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**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.

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**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

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**KDS Proprietary Information**

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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Rich & Cheap Analysis - Risk Measures**

GNR , CI GNR , PA KDS Proprietary Information

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**Rich & Chip Analysis - Cash Flow Holding**

Hedging and risk management strategy is based on the analysis of the projected cash flow. KDS Proprietary Information

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**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

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**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

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**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

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**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

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**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

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**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

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**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()

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**Example I: GNMA 2010-054 Diagram and KDS Waterfall Programming**

BK 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

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**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

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**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

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**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

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**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

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**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

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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

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**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

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**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

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**Agency Index Daily Report**

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TBA Daily Report

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**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.

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**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.

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**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

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**Prepay/Default/Severity Overview**

Model Outputs Prepayment and default probabilities at each time step Delinquency rates Loss severity

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**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

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**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

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**Derivative Hedging On-Demand**

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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.

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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.

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**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.

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**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!

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

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**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.

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**Volatility of Volatility (VXX Surface)**

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**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.

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**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.

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**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

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**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

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**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.

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**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.

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**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).

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**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.

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**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”.

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**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.

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**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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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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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.

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**Personal Income & HPI Forecast**

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HPA Scenarios

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**Unemployment Scenarios**

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**KDS Proprietary Information**

Technology KDS Proprietary Information

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Competitive Expertise**

KDS Proprietary Information

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**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

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**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

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**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

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Sponsor: Dr. K.C. Chang Tony Chen Ehsan Esmaeilzadeh Ali Jarvandi Ning Lin Ryan O’Neil Spring 2010.

Sponsor: Dr. K.C. Chang Tony Chen Ehsan Esmaeilzadeh Ali Jarvandi Ning Lin Ryan O’Neil Spring 2010.

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