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Actuarial Exams > Exam MFE > Flashcards

Exam MFE Flashcards

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
Q

Futures Contract

A
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26
Q

For options on futures contracts, what two substitutions do you need to make?

A
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27
Q

Lognormal Stock Price Model

m = ?

v^2 = ?

A
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28
Q

Lognormal Stock Price Model

A
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29
Q

Lognormal Stock Price Model

A
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30
Q

Lognormal Stock Price Model

A
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31
Q

Lognormal Stock Price Model

Median = ?

A
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32
Q

Lognormal Stock Price Model

A
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33
Q

Lognormal Stock Price Model

A
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34
Q

Lognormal Stock Price Model

A
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35
Q

Lognormal Stock Price Model

A
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36
Q

Lognormal Stock Price Model

A
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37
Q

Conditional Expectation - Lognormal Stock Price Model

A
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38
Q

Conditional Expectation - Lognormal Stock Price Model

A
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39
Q

Lognormal Stock Price Model

A
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40
Q

General Black Scholes

Call Price = ?

A
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41
Q

General Black Scholes

Put Price = ?

A
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42
Q

General Black Scholes

A
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43
Q

General Black Scholes

A
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44
Q

Black Scholes - Stock

Call Price = ?

A
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45
Q

Black Scholes - Stock

Put Price = ?

A
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46
Q

Black Scholes - Stock

A
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47
Q

Black Scholes - Stock

A
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48
Q

Black Scholes - Currency

Three Substitutions

A
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49
Q

Black Scholes - Currency

Call Price = ?

A
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50
Q

Black Scholes - Currency

Put Price = ?

A
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51
Q

Black Scholes - Currency

A
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52
Q

Black Scholes - Currency

A
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53
Q

Black Scholes - Currency

A
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54
Q

Black Scholes - Futures

A
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55
Q

Black Scholes - Futures

A
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56
Q

Black Scholes - Futures

Call Price = ?

A
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57
Q

Black Scholes - Futures

Put Price = ?

A
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58
Q

Black Scholes - Futures

A
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59
Q

Black Scholes - Futures

A
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60
Q

Option Greeks

Detla

A
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61
Q

Option Greeks

Detla

A
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62
Q

Option Greeks

Detla

A
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63
Q

Option Greeks

Gamma

A
64
Q

Option Greeks

Gamma of Call Option is (+/-)?

Gamma of Put Option is (+/-)?

Gamma of Call Option (<, =, >) Gamma of Put Option?

A

Gamma of Call Option is (+)?

Gamma of Put Option is (+)?

Gamma of Call Option = Gamma of Put Option?

65
Q

Option Greeks

Theta

A
66
Q

Option Greeks

Vega

A
67
Q

Option Greeks

Vega of Call Option is (+/-)?

Vega of Put Option is (+/-)?

Vega of Call Option (<, =, >) Vega of Put Option?

A

Vega of Call Option is (+)

Vega of Put Option is (+)

Vega of Call Option = Vega of Put Option

68
Q

Option Greeks

Rho

A
69
Q

Option Greeks

Rho of Call Option is (+/-)?

Rho of Put Option is (+/-)?

A

Rho of Call Option is (+)

Rho of Put Option is (–)

70
Q

Option Greeks

Psi

A
71
Q

Option Greeks

Psi of Call Option is (+/-)?

Psi of Put Option is (+/-)?

A

Psi of Call Option is (–)

Psi of Put Option is (+)

72
Q

Option Greeks

A
73
Q

Option Elasticity

A
74
Q

Option Volatility

A
75
Q

Option Facts

A
76
Q

Portfolio Elasticity

A
77
Q

Portfolio Return

A
78
Q

Delta Hedgeing

A
79
Q

Delta Hedgeing

A
80
Q

Delta-Gamma-Theta Approximation

A
81
Q
A
82
Q

Asain Options

A
83
Q

Asain Options

A
84
Q

Asain Options

A
85
Q

Barrier Options

A
86
Q

Barrier Options

A
87
Q

Barrier Options

A
88
Q

Compound Option

A
89
Q

Compound Option

A
90
Q

Compound Option

A
91
Q

Gap Option

A
92
Q

Gap Option

A
93
Q

Gap Option

A
94
Q

Black Scholes - Exchange Options

A
95
Q

Black Scholes - Exchange Options

A
96
Q

Asset Call

Payoff = ?

Time t Price = ?

A
97
Q

Asset Put

Payoff = ?

Time t Price = ?

A
98
Q

Cash Put

Payoff = ?

Time t Price = ?

A
99
Q

Cash Call

Payoff = ?

Time t Price = ?

A
100
Q

Working with Max and Min Functions

A
101
Q

Working with Max and Min Functions

A
102
Q

Working with Max and Min Functions

A
103
Q

Forward Start Option

A
104
Q

Forward Start Option

A
105
Q

Chooser Option

Three steps to find price of chooser option:

A

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
Q

Simulation

A
107
Q

Simulation

A
108
Q

Risk Neutral Vs True

Use the __________ distribution only when discounting is needed.

Use the __________ distribution when discounting is not needed.

A

Use the Risk Neutral distribution only when discounting is needed.

Use the True distribution when discounting is not needed.

109
Q

Control Variate Method

A
110
Q

Control Variate Method

A
111
Q

Control Variate Method

A
112
Q

Control Variate Method

A
113
Q

Antithetic Variate Method

A
114
Q

Stratified Sampling

A
115
Q

Brownian Motion

A
116
Q

ABM

A
117
Q

ABM

A
118
Q

ABM

A
119
Q

Ornstein-Uhlenbeck Process

A
120
Q

GBM

A
121
Q

GBM

A
122
Q

GBM

A
123
Q

GBM

A
124
Q

GBM

A
125
Q

GBM

A
126
Q

GBM

A
127
Q

GBM

A
128
Q

Ito’s Lemma

A
129
Q

Multiplication Rules for BM

A
130
Q

Sharpe Ratio

A
131
Q

Option Risk Premium =

A

Expected Return on Option minus the Risk Free Rate

132
Q

Risk Free Portfolio

A
133
Q

Risk Free Portfolio

A
134
Q

Risk Free Portfolio

A
135
Q

Risk Free Portfolio

Three steps for creating a risk free portfolio?

A
136
Q

Risk Neutral Vs True

Relate to dZ(t) & Z(t)

A
137
Q

Risk Neutral Vs True

A
138
Q
A
139
Q

Black Scholes Equation

A
140
Q

What is the Black Scholes PDE?

A
141
Q

Interest Rate Models

Delta Gamma Theta Approximation

A
142
Q

Interest Rate Models

Delta Gamma Theta Approximation

A
143
Q

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?)
A

Interest Rate Models

Rendlemen-Bartter Model

  1. Mean Reversion (No)
  2. r can go negative (No)
  3. Volatility varies with r (Yes)
144
Q

Interest Rate Models

Vasicek Model

  1. Mean Reversion (Y/N?)
  2. r can go negative (Y/N?)
  3. Volatility varies with r (Y/N?)
A

Interest Rate Models

Vasicek Model

  1. Mean Reversion (Yes)
  2. r can go negative (Yes)
  3. Volatility varies with r (No)
145
Q

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?)
A

Interest Rate Models

Cox-Ingersoll-Ross Model

  1. Mean Reversion (Yes)
  2. r can go negative (No)
  3. Volatility varies with r (Yes)
146
Q
A
147
Q
A
148
Q
A
149
Q

Black Derman Toy

A

Black Derman Toy

150
Q
A
151
Q

Black’s Formula

Call Price =

A
152
Q

Black’s Formula

Put Price =

A
153
Q

Black’s Formula

A
154
Q

Black’s Formula

A
155
Q

Black’s Formula

A
156
Q

Black’s Formula

A

Actuarial Exams (2 decks)

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