CAIA L2 - 3.1 - Modeling Overview And Interest Rate Models Flashcards
Contrast
Exogenous variable
x
Endogenous variable
3.1 - Modeling Overview and Interest Rate Models
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
Contrast
Normative Strategies
x
Positive Strategies
3.1 - Modeling Overview and Interest Rate Models
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
Contrast
Theoretical Models
x
Empirical Models
3.1 - Modeling Overview and Interest Rate Models
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
Contrast
Applied Models
x
Abstract Models
3.1 - Modeling Overview and Interest Rate Models
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
Contrast
Cross Sectional Models
x
Time-Series Models
x
Panel data set (longitudinal data sets)
3.1 - Modeling Overview and Interest Rate Models
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
Formula
Vasicek Model
(Equilibrium Fixed-Income Models)
3.1 - Modeling Overview and Interest Rate Models
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
Formula
CIR Model
Cox, Ingersoll, and Ross model
(Equilibrium Fixed-Income Models)
3.1 - Modeling Overview and Interest Rate Models
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
Formula
Ho-Lee Model
(one of the arbitrage-free models)
3.1 - Modeling Overview and Interest Rate Models
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
Formula
Up rate = f(r’d’)
r’u’ = ?
BDT model
(one of the arbitrage-free models)
3.1 - Modeling Overview and Interest Rate Models
r’u’ = r’d’ e^(2σ)
3.1 - Modeling Overview and Interest Rate Models
Contrast
p-measure and
q-measure
3.1 - Modeling Overview and Interest Rate Models
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
Describe the Black derman Toy Model (BDT)
LO 3.1.4
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.
