Exam MFE Flashcards by Travis Jones

Q

PCP for Stock

A

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Q

PCP for Exchange Options

A

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Q

Exchange Option Duality

A

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

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Q

PCP for Currency Exchange

Substitutions:

S ⇒ ?

r ⇒ ?

δ ⇒ ?

A

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Q

Bounds for Put Price

Rank the following:

P_Eur 2. P_Amer3. Max(0, Ke^(-rt) - F^P(S) ) 4. K

A

K ≥ P_Amer≥ P_Eur ≥ Max(0, Ke^(-rt) - F^P(S) )

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Q

Bounds for Call Price

Rank the following:

C_Eur 2. C_Amer3. Max(0, F^P(S) - Ke^(-rt)) 4. S

A

S ≥ C_Amer≥ C_Eur ≥ Max(0, F^P(S) - Ke^(-rt))

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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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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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Q

Call Options Prices

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

A

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Q

Put Option Prices

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

A

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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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Q

Replicating Portfolio

Δ = ?

A

V = payoff of the option

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Q

Replicating Portfolio

B = ?

A

V = payoff of the option

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Q

Currency Exchange Duality

A

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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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Q

Risk Neutral Probability Pricing

p* = ?

A

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Q

Risk Neutral Probability Pricing - Option Price Formula

Option Price (V) = ?

A

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Q

Realistic Probability Pricing

p = ?

A

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Q

Realistic Probability Pricing

Option Price (V) = ?

A

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Q

Realistic Probability Pricing

A

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Q

Forward Tree

If u and d are not given,

u = ?

d = ?

A

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Q

Cox-Ross-Rubinstein Tree

u = ?

d = ?

A

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Q

Lognormal Tree (Jarrow-Rudd Tree)

u = ?

d = ?

A

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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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Q

Futures Contract

A

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Q

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

A

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Q

Lognormal Stock Price Model

m = ?

v^2 = ?

A

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Q

Lognormal Stock Price Model

A

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Q

Lognormal Stock Price Model

A

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Q

Lognormal Stock Price Model

A

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Q

Lognormal Stock Price Model

Median = ?

A

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Q

Lognormal Stock Price Model

A

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Q

Lognormal Stock Price Model

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Q

Lognormal Stock Price Model

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Q

Lognormal Stock Price Model

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Q

Lognormal Stock Price Model

A

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Q

Conditional Expectation - Lognormal Stock Price Model

A

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Q

Conditional Expectation - Lognormal Stock Price Model

A

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Q

Lognormal Stock Price Model

A

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Q

General Black Scholes

Call Price = ?

A

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Q

General Black Scholes

Put Price = ?

A

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Q

General Black Scholes

A

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Q

General Black Scholes

A

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Q

Black Scholes - Stock

Call Price = ?

A

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Q

Black Scholes - Stock

Put Price = ?

A

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Q

Black Scholes - Stock

A

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Q

Black Scholes - Stock

A

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Q

Black Scholes - Currency

Three Substitutions

A

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Q

Black Scholes - Currency

Call Price = ?

A

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Q

Black Scholes - Currency

Put Price = ?

A

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Q

Black Scholes - Currency

A

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Q

Black Scholes - Currency

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Q

Black Scholes - Currency

A

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Q

Black Scholes - Futures

A

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Q

Black Scholes - Futures

A

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Q

Black Scholes - Futures

Call Price = ?

A

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Q

Black Scholes - Futures

Put Price = ?

A

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Q

Black Scholes - Futures

A

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Q

Black Scholes - Futures

A

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Q

Option Greeks

Detla

A

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Q

Option Greeks

Detla

A

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Q

Option Greeks

Detla

A

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Q

Option Greeks

Gamma

A

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?

Q

Option Greeks

Theta

A

Q

Option Greeks

Vega

A

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

Q

Option Greeks

Rho

A

Q

Option Greeks

Rho of Call Option is (+/-)?

Rho of Put Option is (+/-)?

A

Rho of Call Option is (+)

Rho of Put Option is (–)

Q

Option Greeks

Psi

A

Q

Option Greeks

Psi of Call Option is (+/-)?

Psi of Put Option is (+/-)?

A

Psi of Call Option is (–)

Psi of Put Option is (+)

Q

Option Greeks

A

Q

Option Elasticity

A

Q

Option Volatility

A

Q

Option Facts

A

Q

Portfolio Elasticity

A

Q

Portfolio Return

A

Q

Delta Hedgeing

A

Q

Delta Hedgeing

A

Q

Delta-Gamma-Theta Approximation

A

Q

A

Q

Asain Options

A

Q

Asain Options

A

Q

Asain Options

A

Q

Barrier Options

A

Q

Barrier Options

A

Q

Barrier Options

A

Q

Compound Option

A

Q

Compound Option

A

Q

Compound Option

A

Q

Gap Option

A

Q

Gap Option

A

Q

Gap Option

A

Q

Black Scholes - Exchange Options

A

Q

Black Scholes - Exchange Options

A

Q

Asset Call

Payoff = ?

Time t Price = ?

A

Q

Asset Put

Payoff = ?

Time t Price = ?

A

Q

Cash Put

Payoff = ?

Time t Price = ?

A

Q

Cash Call

Payoff = ?

Time t Price = ?

A

Q

Working with Max and Min Functions

A

Q

Working with Max and Min Functions

A

Q

Working with Max and Min Functions

A

Q

Forward Start Option

A

Q

Forward Start Option

A

Q

Chooser Option

Three steps to find price of chooser option:

A

Chooser Option

Three steps to find price of chooser option:

Draw a time diagram.
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
Discount to time 0

Q

Simulation

A

Q

Simulation

A

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.

Q

Control Variate Method

A

Q

Control Variate Method

A

Q

Control Variate Method

A

Q

Control Variate Method

A

Q

Antithetic Variate Method

A

Q

Stratified Sampling

A

Q

Brownian Motion

A

Q

ABM

A

Q

ABM

A

Q

ABM

A

Q

Ornstein-Uhlenbeck Process

A

Q

GBM

A

Q

GBM

A

Q

GBM

A

Q

GBM

A

Q

GBM

A

Q

GBM

A

Q

GBM

A

Q

GBM

A

Q

Ito’s Lemma

A

Q

Multiplication Rules for BM

A

Q

Sharpe Ratio

A

Q

Option Risk Premium =

A

Expected Return on Option minus the Risk Free Rate

Q

Risk Free Portfolio

A

Q

Risk Free Portfolio

A

Q

Risk Free Portfolio

A

Q

Risk Free Portfolio

Three steps for creating a risk free portfolio?

A

Q

Risk Neutral Vs True

Relate to dZ(t) & Z(t)

A

Q

Risk Neutral Vs True

A

Q

A

Q

Black Scholes Equation

A

Q

What is the Black Scholes PDE?

A

Q

Interest Rate Models

Delta Gamma Theta Approximation

A

Q

Interest Rate Models

Delta Gamma Theta Approximation

A

Q

Interest Rate Models

Rendlemen-Bartter Model

Mean Reversion (Y/N?)
r can go negative (Y/N?)
Volatility varies with r (Y/N?)

A

Interest Rate Models

Rendlemen-Bartter Model

Mean Reversion (No)
r can go negative (No)
Volatility varies with r (Yes)

Q

Interest Rate Models

Vasicek Model

Mean Reversion (Y/N?)
r can go negative (Y/N?)
Volatility varies with r (Y/N?)

A

Interest Rate Models

Vasicek Model

Mean Reversion (Yes)
r can go negative (Yes)
Volatility varies with r (No)

Q

Interest Rate Models

Cox-Ingersoll-Ross Model

Mean Reversion (Y/N?)
r can go negative (Y/N?)
Volatility varies with r (Y/N?)

A

Interest Rate Models

Cox-Ingersoll-Ross Model

Mean Reversion (Yes)
r can go negative (No)
Volatility varies with r (Yes)

Q

A

Q

A

Q

A

Q

Black Derman Toy

A

Black Derman Toy

Q

A

Q

Black’s Formula

Call Price =

A

Q

Black’s Formula

Put Price =

A

Q

Black’s Formula

A

Q

Black’s Formula

A

Q

Black’s Formula

A

Q

Black’s Formula

A