1. 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.

2. KDS Proprietary Information
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

3. KDS Proprietary Information
Value-Added Solution
Profit
Decision
Knowledge
Information
Data
（－）
（＋）
Inter database operation, sorting, indexing,
Global combinatorial optimization
KDS Proprietary Information

4. Champion Challenger Platform
Trading Operations
Issuance
Risk Management
Knowledge Decision Workflow Platform : SOD, EOD
Champion Challenger Valuations MCS_OAS & Econ Scenarios Platform : VOD, EOD
OAS, YIELDS, PX, CF, Var99
Px, Impl Vol, Risk Measures
SCW Engine
QED Engine
KDS Models
Calibration, Pricing
Quantum Electric Dynamic Field Theory
User Models
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 mapping XM
FN/FH/GN
All Servicers
Prospectus & Remittance
3rd Party Market Data
Raw Loan-Level Data Real-Time Trading Data XB
Equity/Derivative
Market Data
Equity Streaming Data Mapping
3rd Party Models 4

5. UBX Core Technology Inter database operation, sorting, indexing,
Valuation & Monte Carol Models:
HJM + Forward Curve
Prepayment, Delinquency, Default, Loss
The Structured Cashflow
Macro-economics
Monte Carol Simulations
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
Real Time Query Analysis
Advanced Mathematical Physics Library
Quantum Field Theory
Differential Geometry
Manifold Topology Analytics
Complex Indexed Field Analytics 
Global Combinatorial Optimization
Nonlinear Regression Analytics
Patented Sorting Algorithm
Virtual Table Join Index
Distributed Query and Join
Inter-UBX Index Operations
UBFile Row & Column-wise update
UBX Patented Technology
2,000 CPU + GPU
1,000 TB loan/Asset pool data
Inter database operation, sorting, indexing,
Global combinatorial optimization
KDS Proprietary Information

6. KDS Proprietary Information
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 #
O(N)  N not N*log N
Superior ability to process large datasets.
KDS Proprietary Information

7. 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

8. 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

9. KDS Proprietary Information
Real-time Analysis
High efficiency, real-time
Provide market real-time snapshot to capture market movements.
Flash Report
Customize on-demand
Provide customized services for our clients
IOS Report
Comprehensive, clear
Provide various statistics of market indicators to catch market dynamics.
Servicer -Specpool
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 can provide timely and accurate market information, which serves as the crucial reference for tens of trillion dollars volume seconds trading conducted by Wells Fargo Bank and other world's top financial institutions, and bring huge benefits to them every second.
KDS Proprietary Information

10. Monte Carlo Workflow + IAS 39 MSR Risk Mgmt FASB157 Hedging
Equity Valuation
IAS 39
Pricing
Collateral
(Residential Mortgage Loans)
Collateral
(Residenti
Equity Pricing +
Prepayment & Default Models
Interest Rate and HPA Models: MC simulations or Rep Paths for stress testing
Structured Cashflow Waterfalls (SCW)
MSR
Prepay
Risk Mgmt
Delinquency
Equity +
Equity Derivatives
FASB157
Roll Rates
Default
Hedging
Macro Economic Factors & Assumptions:
Rates and HPA
Equity On-Demand
Loss Severity
Securitization
Applications
Input
Models
Output
Calculators

11. 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

12. 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 pool-level 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

13. Rich & Cheap Analysis – Monte Carlo Simulation
GNR , CI
GNR , PA
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.
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

14. Rich & Cheap Analysis - Risk Measures
GNR , CI
GNR , PA
KDS Proprietary Information

15. Rich & Chip Analysis - Cash Flow Holding
Hedging and risk management strategy is based on the analysis of the projected cash flow.
KDS Proprietary Information

16. 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
Three factor LMM key features -
Construction is arbitrage free
No yield curve calibration
Intuitive volatility and correlation calibration
Accommodate arbitrary number of factors
No need to mean-reversion parameters in LMM (no true economic meaning)
Better than Hull-White methodologies
Monte Carlo/OAS Pricing Model
Precision and speed of convergence for pricing
Based on 3x360high dimensional quasi-random sequence generator
Proprietary moment matching algorithms and controlled variable techniques to achieve faster convergence
Parallel processing of large portfolio implemented by application distributed on CPU farm in San Jose
Back-end system
Patented “Virtual Pocket Sorter” with all fields indexing we achieve
7x floating point calculation
5x integer calculation
3x character strings
Parallel modeling application on Monte Carlo simulation – an effective architecture pipeline
Flexibility and open source components

17. Structured Assets Valuation Engine
Pre-Issuance
Issuance
Post-Issuance
Extraction
Translation
Loading
RA Loan Loss/Credit Model
Pipeline Management
Slice & Dice
Scripting
Waterfall
RA Bond Sizing
Pricing/Valuation
Hedging
VOD
MCS_OAS
Econ Scenarios
Pool
Optimization
Bond Sizing
Surveillance
POD
DOD
Rosetta
Stone
Tax
AssetDatabase

18. 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

19. Collateral Data Management
Slice and Dice Engine applied in Pooling, Optimization, and Surveillance
Complete database for agency (FN, FH, GN) Pass-Through’s
Fully expanded Mega-pools, Giants, Platinum’s, STRIPs, CMO’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
Roll rate analysis
Various breakout analysis
Portfolio feature: simple or with weights
S-Curve: pre-defined or user-supplied rate incentives with lag-weights

20. SCW Deal Structuring Collateral CF Engine Scripting 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

21. 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

22. 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) SetTrancheParameters(('A1A','A1B','A2','A3','A4','A5') ('target_paydown_pct',59.80) ) SetTrancheParameters('A1A', ('cuc_multiplier', 2), ('coupon_spread', 0.17) SetTrancheParameters('M1', ('cuc_multiplier', 1.5), ('coupon_spread', 0.30), ('target_paydown_pct',66.20)
# compute and swap flag and swap in/out amount
SetSwap()
# set bond coupon based CUC multipliers and coupon spread
SetCoupon(['A1A','A1B','A2','A3','A4','A5','M1','M2','M3','M4','M5','M6','M7','M8','M9'])
# compute stepdown flag from senior enhancement
SetStepDown(['A1A','A1B','A2','A3','A4','A5'])
# compute NEC
SetNetMonthlyExcessCF()
# compute DLQ trigger
SetDlqTrigger()
# compute loss trigger
SetLossTrigger()
# compute sequential trigger
SetSeqTrigger()
# compute principal distributions
SetPrincipalDistributions()

23. Example I: GNMA 2010-054 Diagram and KDS Waterfall ProgrammingBK BK BK
PAC II Principal
PAC II Principal
PAC II Principal
Total_Int = deal.COLL_TOTAL_INT
Total_Prin = deal.COLL_TOTAL_PRIN + deal.TRANCHE['BZ'].TR_ZACCRUAL BK
PAC II Principal
PAC II
PAC II
PAC II
PAC I Principal
PAC I Principal
PAC I Principal PA PA PA PA PA PA IA IA IA IA IA IA
PayIntDue(['BX','BZ', 'IA', 'IB', 'IC', 'ID', 'PA', 'PB', 'PC', 'PD'], AS=[], FROM= [Total_Int])
# 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])
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])
# 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])
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])
PAC II
PAC I Principal PA PA IA IA PB PB PB IB IB IB
PAC I
PAC I
PAC I PB IB
PAC I PC PC PC IC IC IC PC IC
Accretion
Principal PD PD PD ID ID ID PD ID BZ BZ BZ BZ
# BZ Allocation
PayPrin(['BK'] , FROM = [Total_Prin]) BK BK BK
Remaining Principal
Remaining Principal
Remaining Principal PA PA PA BK
Remaining Principal PB PB PB
# Remaining Without Regarding to PACs
PayPrin(['BK'] , FROM= [Total_Prin])
PayPrin(['PA', 'IA'] , FROM= [Total_Prin])
PayPrin(['PB', 'IB'] , FROM= [Total_Prin])
PayPrin(['PC', 'IC'] , FROM= [Total_Prin])
PayPrin(['PD', 'ID'] , FROM= [Total_Prin]) PA IA PC PC PC PB IB PD PD PD PC IC PD ID

24. Example II: FNMA 07082 Structuring Diagram
Dated Date: 07/01/2007
Settlement Date: 07/30/2007
Payment Date: 08/25/2007
Delay Day: 24
MACR Recombination Classes (RCR) PA PM SA
ZA (Z ) A B VA FA SQ SU FC SC
Gourp
II Classes KP LP
Group I
Principal
Dsitribution II
Distribution
III ZA -
accrual
Until
VA/B
payoff
78.57%
21.43%
Until Planned
Bal
Until Targeted
I Classes PK PL PB PC
85.71%
14.29%
Until 0.0

25. 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

26. 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

27. 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

28. 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

29. 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

30. DYNAMIC CMBS MODEL KDS Proprietary Information CMBS PRICING REPORT
LARGE CMBS PORTFOLIO
For each CMBS deal in the portfolio, the underlying loans and properties are identified and passed into the loan-level analysis and pricing engine.
REAL ESTATE DATA
Baseline SEVERITY (given default) values projected per property type
Baseline NOI time-series projected per property type
Ex) MSA: New York
OFFICE
BASE SEVERITY
RETAIL
BASE SEVERITY
Property Analyzer breaks down collateral pools into property types by MSA
OFFICE
NOI PROJECTION
MULTI-FAMILY
BASE SEVERITY
RETAIL
NOI PROJECTION
HOTEL
BASE SEVERITY
MULTI-FAMILY
NOI PROJECTION
INDUSTRIAL
BASE SEVERITY
Property and tenant database tracks and monitors high-risk loans and tenants.
HOTEL
NOI PROJECTION
HEALTH-CARE
BASE SEVERITY
INDUSTRIAL
NOI PROJECTION
HEALTH-CARE
NOI PROJECTION
SELF-STORAGE
BASE SEVERITY
SELF-STORAGE
NOI PROJECTION
DYNAMIC CMBS MODEL
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 loan-modifications are also projected at this step. Manual overrides on defined parameters are possible.
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.
Data source containing latest and historical performance data for CMBS/CRE properties
Loan-level NOI projections translated into loan-level Implied DSCR Projections
PREPAYMENT MODEL: Prepayment projection curves generated for all loans, based on property details (e.g. type, geography, call protection, etc.)
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.
MARKET DATA
KDS Cash-flow Model
DISCOUNT MARGIN: Pricing spreads are determined based on CMBS deal performance, default behavior, and market data.
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)
CMBS PRICING REPORT
KDS Proprietary Information

31. 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

32. Agency Index Daily Report

33. TBA Daily Report

34. 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.

35. Prepay/Default/Severity Overview
Based on a proprietary highly non-linear non-parametric methodology with parameters estimated from non-agency loan-level data.
Prepay and default are jointly estimated in a competing risk framework.

36. 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 state- or 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

37. Prepay/Default/Severity Overview
Model Outputs
Prepayment and default probabilities at each time step
Delinquency rates
Loss severity

38. Derivative Hedging On-Demand
All forward curves are generated using proprietary non-parametric 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

39. 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

40. Derivative Hedging On-Demand

41. 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.

42. 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.

43. 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.

44. Pricing Methodologies
REAL-TIME probability distributions of option prices, as well as REAL-TIME 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 Black-Scholes-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!

45. American Short-Range Jump Diffusion Model: 100K Pricing Paths for IWM (iShares Russell 2000 Index)

46. 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.

47. Volatility of Volatility (VXX Surface)

48. 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.

49. 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 fat-tails is shifting in REAL-TIME.
Having this fat-tail probability distribution framework allows us to effectively DISCOVER the market inefficiencies throughout the trading day.

50. 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

51. 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

52. 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.

53. Traditional Short Rate Models
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 first-derivative 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.

54. Traditional Short Rate Models
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).

55. Traditional Short Rate Models
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.

56. Traditional Short Rate Models
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”.

57. 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 arbitrage-free 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.

58. 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. 

59. 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.

60. 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.

61. 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.

62. Home Price Model Mean-reverting
Targets long-term HPA using a historical “mean”.
Mean-reversion parameters tunable for faster or slower reversion.

63. Personal Income & HPI Forecast

64. HPA Scenarios

65. Unemployment Scenarios

66. KDS Proprietary Information
Technology
KDS Proprietary Information

67. UBX Architecture KDS Proprietary Information Client Browser FTP Server
Network Attached
Internet, Intranet, Extranet, IP Packet Network,
Optical Network N
SysGovernor
Client Browser 1
Web Engine
FTP Server
Super
Client Browser/Apps
OLTP Database
Fiberoptic Switching Complex
Existing
ComputeNode
Index
Data Set
8 CPU
64GB RAM
SSD Cache
HAV CPU Node
CPU + GPU
GPU Enhanced Compute Nodes
HAV: High-Availability Virtualization based on Xen Cloud Platform (XCP)
Gigbit Ethernet Switch
HAS: N+3 redundancy, SSD buffer, High Availability Storage
HAS: High Availability
Storage Complex
KDS Proprietary Information

68. KDS Proprietary Information
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

69. KDS Proprietary Information
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

70. KDS Proprietary Information
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

71. KDS Proprietary Information
UBX Advantage
Virtual Tables: tables can be combined to form virtual logical tables
Combined Table
Vertical File: Horizontal File:
UBFile1
UBFile2
UBFileN
UBFile1
UBFile2
UBFileN
KDS Proprietary Information

72. Data Storage/Analysis Complexity
UBX: The Sweet Spot
UBX Advantage
Data Storage/Analysis Complexity
UBX
Processing Time
Traditional System
For larger datasets and complex situations, UBX advantage is obvious, compared with traditional data processing system.
KDS Proprietary Information

73. Nonlinear Least Square Regression Benchmark Performance
Traditional System
UBX
No. of Record
Date
Size
(MB)
Number
Node
Nonlinear Cycles
Time (s)
45,889
3.15 1 6 9 5
4,254,142
09/ /01
896.61 12 8
288
8,243,801
09/99 – 08/01
1,737.48 24
353
12,606,708
09/98 – 08/01
2,657.02 36
456
19,953,262
09/96 – 08/01
4,205.39 60
682
24,621,612
09/94 – 12/00
5,189.30 83
709
KDS Proprietary Information

74. Embedded System Crossbar Switch Field Programmable Gate Array(FPGA)
64 GB ECC DRAM
Very Long Word
Instruction SRAM
64 bit 66 MHz PCI
PCI Interface
KDS Proprietary Information

75. KDS Proprietary Information
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 = ( * GetSMM(i)) * sBal;
pCashFlow_[i - 1] = c1 * loan_.sfee_ / 1200.;
c0 = c1; }
1,641 clock ticks for each
Iteration of the for loop
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

76. Pipeline Case: calculation of cash flow
Embedded System
Pipeline Case: calculation of cash flow
C++
sBAL calculation
as quanta
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 = ( * GetSMM(i)) * sBal;
pCashFlow_[i - 1] = c1 * loan_.sfee_ / 1200.;
c0 = c1; }
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
WAM f b c g h d k e m
sBAL a
Loan_Coupon
WAM c0
Each quanta is implemented in FPGA reconfigurable resources.
KDS Proprietary Information

77. KDS Proprietary Information
Embedded System
Pipeline Case: calculation of cash flow f b c g h d k e m
sBAL a
Loan_Coupon
WAM c0
CLOCK TICK 1 f b c g h d k e m
sBAL a
Loan_Coupon
WAM c0
CLOCK TICK 2
CLOCK TICK 3 f b c g h d k e m
sBAL a
Loan_Coupon
WAM c0
WAM
At each time tick the data moves to the next calculation.
A data calculation is completed for each time tick.
KDS Proprietary Information

78. Competitive Expertise
KDS Proprietary Information

79. Expertise on 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

80. 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

81. 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