Knowledge Decision Services, LLC .

1. Knowledge Decision Services, LLC. Moving at the Speed of Thoughts KDS Confidential & Proprietary Information. Do not Distribute without written permission from Knowledge Decision Services, LLC.

2. Who We Are Knowledge Decision Services, LLC provides the financial engineering On-Demand Services for investment banks, mortgage originators and servicers, and portfolio management (mortgage securities & equity derivatives): • A massive parallel computing center for predictive loan-level econometric, and Value At Risk (VAR) models • Custom petabyte data matrix arrays for nonlinear computational analytics in UBSystem, • Suite of On-Demand Services for all structured products and equity and equity derivatives • Custom OAS model calibrations based on real-time market data, • Champion challenger Valuation On-Demand Services based on Monte Carlo simulations infrastructure.

3. 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

4. Champion Challenger Platform Knowledge Decision Workflow Platform : SOD, EOD Issuance Trading Operations Risk Management Champion Challenger Valuations MCS_OAS & Econ Scenarios Platform : VOD, EOD OAS, YIELDS, PX, CF, Var99 Px, ImplVol, Risk Measures OAS, YIELDS, PX, CF, Var99 SCW Engine SCW Engine ASD Engine KDS Models Calibration, Pricing Equity: Heston Based, Variance Gamma 3rd Party Models Prepayment Delinquency default, Loss Equity Valuation User Models Prepayment Delinquency default, Loss Equity Valuation Data Hosting Platform : POD, DOD, EOD ‘Sliceand Dice’ to achieve: Time Series, A-Curve, S-Curve, Loan by Loan, Origination analytics Deal, Tranche, CUSIP to loan-level mapping Equity Streaming Data Mapping LP LT XM XB Agency Servicers Prospectus & Remittance 3rd Party Market Data Equity/Derivative Market Data Raw Loan-Level Data Real-Time Trading Data

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

6. 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

7. MCS OAS Pricing Methodology • Generate MonteCarlo 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

8. StructuredAssetsValuationEngineSAVE 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

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

10. 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

11. 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

12. 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

13. 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

14. SCW Structuring Scripting Module # 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() 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)

15. Example I: GNMA 2010-054 Diagram and KDS Waterfall Programming BK BK BK PAC II Principal PAC II Principal PAC II Principal BK PAC II PAC II PAC II PAC II Principal PAC I Principal PAC I Principal PAC I Principal PA PA PA IA IA IA PA PA PA IA IA IA PAC II IA PAC I Principal PA IA PA IB IB IB PB PB PB PAC I PAC I PAC I IB PB PAC I IC IC IC PC PC PC IC PC ID ID ID PD PD PD Accretion Principal ID PD BZ BZ BZ BZ BK BK BK Remaining Principal Remaining Principal Remaining Principal PA PA PA BK Remaining Principal PB PB PB IA PA PC PC PC IB PB PD PD PD IC PC ID PD

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

17. 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

18. 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

19. 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

20. 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

21. 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

23. 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

24. Agency Index Daily Report

25. TBA Daily Report

26. 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.

27. 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.

28. 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

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

30. 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

31. 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

32. Derivative Hedging On-Demand

33. 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.

34. 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.

35. 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.

36. 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!

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

38. 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.

39. Volatility of Volatility (VXX Surface)

40. 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.

41. 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.

42. 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.

43. 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

44. 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.

45. 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.

46. 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).

47. 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.

48. 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”.

49. 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.

50. 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. • Durationresult is off from market expectation. • This most likely has to do with its prepayment model and it's interest rate model. • OAS/interest rate modeluses 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.