functions_
101
_Working with Max and Min Functions_
102
_Working with Max and Min Functions_
103
_Forward Start Option_
104
_Forward Start Option_
105
_Chooser Option_ Three steps to find price of chooser option:
_Chooser Option_ Three steps to find price of chooser option: 1. Draw a time diagram. 2. Find the time t price 1. Max(C,P) ⇒ Max(0, P-C) + C or Max(C-P, 0) + P 2. Apply the PCP to substitue the C-P or P-C Term 3. Factor out the coefficient of S 3. Discount to time 0
106
_Simulation_
107
_Simulation_
108
_Risk Neutral Vs True_ Use the __________ distribution only when discounting is needed. Use the __________ distribution when discounting is not needed.
Use the **_Risk Neutral_** distribution only when discounting is needed. Use the **_True_** distribution when discounting is not needed.
109
_Control Variate Method_
110
_Control Variate Method_
111
_Control Variate Method_
112
_Control Variate Method_
113
_Antithetic Variate Method_
114
_Stratified Sampling_
115
_Brownian Motion_
116
_ABM_
117
_ABM_
118
_ABM_
119
_Ornstein-Uhlenbeck Process_
120
_GBM_
121
_GBM_
122
_GBM_
123
_GBM_
124
_GBM_
125
_GBM_
126
_GBM_
127
_GBM_
128
_Ito's Lemma_
129
_Multiplication Rules for BM_
130
_Sharpe Ratio_
131
Option Risk Premium =
Expected Return on Option minus the Risk Free Rate
132
**_Risk Free Portfolio_**
133
**_Risk Free Portfolio_**
134
**_Risk Free Portfolio_**
135
**_Risk Free Portfolio_** Three steps for creating a risk free portfolio?
136
**_Risk Neutral Vs True_** Relate to dZ(t) & Z(t)
137
**_Risk Neutral Vs True_**
138
139
**_Black Scholes Equation_**
140
What is the Black Scholes PDE?
141
_Interest Rate Models_ Delta Gamma Theta Approximation
142
_Interest Rate Models_ Delta Gamma Theta Approximation
143
_Interest Rate Models_ Rendlemen-Bartter Model 1. Mean Reversion (Y/N?) 2. r can go negative (Y/N?) 3. Volatility varies with r (Y/N?)
**_Interest Rate Models_** Rendlemen-Bartter Model 1. Mean Reversion (**No**) 2. r can go negative (**No**) 3. Volatility varies with r (**Yes**)
144
_Interest Rate Models_ Vasicek Model 1. Mean Reversion (Y/N?) 2. r can go negative (Y/N?) 3. Volatility varies with r (Y/N?)
**_Interest Rate Models_** Vasicek Model 1. Mean Reversion (**Yes**) 2. r can go negative (**Yes**) 3. Volatility varies with r (**No**)
145
_Interest Rate Models_ Cox-Ingersoll-Ross Model 1. Mean Reversion (Y/N?) 2. r can go negative (Y/N?) 3. Volatility varies with r (Y/N?)
**_Interest Rate Models_** Cox-Ingersoll-Ross Model 1. Mean Reversion (**Yes**) 2. r can go negative (**No**) 3. Volatility varies with r (**Yes**)
146
147
148
149
**_Black Derman Toy_**
**_Black Derman Toy_**
150
151
**_Black's Formula_** Call Price =
152
**_Black's Formula_** Put Price =
153
**_Black's Formula_**
154
**_Black's Formula_**
155
**_Black's Formula_**
156
**_Black's Formula_**

Actuarial Exams (2 decks)

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