CAIA L2 - 3.1 - Modeling Overview And Interest Rate Models Flashcards

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1
Q

Contrast

Exogenous variable
x
Endogenous variable

3.1 - Modeling Overview and Interest Rate Models

A

Exogenous variable
comes from a source outside of the model
Essentially an independent variable

Endogenous variable
comes from within the model.
It is essentially a dependent variable

3.1 - Modeling Overview and Interest Rate Models

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2
Q

Contrast

Normative Strategies
x
Positive Strategies

3.1 - Modeling Overview and Interest Rate Models

A

Normative model
(How people and asset prices) should behave

Positive model
(How people and asset prices) actually behave

Dica:
____tive = ter = ____have = behave

3.1 - Modeling Overview and Interest Rate Models

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3
Q

Contrast

Theoretical Models
x
Empirical Models

3.1 - Modeling Overview and Interest Rate Models

A

Theoretical Models
Based on assumptions about behaviour
Usage - in simplified situations. Ex: put-call parity

Empirical Models
Based on observed behaviour
observations that can be statistically proven

Usage:
* large data
* complex behaviour
* relationship changes over time

Dica:
____cal = base = Based on

3.1 - Modeling Overview and Interest Rate Models

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4
Q

Contrast

Applied Models
x
Abstract Models

3.1 - Modeling Overview and Interest Rate Models

A

Applied Models
Adresses real world problems
Usage
* Markowit
* Asset Pricing Model
* widely used by alt managers

Abstract Models (= Basic Model)
Adresses hypothetical problems (situations)

Dica:
AAA - Applied / Abstract => Address

3.1 - Modeling Overview and Interest Rate Models

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5
Q

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Cross Sectional Models
x
Time-Series Models
x
Panel data set (longitudinal data sets)

3.1 - Modeling Overview and Interest Rate Models

A

Cross Sectional Models
Analyze relatioships at a specific point in time

Time-Series Models
Analyze behaviour over a period

Panel data set (longitudinal data sets)
multiple variables + over time

3.1 - Modeling Overview and Interest Rate Models

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6
Q

Formula

Vasicek Model
(Equilibrium Fixed-Income Models)

3.1 - Modeling Overview and Interest Rate Models

A

r’t+1’ = r’t’ + k(μ−r’t’) + σ ε’t+1’

r’t+1’ = next period’s short-term rate
r’t’ = current short-term rate
µ = long-term average of the short-term rate
k = speed of the mean-reverting adjustment
σ = volatility of change in interest rates
ε’t+1’ = normally distributed with a mean of zero and a standard deviation of 1.

Vasicek assumes:
1. constant volatility
2. mean reversion

Negative: assumption of constant volatility and ability to permit negative rates.

3.1 - Modeling Overview and Interest Rate Models

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7
Q

Formula

CIR Model
Cox, Ingersoll, and Ross model
(Equilibrium Fixed-Income Models)

3.1 - Modeling Overview and Interest Rate Models

A

r’t+1’ = r’t’ + k(μ−r’t’) + √(r’t’) σ ε’t+1’
“corrects” Vasicek => disallows negative rates by using variance and not volatility

3.1 - Modeling Overview and Interest Rate Models

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8
Q

Formula

Ho-Lee Model

(one of the arbitrage-free models)

3.1 - Modeling Overview and Interest Rate Models

A

r’t+1’ = r’t’ + θ’t’ + σ ε’t+1’

Assumes
* Normal distribution for short term rates
* incorporates a drift parameter that directly connects the model with the yield curve
* begins the pricing process with the price of zero-coupon bonds
* Baisc idea = arbitrage should not exist

3.1 - Modeling Overview and Interest Rate Models

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9
Q

Formula

Up rate = f(r’d’)
r’u’ = ?

BDT model
(one of the arbitrage-free models)

3.1 - Modeling Overview and Interest Rate Models

A

r’u’ = r’d’ e^(2σ)

3.1 - Modeling Overview and Interest Rate Models

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10
Q

Contrast

p-measure and
q-measure

3.1 - Modeling Overview and Interest Rate Models

A

p-measure (a.k.a. the real-world measure) - factors probabilities using historical data without making assumptions
uses the customized rate for discounting future cash flows.

q-measure (a.k.a. the risk-neutral measure) - ASSUME ARBITRAGE FREE APPROACH (ideal for valuing derivatives)
uses the risk-free rate for discounting future cash flows.

3.1 - Modeling Overview and Interest Rate Models

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11
Q

Describe the Black derman Toy Model (BDT)

LO 3.1.4

A

The BDT model can calculate spot rates or forward rates to value fixed-income derivatives. It remains consistent with the current yield curve and the observed implied volatility on time-relevant interest rate caplets. These intuitive constraints enable arbitrage-free pricing of fixed-income derivatives.

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