Knowledge Decision Securities, LLC.
Moving at the Speed of Thoughts
KDS Confidential & Proprietary Information. Do not Distribute without written permission from Knowledge Decision Securities, LLC.
Who We Are
Knowledge Decision Securities, LLC provides the financial engineering
On-Demand Services for investment banks, mortgage originators and
servicers, and portfolio management (mortgage securities & equity
derivatives):
 A massive parallel computing center for predictive loan-level
econometric, and Value At Risk (VAR) models
 Custom petabyte data matrix arrays for nonlinear computational
analytics in UBSystem,
 Suite of On-Demand Services for all structured products and equity and
equity derivatives
 Custom OAS model calibrations based on real-time market data,
 Champion challenger Valuation On-Demand Services based on Monte
Carlo simulations infrastructure.
2
On-Demand Services
Mortgage

POD/DOD: Prepayment/Default On-Demand
– A portal service provides slice and dice of Agency prepayment data for MBS
analytics

VOD: Valuation On-Demand
– A portal service provides all asset classes Monte Carlo Simulations (MCS)
OAS and Scenarios valuations

SOD: SCW On-Demand
– A portal service for Structured Cashflow Waterfall (SCW) product issuance,
analytics, and surveillance

Equity
EOD: Equity Derivative On-Demand
– A portal service for ETF & its Derivatives via Monte Carlo Simulation
3
Champion Challenger Platform
Knowledge Decision Workflow Platform : SOD, EOD
Trading
Operations
Issuance
Risk Management
Champion Challenger Valuations MCS_OAS & Econ Scenarios Platform : VOD, EOD
OAS, YIELDS, PX, CF, Var99
Px, Impl Vol, Risk Measures
SCW Engine
ASD Engine
OAS, YIELDS, PX, CF, Var99
SCW Engine
3rd Party Models
KDS Models
User Models
Prepayment Delinquency default,
Loss
Calibration, Pricing
Prepayment Delinquency default,
Loss
Equity Valuation
Equity: Heston Based, Variance
Gamma
Equity Valuation
Data Hosting Platform : POD, DOD, EOD
‘Slice and Dice’ to achieve:
Time Series, A-Curve, S-Curve, Loan by Loan, Origination analytics
Deal, Tranche, CUSIP to loan-level
Equity Streaming Data Mapping
mapping
LP
LT
XM
XB
Agency
Servicers
Raw Loan-Level Data
Prospectus & 3rd Party Equity/Derivative
Market Data
Remittance Market Data
Real-Time Trading Data
Monte Carlo Workflow
Collateral
•Collateral
(Residential
Mortgage
Loans)
•(Residenti
Equity Valuation
Equity Pricing
+
Equity
Prepayment &
Default
Models
+
+
Equity
Derivatives
Interest Rate
and HPA
Models: MC
simulations or
Rep Paths for
stress testing
Macro Economic
Factors &
Assumptions:
Prepay
Delinquency
Structured
Cashflow
Waterfalls
(SCW)
MSR
Risk Mgmt
FASB157
Roll Rates
IAS 39
Default
Loss Severity
Pricing
Hedging
Equity OnDemand
Securitization
Calculators
Applications
Rates and HPA
Input
Models
Output
5
Monte Carlo Simulations Model
Very fast convergence achieved with the combinations of:
 High-dimensionality proprietary quasi-random number sequence
(3x360 dimensions)
 Proprietary controlled variate technique
 Proprietary moment matching technique
6
MCS OAS Pricing Methodology
 Generate Monte Carlo Simulations (MCS) interest rate and HPA
up to 3000 paths at end-of-market, store in binary format to be
used by OAS pricing programs.
 Calibrate OAS spread matrix to Agency TBAs using KDS poollevel agency prepay models
 Calibrate OAS spread matrix to most recent market surveys of
benchmark ABS tranches (BC, ALT-A, JUMBO and Options
ARM deals) using KDS loan-level prepay and loss models
 Calibrate OAS spread matrix to most recent whole-loan
transactions (market-driven, excluding distressed liquidations).
 Run client MBS/ABS portfolios using calibrated OAS matrices
on KDS’ proprietary 1024 CPU farm
7
Structured Assets Valuation Engine
SAVE integrates the following 5 subsystems:
 Three-factor LIBOR market interest rate model
 Prepayment, Delinquency, Default & Loss model
 Stochastic macro-econometric model
 Structured Cashflow Waterfalls (SCW) model
 Monte Carlo Simulations (MCS) OAS model
8
Structured Assets Valuation Engine
Post-Issuance
Extraction
Translation
Loading
Scripting
Waterfall
VOD
MCS_OAS
Econ Scenarios
Pool
Optimization
POD
DOD
Bond Sizing
Rosetta
Stone
Hedging
RA Bond Sizing
Pricing/Valuation
Issuance
Pipeline Management
Slice & Dice
RA Loan Loss/Credit Model
Pre-Issuance
Surveillance
Tax
AssetDatabase
9
Collateral Data ETL

Data Extraction, Transformation, and Loading

Remittance PDF report -> flash reports

80 ABX deals, 80 PrimeX deals, 125 CBMX deals

Custom defined deals remittance flash reports delivered real-time

Agency prepayment flash reports delivered real-time

Data Center Hosting on behalf of Clients:
– Loan level data from LP, Intex, Lewtan
– Loan level data from private firms
10
Collateral Data Management


Slice and Dice Engine applied in Pooling, Optimization, and
Surveillance
Complete database for agency (FN, FH, GN) Pass-Through’s
–

Complete Loan Performance, Lewtan, and Intex loan level database
for prepayment and default analysis:
–
–

mapped to groups, bonds, and Intex, Lewtan ground groups
Macro-Economic data integrated: HPI’s, unemployment, etc
Time Series and Aging Curves: web-based GUI
–
–
–

Fully expanded Mega-pools, Giants, Platinum’s, STRIPs, CMO’s
Roll rate analysis
Various breakout analysis
Portfolio feature: simple or with weights
S-Curve: pre-defined or user-supplied rate incentives with lag-weights
11
SCW Deal Structuring
 Collateral CF Engine
– Period based (amortization, scheduled payment/coupon,
calendar, fee, OPT/ARM, Strips, Interest Reserve, Tax, etc..)
 Scripting Engine
– Python based waterfall programming with Customizable and
Modulated Script Command Call
– Y/H/SEQ/ProRata/OC/Shifting-Interest
– Credit Enhancement




–
–
–
–
Bond/Pool Insurance Policies
Surety Bond Guarantee
Derivatives (SWAP, Cap/Floor)
Reserve Account
Triggers Modules – DLQ, Loss
NAS/PAC/TAC
RE-REMIC
Pricing/Update/Payment Modes
12
SCW Deal Structuring
 Application
– Valuation On-Demand
 MCS_OAS
 Econ Scenarios
– Payment and performance surveillance &
verification
– Risk Management
 Market Risk Hedging
 MSR
– REMIC (Projected) Tax
13
SCW Structuring Scripting Module
SetDealParameters(('strike_rate', 5.05),
('index_name', 'LIBOR_1MO'),
('cuc_level_pct', 10),
('sen_enhance_threshold_pct', 40.20),
('stepdown_month', 37),
('oc_floor_pct', 0.50),
('oc_target_pct', 4.25),
('dlq_trigger_threashold_pct', 39.80),
('loss_trigger_threashold_pct', 1.35)
# compute and swap flag and swap in/out amount
SetSwap()
SetTrancheParameters(('A1A','A1B','A2','A3','A4','A5')
('target_paydown_pct',59.80)
)
# compute NEC
SetNetMonthlyExcessCF()
SetTrancheParameters('A1A',
('cuc_multiplier', 2),
('coupon_spread', 0.17)
)
SetTrancheParameters('M1',
('cuc_multiplier', 1.5),
('coupon_spread', 0.30),
('target_paydown_pct',66.20)
# set bond coupon based CUC multipliers and coupon spread
SetCoupon(['A1A','A1B','A2','A3','A4','A5','M1','M2','M3','M4','M
5','M6','M7','M8','M9'])
# compute stepdown flag from senior enhancement
SetStepDown(['A1A','A1B','A2','A3','A4','A5'])
# compute DLQ trigger
SetDlqTrigger()
# compute loss trigger
SetLossTrigger()
# compute sequential trigger
SetSeqTrigger()
# compute principal distributions
SetPrincipalDistributions()
14
Example I: GNMA 2010-054 Diagram and KDS
Waterfall Programming
Total_Int = deal.COLL_TOTAL_INT
•BK
Total_Prin = deal.COLL_TOTAL_PRIN + deal.TRANCHE['BZ'].TR_ZACCRUAL
PayIntDue(['BX','BZ', 'IA', 'IB', 'IC', 'ID', 'PA', 'PB', 'PC', 'PD'], AS=[], FROM= [Total_Int])
•PAC II
•I
A
•PA
•PA
•IA
# PAC I Principal Distribution
PAC_I_AMT = GetTotalBalance('PA', 'PB', 'PC', 'PD') - deal.PAC_BAL['PACI']
PayPrin(['PA', 'IA'], FROM= [PAC_I_AMT , Total_Prin])
•PAC I
•PC
•IB
•PAC II Principal
•PAC I Principal
PayPrin(['PB', 'IB'], FROM= [PAC_I_AMT , Total_Prin])
PayPrin(['PC', 'IC'], FROM= [PAC_I_AMT , Total_Prin])
PayPrin(['PD', 'ID'], FROM= [PAC_I_AMT , Total_Prin])
•IC
# PAC II Principal Distribution
PAC_II_AMT = GetTotalBalance('BK', 'PA', 'PB', 'PC', 'PD') - deal.PAC_BAL['PACII']
PayPrin(['BK'], FROM= [PAC_II_AMT , Total_Prin])
PayPrin(['PA', 'IA'], FROM= [PAC_II_AMT , Total_Prin])
•PD
•ID
PayPrin(['PB', 'IB'], FROM= [PAC_II_AMT , Total_Prin])
PayPrin(['PC', 'IC'], FROM= [PAC_II_AMT , Total_Prin])
PayPrin(['PD', 'ID'], FROM= [PAC_II_AMT , Total_Prin])
•BZ
# BZ Allocation
PayPrin(['BK'] , FROM = [Total_Prin])
•BK
•Remaining Principal
•Accretion
•Principal
•PB
# Remaining Without Regarding to PACs
•PA
•IA
PayPrin(['BK'] , FROM= [Total_Prin])
•PB
•IB
PayPrin(['PA', 'IA'] , FROM= [Total_Prin])
•PC
•IC
•PD
•ID
PayPrin(['PB', 'IB'] , FROM= [Total_Prin])
PayPrin(['PC', 'IC'] , FROM= [Total_Prin])
PayPrin(['PD', 'ID'] , FROM= [Total_Prin])
Example II: FNMA 07082 Structuring Diagram
Dated Date: 07/01/2007
Settlement Date: 07/30/2007
Payment Date: 08/25/2007
Delay Day: 24
GroupII
Principal
Distribution
GroupI
Principal
Dsitribution
GroupIII
Principal
Distribution
Until Planned
Bal
A
VA
78.57%
B
Until Planned
Bal
GroupI Classes
PK
PL
PB
PC
GourpII Classes
KP
LP
21.43%
85.71%
14.29%
FC
SC
B
Until Targeted
Bal
VA
ZAaccrual
Until
VA/B
payoff
SQ
FA
SU
ZA (Z)
Until 0.0
Until 0.0
SQ
GourpII Classes
KP
LP
Until 0.0
GroupI Classes
PK
PL
PB
PC
SQ
MACR Recombination Classes (RCR)
PA
PM
SA
16
Example III:
JP MORGAN MORTGAGE TRUST 2007-CH3
 Closing Date 5/15/2007
 Collateral Type
– Subprime Home Equity
 Capital Structure:
– Overcollateralization
– SEN/MEZZ/JUN Y Structure
– Net SWAP cover OC Deficiency, Interest Shortfall, Realized
Loss, NetWAC Carryover
– Cross-Collateralization
 Triggers in
–
–
–
–
Enhancement Delinquency
Cumulative Loss
Sequential Trigger
OC and Subs Test
17
Example IV:
NEW CENTURY HEL TRUST 2006-2
 Closing Date 06/29/2006
 Collateral
– Subprime Home Equity
 Capital Structure:
– Overcollateralization
– SEN/JUN Sequential
– Net SWAP cover OC Deficiency, Interest Shortfall, Realized
Loss, NetWAC Carryover
– Cross-Collateralization (on Group I & I Notes Sen)
 Triggers in
–
–
–
–
Enhancement Delinquency
Cumulative Loss
Sequential Trigger
OC and Subs Test
18
RMBS Valuation Models
 Prepay, Default, Severity, Delinquency
– Modeling Approach
 Delinquency Transitions
 Prepay/Default Competing Risks
– Agency and Non-Agency Collateral:







Prime Jumbo
Alt-A
Option ARM
Subprime
HELOC
Fannie/Freddie
FHA/VA
19
TBA Analytics
–
–
–
–
De Facto Standard Pool pricing
Worst to Delivery Slice-and-Dice and Priding
Absolute value: Yield to Maturity, OAS, Total Return
Relative value: return vs. other securities (corporate bonds,
swaps, agency debt, etc.), vs. sector benchmark (TBA,
current coupon, index), vs. intra-sector alternatives (vs. Gold,
vs. GN, vs. 15-year, etc.)
– Historical rich/cheap analysis: time series mean reversion
20
CMBS Valuation Models
 Prepay, Default, Timing of Default, Severity, Extension
– Key Inputs: Property Type, LTV, DSCR, NOI, Underwriting,
MSA, Cap Rate, Refi Threshold, Call Protection, Tenant Attributes
– Subsystems
 APOLLO: NOI Generator, Scenario/Monte Carlo Simulation
 HELIOS: Loan Level Prepay/Default Generator
 Market Calibration
– CMBX, TRX
– Conversion from TRX to OAS
21
22
Index Derivative Analytics
 Complete coverage in PRIMEX, ABX, CMBX, MBX/IOS/PO
 Calculate Market Implied Spread(OAS) based on Economic
Scenarios and 3000 paths Monte Carlo Simulation
 Monte Carlo Simulation based risk measures in
–
–
–
–
–
–
–
Mode
Skewness (Pearson's first)
Mean
Sigma
Var
1-dVar
Risk Score
 Daily and Weekly Reports based on Market Close Price
23
Agency Index Daily Report
24
TBA Daily Report
25
Prepay/Default/Severity Overview
 Projects monthly prepayment, delinquency, default and
loss severity rates of new (at purchase) or seasoned
(portfolio) loans.
 Takes into account of loan, borrower and collateral risk
characteristics as well as macro economic variables on
rates and home prices.
 Based on a hybrid delinquency transition rate and
competing risks survivorship model where the prepay &
default risk parameters are estimated from historical
loan-level data.
26
Prepay/Default/Severity Overview
 Based on a proprietary highly non-linear nonparametric methodology with parameters estimated
from non-agency loan-level data.
 Prepay and default are jointly estimated in a
competing risk framework.
27
Prepay/Default/Severity Overview
 Model Inputs
– Collateral type (e.g., alt-a, non-conforming balance, no prepay
penalty).
– Age, Note rate, Mortgage rates, Yield curve slope.
– Home price (zip/CBSA-level if used at loan-level, otherwise stateor national-level)
– Unemployment rate
– Loan size, Documentation, Occupancy, Purpose, State, FICO, LTV,
Channel.
– Delinquency history and status (past due, bankruptcy, REO)
– Negative amortization limit (recast) for option ARM
– Modification type, size, and timing
– Servicer
28
Prepay/Default/Severity Overview
 Model Outputs
– Prepayment and default probabilities at each time step
– Delinquency rates
– Loss severity
29
Derivative Hedging On-Demand
 All forward curves are generated using proprietary nonparametric calibration technique that is guaranteed with
maximum smoothness
 The forward curves are consider “trading quality” and
“battle tested” have been by various trading desks for
trades in excess of $1T worth of derivatives
 These should not be compared with forward curves from
Bloomberg where they are only for informational purposes,
or with many leading Asset/Liability software venders
where the forward curves are usually used for monthly
portfolio valuation (i.e., accounting purposes) rather than
for trading purposes
30
Derivative Hedging On-Demand
 All flavors of interest rate swaps (including swaps with
embedded options, both European and Bermudan)
 Swaptions (European, Bermudan and/or custom)
 LIBOR, CMS/CMT caps/floors
 CMM (constant maturity mortgage) swaps, FRAs (forward
rate agreements), and swaptions (this includes our
mortgage current model)
 Mortgage options
 Treasury note/bond futures and options
 Other customized derivatives
31
Derivative Hedging On-Demand
32
Equity On-Demand
•
Hedge-funds and investment banks that develop these type of tools to
capture mispricings in equity derivatives markets keep them proprietary and
do not share with them anyone.
•
The KDS option model and trading platform, also known as EOD, tackles
all of these challenges and makes the proper tools available for traders so
that they can profit from mispricings everyday!
•
The EOD allows traders to wake up in the morning with trading strategies
that are indifferent to whether the market is bullish or bearish. Instead, they
can focus on profiting using high probabilities in both up and down markets.
This eliminates trading based on human emotion, which is the cause for
most financial mistakes!
•
The Bullish vs. Bearish paradigm was created by the Technical Model
mindset. Using volatility based analysis and high-probability trading means
that the so-called “Bullish” or “Bearish” trade is no longer meaningful, and
profitability does not depend on the direction of the market!
•
In this presentation, we will cover the different parts of the EOD system,
describe how to use the system, and most importantly show how to execute
trading strategies and make money consistently using the EOD.
33
EOD Option Pricing

EOD platform utilizes advanced option pricing models.

Based on trader’s “Risk Appetite,” he or she can use EOD to create trading
strategies such as:
– High Probability Mean Reversion strategies
– Time decay (Theta) strategies
– Spread based strategies (vertical/calendar spreads)
– Underlying ETF buy/sell strategies

“Risk Appetite” is based on confidence levels, or probability ranges, that are
used for mean-reversion trades and also allow traders to tweak their risk
tolerance using precise metrics.
For example, a confidence level gives the trader ability to know the exact
probability that a buyer of an option will exercise, at any given time. This is
very important for HPMR trades!
EOD successfully eliminates subjectivity from options trading by specifying
strike price targets and buy/sell thresholds.


34
Pricing Methodologies





Our underlying option models use advanced techniques from quantum physics
and nonlinear mathematics, applied to financial analysis and trading.
The models are applied to finance using fundamental laws of physics and
mathematics, and utilize coordinate transformations in Space, Time, Force,
Momentum, and Energy.
Since option prices have diffusion properties, we can use systems of partial
differential equations to model price behavior.
We model the randomness observed in prices and volatilities by using
stochastic frameworks such as Variance Gamma and Long-Range Stochastic
Volatility (discussed later).
Since solutions to these stochastic and highly nonlinear system of PDE’s are
unsolvable via analytical methods, we must utilize massive parallel-processing
computational power to run extremely large numbers of scenarios at
infinitesimal (intra-day) time steps.
35
Pricing Methodologies



REAL-TIME probability distributions of option prices, as well as REALTIME option chains pricing solutions, are calculated through evaluating the
large number of intra-day scenarios.
Unlike EOD, most option pricing models in the market-place use BlackScholes-Merton (BSM) framework as the underlying theory.
There are many problems with using this BSM framework to do real-time
options trading, most importantly:
–
–
–
–
Probability distributions do not have FAT-TAILS as observed in the markets.
Prices utilize a single volatility, which is clearly not true in reality.
BSM framework does not have ability to imply a Volatility Skew or Volatility Smile.
BSM framework was created for European-style options which can only be exercised
at maturity. In reality, most ETFs that trade on exchanges are American-style,
which can be exercised any time.
– There is no ability to capture and quantify JUMPS (both up and down) in prices of
options and underlying Equity Index/ETF.
– BSM Equations were designed by professors (not traders) to allow “analytical
solutions” for their convenience. In practice, we don’t care about elegant “analytical
solutions” if the prices are WRONG!
36
American Short-Range Jump Diffusion Model: 100K Pricing
Paths for IWM (iShares Russell 2000 Index)
37
Volatility Surface Smile: TZA vs. TNA
• The volatility surface of the inverse 3x leverage TZA compared against the positive
3x leverage TNA indicates an inverse relationship.
• However, the relationship is not precisely inverse due to the fact that both TZA and
TNA are separate tradable securities, with unique option chain dynamics.
• Therefore, we are able to capture not only the intrinsic inverse relationship, but also
the individual supply/demand dynamics for each ETF.
Volatility of Volatility (VXX Surface)
American Short-Range Jump Diffusion Model






In addition to Stochastic Volatility, the VGSV based framework
enables us to price options using American exercisability.
The American exercise feature utilizes a Least-Squares Monte Carlo
(LSM) methodology which iteratively quantifies the probability of
exercise PER timestep.
VGSV framework also allows us to model the Jump up and Jump
down impact under a Short-Range (i.e. intra-day) time period.
Jump processes are modeled via the sampling of gamma and
exponential distribution variates over a large number of paths and
trajectories.
For these reasons, we also refer to our option pricing model as the
American Short-Range Jump diffusion (ASD) model.
For the long-range (20+ days) option chains, we utilize the America
Long-Range Jump diffusion (ALD) model which allows us to capture
the longer term convergence properties of option pricing.
40
Fat-Tail Distributions





EOD uses proprietary methods based around Short-Range Variance Gamma
stochastic volatility (VGSV) and Long-Range stochastic volatility models.
Within our framework, we are able to produce probability distributions that
accurately capture the FAT-TAILS (left and right) implied by the market.
Since most of the mispricings (i.e. Money-Making Opportunities) exist near
the TAILS of the distribution (OTM options), precisely capturing fat-tails is
VERY IMPORTANT!
The REAL-TIME display of the probability distributions (“Histograms”) allows
traders to not only see the fat-tails, but also track how the area under the fattails is shifting in REAL-TIME.
Having this fat-tail probability distribution framework allows us to effectively
DISCOVER the market inefficiencies throughout the trading day.
41
Interest Rate Model
 Three-Factor BGM/Libor Market Model (LMM)
 Forward curve calibrated to a daily mixture of Libor,
Euro$ Futures, Euro$ futures options, and
intermediate to long term swap rates
 Volatility calibrated to daily end-of-market swaption
volatility surface
 The “battle tested” forward curves for trading &
valuations are guaranteed with the maximum
smoothness.
42
Libor Market Model
 Also known as the BGM (Brace-Gatare-Musiela) model.
 It is the “modern” implementation of the well-known
Heath-Jarrow-Morton Model
 Considered the “second-generation” of interest rate
models. The “first-generation” being the Hull-White
family of short-rate models
43
Key Features of Libor Market Model
 Model construction is automatically arbitrage free.
 No need for yield curve calibration. Avoided the
problem of convergence when calibrating most type of
short rate models.
 Intuitive volatility and correlation calibration.
 Can accommodate arbitrary number of factors in a
straight forward way.
44
Libor Market Model vs.
Traditional Short Rate Models
 No need to iteratively search for a set of calibration
parameters in order to match the yield curve.
 E.g., Hull-White model is calibrated to the firstderivative of the forward curve, which can be oscillatory
sometimes. LMM does not suffer from this problem.
 For most short-rate models, rates would have to be
sampled from some simple lattice (either binomial or
trinomial). I.e., rates can only go up or down, but not
from a normal distribution.
45
Libor Market Model vs.
Traditional Short Rate Models
 Can sample from short rate model equations using normal
distribution, but since the model parameters are calibrated on the
lattice, “equation sampling” will not be arbitrage free, i.e, incorrect in
most cases.
 No need for mean-reversion parameter in LMM, which has no true
economic meaning (see “Interest Rate Option Models”, R.
Rebonato). Therefore no need to calibrate the model to this artificial
parameter.
 Volatility calibration is more intuitive in LMM vs. short rate models
(see papers by the author of LMM, and John Hull).
46
Libor Market Model vs.
Traditional Short Rate Models
 Multifactor version of the short rate models are limited to
two-factor models. Calibrating these models to market
instruments are extremely difficult (see “Interest Rate
Option Models”, R. Rebonato).
 Because of this difficulty, virtually no software vendors
offers this functionality except a select few such as
Numerix (expensive…) and some Wall Street trading
desks. QRM has a “place holder” for a two-factor model,
but I was told it’s essentially useless and no client uses
it.
47
Libor Market Model vs.
Traditional Short Rate Models
 LMM/HJM models have been adopted by more Wall
Street MBS trading desks recently, as they “upgrade”
from the older short rate models.
 Quote from J. Hull’s book (the author of most short-rate
models):
“because they are heavily path dependent, mortgage-backed
securities usually have to be valued using Monte Carlo simulation.
These are therefore ideal candidates for applications of the HJM model
and Libor market models”.
48
Competitor I Interest Rate Models
 Single-Factor Black-Karasinski (BK)
 Single-Factor Hull-White (HW)
 Better suited for lattice-based pricing applications, such as
Bermudan Swaptions, CMS cap/floors, etc. ; issues with arbitragefree in a simulation setting because parameters are calibrated on
the lattice but Monte Carlo rates are generated from the stochastic
equation (see J Hull book on this issue).
 Volatility and mean-reversion parameters in Competitor I’s versions
of BK & HW are “user inputs”, instead of optimized to fit a series of
market option prices (see extensive discussion on this issue in J.
Hull’s book); this could problematic because the mean reversion
parameter does not have intuitive true economic meaning.
 Interest rate models are not truly arbitrage-free by design (this is
separate from the sampling error issue of Monte Carlo), and the
mean-reversion and volatility parameters are not calibrated to
market vols.
49
Competitor II Interest Rate Models
 Prepayment model is not up to standard.
 The turnover and refi components are not handled well.
 The refi component is part of prepayment model deals with
interest rate sensitivity.
 Burnout/season component part of the model is also not
handled well.
 Duration result is off from market expectation.
 This most likely has to do with its prepayment model and it's
interest rate model.

 OAS/interest rate model uses its own version of the lognormal
model.
 It is quite different than either the HJM class of the HULL White
class of models.
 Besides prepayment models, duration calculation can also be
sensitive to one's implementation of the OAS/interest rate model.
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KDS Interest Rate Model
 Matching discount bond prices from simulated paths and those
from the yield curve.
 Expect some small mismatch due to the nature of Monte Carlo
sampling
 A three-factor model, better pricing for RMBS/REMIC/CMO type of
assets that depends on both long and short rates.
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KDS Interest Rate Model
 KDS’s LMM can be calibrated to most volatility term structure shapes
 Typical volatility calibration
 Interest rate paths from KDS’s interest rate model are completely
“open” - can be tested by any user on any given day for pricing any
benchmark or custom fixed income assets.
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Interest Rate Model Summary
 Interest rate modeling is at the center of interest rate
risk management.
 Sophisticated interest rate risk management
demands state-of-the art interest rate models.
 Libor Market/HJM models are current state-of-the
art and ideally suited for pricing and risk managing
mortgage securities.
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Home Price Model
 Mean-reverting
 Targets long-term HPA using a historical “mean”.
 Mean-reversion parameters tunable for faster or
slower reversion.
HPA Projection
250
HPA (%)
200
150
100
50
0
1989
1994
1999
2004
2009
2014
2019
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Personal Income & KDS HPI Forecast
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KDS HPI Scenarios
56
KDS Unemployment Scenarios
57