Prepayment model - Knowledge Decision Services LLC

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Knowledge Decision Services, LLC.
Moving at the Speed of Thoughts
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Who We Are
 Utilize high performance patented virtual computing and storage technology
to our value-added workflow processes with embedded adaptive control
feedback to achieve maximum performance results and efficiency.
 Manage and architect 2000 CPU and GPU sysgovernor, computing nodes,
and more than 1000TB storage capacity and advanced mathematical
modeling tools( Including Quantum Field Theory, Pattern Recognition,
Manifold Topology and Differential Geometry) to quantify the eigenfunction of
the data structures.
 Specialize in maximizing investors profit by building real-time calibrated
Monte Carlo Simulations pricing model by using millisecond resolution
timestamp of market data for pricing loans or mortgage-backed securities,
asset-backed securities, futures and options, as well as risk management
analysis.
 Deliver customized value-added solution for mortgage issuers and servicers,
banks, investment banks, finance companies, broker-dealers, rating agencies
and most importantly, the fixed income investor. Offers our clients with the
critical mass of resources and experience to get the job done in a timely
manner.
KDS Proprietary Information
•2
Value-Added Solution
Profit
Decision
Knowledge
(+)
Information
(-)
Data
KDS Proprietary Information
•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
QED Engine
SCW Engine
KDS Models
User Models
3rd Party Models
OAS, YIELDS, PX, CF, Var99
Calibration, Pricing
Prepayment Delinquency
Default, Loss
Quantum Electric Dynamic Field
Theory
Prepayment Delinquency
Default, Loss
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
3rd Party
Market Data
XM
XB
FN/FH/GN
All Servicers
Raw Loan-Level Data
Prospectus &
Remittance
Real-Time Trading Data
Equity/Derivative
Market Data
UBX Core Technology
Real Time Query Analysis
4-Dimension Vectors :
Y Value
X By_variables
Z Filters
T Time
Analysis Types:
Time Series
Aging Curve
Spread Curve
Loan by Loan
Origination Solicitation
Advanced Mathematical Physics Library
Quantum Field Theory
Differential Geometry
Manifold Topology Analytics
Complex Indexed Field Analytics
Global Combinatorial Optimization
Nonlinear Regression Analytics
UBX Patented Technology
2,000 CPU + GPU
1,000 TB loan/Asset pool data
Valuation & Monte Carol Models:
HJM + Forward Curve
Prepayment, Delinquency, Default, Loss
The Structured Cashflow
Macro-economics
Monte Carol Simulations
Patented Sorting Algorithm
Virtual Table Join Index
Distributed Query and Join
Inter-UBX Index Operations
UBFile Row & Column-wise update
KDS Proprietary Information
•5
UBX Advantage
•Virtual Pocket Sorter
• Linear sort
• All the housekeeping is done in
parallel with the data memory
access so the total sort time is
the time it takes to access each
character of the sorted field one
time only.
•Patented UBX Sorter
• Base on US Patent # 5278987
• O(N)  N not N*log N
• Superior ability to process large
datasets.
KDS Proprietary Information
6
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
7
Real-time Analysis and Query - Monthly Statistics
•
About 13,500 query analysis per month
•
2.2 trillion dollars MBS trading will be affected per month
•
Dynamic simulation and price projection of rich/cheap analysis
KDS Proprietary Information
•8
Real-time Analysis
Flash Report
IOS Report
Servicer -Specpool
•High efficiency, real-time
•Provide market real-time snapshot to capture
market movements.
•Customize on-demand
•Provide customized services for our clients
• Comprehensive, clear
•Provide various statistics of market indicators
to catch market dynamics.
•KDS can provide
timely and accurate
market information,
which serves as the
crucial reference for
tens of trillion
dollars trading
within seconds by
Wells Fargo and
other world's top
financial institutions,
and make huge
profits.
KDS Proprietary Information
•9
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
10
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
11
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
12
Rich & Cheap Analysis – Monte Carlo Simulation
•GNR2013-122, CI
•Two graphs show the
different dynamic
results. The first graph
is the better one in
which mean is larger
than mode.
•The second graph has
the reverse result.
•GNR2013-122, PA
•Dynamic rich/cheap
price simulation can be
conducted by using
mean and mode, which
can also be used for
hedging and risk
management.
KDS Proprietary Information
•13
Rich & Cheap Analysis - Risk Measures
•GNR2013-122, CI
•GNR2013-122, PA
KDS Proprietary Information
•14
Rich & Chip Analysis - Cash Flow Holding
•Hedging and risk management strategy is based on the analysis of the
projected cash flow.
KDS Proprietary Information
•15
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
16
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
17
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
18
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
19
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
20
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
21
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()
22
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
24
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
25
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
26
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
27
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
28
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
29
•LARGE
•REAL ESTATE
DATA
•For each CMBS deal in the portfolio,
the underlying loans and properties are
identified and passed into the loan-level
analysis and pricing engine.
CMBS
PORTFOLIO
•DYNAMIC CMBS MODEL
•Ex) MSA: New
York
•OFFICE
•Property Analyzer breaks
down collateral pools into
property types by MSA
•RETAIL
•MULTI-FAMILY
•Property and
tenant database
tracks and monitors
high-risk loans and
tenants.
•Data source containing
latest and historical
performance data for
CMBS/CRE properties
•MARKET DATA
•Baseline NOI
time-series
projected per
property type
•NOI PROJECTION
•INDUSTRIAL
•NOI PROJECTION
•HEALTH-CARE
•NOI PROJECTION
•SELF-STORAGE
•NOI PROJECTION
•DYNAMIC CALIBRATION : Defines initial NOI
surface for all properties in portfolio, and utilizes
the Baseline NOI feed to define Specific (Absolute)
NOI Projections for all properties in portfolio.
•DISCOUNT MARGIN: Pricing
spreads are determined based
on CMBS deal performance,
default behavior, and market
data.
•BASE SEVERITY
•BASE SEVERITY
•HOTEL
•BASE SEVERITY
•INDUSTRIAL
•BASE SEVERITY
•HEALTH-CARE
•BASE SEVERITY
•SELF-STORAGE
•BASE SEVERITY
•Loan-level NOI
projections translated
into loan-level Implied
DSCR Projections
•PRICING MODEL: Utilizes information
and projections from component
models to setup pricing scenarios for
each CMBS deal in the portfolio, and
interacts with KDS cash flow engine to
produce price/cash flow projections for
the corresponding CMBS tranches.
•LEGEND
•Main Input/Output File
•External data source
•KDS low intensity computing module
•KDS moderate intensity computing module
•KDS high intensity computing module
•External pricing engine
•Baseline projections/scalars, generated in-house or obtained via subscription (e.g. PPR)
•BASE SEVERITY
•RETAIL
•NOI PROJECTION
•NOI PROJECTION
•OFFICE
•MULTI-FAMILY
•NOI PROJECTION
•HOTEL
•PREPAYMENT MODEL: Prepayment
projection curves generated for all
loans, based on property details (e.g.
type, geography, call protection, etc.)
•Baseline SEVERITY (given
default) values projected per
property type
•CMBS
PRICING
REPORT
KDS Proprietary Information
30
•CREDIT MODEL: Projects loan-level
defaults, timing of defaults and liquidations,
and loss-given-defaults, based on DSCR
curves and baseline severities provided.
Extensions, work-outs, and loanmodifications are also projected at this step.
Manual overrides on defined parameters are
possible.
•KDS Cashflow Model
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
31
Agency Index Daily Report
32
TBA Daily Report
33
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.
34
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.
35
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
36
Prepay/Default/Severity Overview
 Model Outputs
– Prepayment and default probabilities at each time step
– Delinquency rates
– Loss severity
37
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
38
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
39
Derivative Hedging On-Demand
40
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.
41
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.


42
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.
43
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!
44
American Short-Range Jump Diffusion Model: 100K Pricing
Paths for IWM (iShares Russell 2000 Index)
45
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.
48
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.
49
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.
50
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
51
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.
52
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.
53
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).
54
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.
55
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”.
56
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.
57
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.
58
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.
59
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.
60
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.
61
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
62
Personal Income & HPI Forecast
63
HPA Scenarios
64
Unemployment Scenarios
65
Technology
KDS Proprietary Information
•66
UBX Architecture
•FTPServer
Server
•FTP
•ClientBrowser/Apps
Browser
•Client
•Internet,
Intranet,
Extranet,
IP Packet IP
Network,
•Internet,
Intranet,
Extranet,
Packet
•OLTP Database
Network,
•Optical Network
•Optical
Network
•N
•1
•1
•Super
•SysGovernor
•Web
•Web
Engine
•SysGovernor
•Index
••1
•Data Set
•Existing
•ComputeNode
•Index
•1
•8 CPU
•64GB RAM
•SSD Cache
•HAV CPU Node
••1
•1
•8 CPU
•64GB RAM
•SSD Cache
•Data Set
•1
•Network Attached
HAS: High Availability
Storage Complex
Engine
•Existing
•Existing
•ComputeNode
•HAS: N+3 redundancy, SSD buffer,
High Availability Storage
•N
•1
•HAV CPU Node
•ComputeNode
•Index
••1
•1
•8 CPU
•64GB RAM
•SSD Cache
•Data Set
•CPU + GPU
•64GB RAM
•SSD•CPU
Cache+ GPU
•64GB RAM
•SSD Cache
•Fiberoptic Switching
Complex
•Gigbit Ethernet Switch
•1
•HAV CPU Node
•GPU Enhanced
Compute Nodes
•HAV: High-Availability Virtualization based on Xen Cloud Platform (XCP)
KDS Proprietary Information
67
UBX Advantage



Index: Index all the data by UBX sorter.
–
Index take only 40% storage
–
Randomly search abilities
–
Easy maintenance
Parallel Model: several parallel optimization methods can be carried on in
UBX:
–
Local Optimization: NLIN, SLSQP, LSBFGS, COBYLA, BOBYQA, etc
–
Global Optimization: DIRECT, CRS, StoGO, ISRES, etc
–
Used to calibrate the QED Pricing Model
Flexibility: new business rules and definitions can be implemented
within minutes using high performance scripting languages

Efficiently take advantage of open source module
KDS Proprietary Information
•68
UBX Advantage
 High-speed data acquisition: Use core system function to reduce
unnecessary cost.
 High Volume Data: Overlapping I/O tasks with computation tasks.
 Parallelism: Large datasets are partitioned into smaller portions
and processed in parallel on multiple computational nodes.
 Expansibility: As a result of the inherent parallelism of our model,
as more nodes are added, larger datasets can be processed at
reduced time.
 Streaming: Multivariate solution is done in a scan.
KDS Proprietary Information
69
UBX Advantage
 SPMD: Single Process Multiple Data, data mining, VOD
 MPMD: Multiple Process Multiple Data, model calibration, MCS
 Virtual fields: fields can be mathematical formula to save storage
and extend the usage
 Table Join: table can be joined to re-use existing fields
 Table can be combined horizontally and vertically to extend the
usage
KDS Proprietary Information
70
UBX Advantage
 Virtual Tables: tables can be combined to form
virtual logical tables
•Combined Table
•Vertical File:
•UBFile1
Horizontal File:
•UBFile1
•UBFile2
•UBFileN
•UBFile2
•UBFileN
KDS Proprietary Information
71
•Processing Time
UBX: The Sweet Spot
•Traditional System
•UBX
Advantage
•UBX
•Data Storage/Analysis Complexity
For larger datasets and complex situations, UBX advantage is obvious,
compared with traditional data processing system.
72
KDS Proprietary Information
Nonlinear Least Square Regression Benchmark Performance
800
•Traditional
System
700
•UBX
Time in seconds
600
500
400
300
200
100
0
0
5,000,000
10,000,000
15,000,000
20,000,000
25,000,000
Num be r of r e cor ds
No. of Record
Date
Size
(MB)
45,889
Number
Node
Nonlinear
Cycles
Time (s)
3.15
1
6
9
5
4,254,142
09/00 - 08/01
896.61
12
6
8
288
8,243,801
09/99 – 08/01
1,737.48
24
6
8
353
12,606,708
09/98 – 08/01
2,657.02
36
6
8
456
19,953,262
09/96 – 08/01
4,205.39
60
6
8
682
24,621,612
09/94 – 12/00
5,189.30
83
6
8
709
KDS Proprietary Information
73
Embedded System
Crossbar Switch
•PCI Interface
74
Field Programmable Gate Array(FPGA)
•64 bit 66 MHz PCI
KDS Proprietary Information
64 GB ECC
DRAM
Very Long Word
Instruction SRAM
Embedded System
Pipeline Case: calculation of cash flow
void OAS2Price::GetCF() {
double c0 = loan_.cash0_, c1;
double sBal;
for(int i = 1; i <= pIntRatePaths_->nTimes_; ++i) {
int WAM = pIntRatePaths_->nTimes_ - (i - 1);
sBal = c0 * (1. - pow(1. + loan_.coupon_ / 1200., 1 - WAM))
/ (1. - pow(1. + loan_.coupon_ / 1200., - WAM));
c1 = (1. - .01 * GetSMM(i)) * sBal;
1,641 clock ticks for each
Iteration of the for loop
pCashFlow_[i - 1] = c1 * loan_.sfee_ / 1200.;
c0 = c1;
}
}



75
The time quanta for the FPGA is equal to 10 clocks of a 1GHZ processor.
For this example the embedded system is about 160 times faster then
the C++ open environment.
The rate of completed calculations is independent of the
analysis complexity and the data size.
KDS Proprietary Information
Embedded System
Pipeline Case: calculation of cash flow
C++
void OAS2Price::GetCF() {
double c0 = loan_.cash0_, c1;
double sBal;
for(int i = 1; i <= pIntRatePaths_->nTimes_; ++i) {
int WAM = pIntRatePaths_->nTimes_ - (i - 1);
sBal = c0 * (1. - pow(1. + loan_.coupon_ / 1200., 1 - WAM))
/ (1. - pow(1. + loan_.coupon_ / 1200., - WAM));
c1 = (1. - .01 * GetSMM(i)) * sBal;
pCashFlow_[i - 1] = c1 * loan_.sfee_ / 1200.;
c0 = c1;
}
WAM
}
c
b
Loan_Coupon
a
WAM
f
g
d
e
sBAL calculation
as quanta
a = loan_.coupon_ / 1200
b=1+a
c = 1 – WAM
d = bc
e=1–d
f = 1+ a
g = -WAM
h = fg
k=1–h
m=e/k
sBal = c0 * m
•c0
m
h
sBAL
k
Each quanta is implemented in FPGA reconfigurable resources.
76
KDS Proprietary Information
Embedded System
Pipeline Case: calculation of cash flow
CLOCK TICK 1
Loan_Coupon
WAM
a
b
WAM
f
WAM
CLOCK TICK 2
Loan_Coupon
a
b
WAM
f
CLOCK TICK 3
Loan_Coupon
WAM
a
b
WAM
f
c
g
c
g
c
g
d
e
m
h
d
e
c0
m
h
d
KDS Proprietary Information
sBAL
k
e
c0
m
h
sBAL
k
k
At each time tick the data moves to the next calculation.
A data calculation is completed for each time tick.
77
c0
sBAL
Competitive Expertise
KDS Proprietary Information
•78
Expertise on Marketable Securities
• Marketable securities
•
•
•
•
U.S. agency mortgage backed securities (Fannie, Freddie, Ginnie)
Non agency mortgage backed securities (private label)
Collateralized debt obligations (CDOs)
Securitization of assets
• Valuation on demand platform
•
•
•
•
Massive database on U.S. securities
Real time feed of market information
Advanced interest rate model and forward curve
Multiple variable credit and prepayment models
KDS Proprietary Information
79
Expertise on Consumer Lending
• Lending products
• Residential mortgage loans
• Consumer and small business credit card loans
• Peer-to-peer installation loans
• Extensive in-depth management experience
•
•
•
•
•
•
•
Marketing solicitation
Credit underwriting
Portfolio management
Collection strategies
Basel II implementation
Credit risk scoring
Credit bureau management
KDS Proprietary Information
80
Expertise on Derivative Valuation
• Derivative instruments
•
•
•
•
•
•
Swap
European Swaption
American Swaption
Floating rate bond
Fixed rate bond
Cap floor
• Valuation on demand platform
•
•
•
•
Advanced interest rate model
Market calibrated forward curve
New quantum field pricing model
Counterparty Valuation Adjustment (CVA)
KDS Proprietary Information
81

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