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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. Who We Are Utilize high performance patented virtual computing and storage technology to our value-added workflow processes with embedded adaptive control feedback to achieve maximum performance results and efficiency. Manage and architect 2000 CPU and GPU sysgovernor, computing nodes, and more than 1000TB storage capacity and advanced mathematical modeling tools( Including Quantum Field Theory, Pattern Recognition, Manifold Topology and Differential Geometry) to quantify the eigenfunction of the data structures. Specialize in maximizing investors profit by building real-time calibrated Monte Carlo Simulations pricing model by using millisecond resolution timestamp of market data for pricing loans or mortgage-backed securities, asset-backed securities, futures and options, as well as risk management analysis. Deliver customized value-added solution for mortgage issuers and servicers, banks, investment banks, finance companies, broker-dealers, rating agencies and most importantly, the fixed income investor. Offers our clients with the critical mass of resources and experience to get the job done in a timely manner. KDS Proprietary Information •2 Value-Added Solution Profit Decision Knowledge （＋） Information （－） Data KDS Proprietary Information •3 Champion Challenger Platform Knowledge Decision Workflow Platform : SOD, EOD Trading Operations Issuance Risk Management Champion Challenger Valuations MCS_OAS & Econ Scenarios Platform : VOD, EOD OAS, YIELDS, PX, CF, Var99 Px, Impl Vol, Risk Measures SCW Engine QED Engine SCW Engine KDS Models User Models 3rd Party Models OAS, YIELDS, PX, CF, Var99 Calibration, Pricing Prepayment Delinquency Default, Loss Quantum Electric Dynamic Field Theory Prepayment Delinquency Default, Loss Data Hosting Platform : POD, DOD, EOD ‘Slice and Dice’ to achieve: Time Series, A-Curve, S-Curve, Loan by Loan, Origination analytics Deal, Tranche, CUSIP to loan-level Equity Streaming Data Mapping mapping 3rd Party Market Data XM XB FN/FH/GN All Servicers Raw Loan-Level Data Prospectus & Remittance Real-Time Trading Data Equity/Derivative Market Data UBX Core Technology Real Time Query Analysis 4-Dimension Vectors : Y Value X By_variables Z Filters T Time Analysis Types: Time Series Aging Curve Spread Curve Loan by Loan Origination Solicitation Advanced Mathematical Physics Library Quantum Field Theory Differential Geometry Manifold Topology Analytics Complex Indexed Field Analytics Global Combinatorial Optimization Nonlinear Regression Analytics UBX Patented Technology 2,000 CPU + GPU 1,000 TB loan/Asset pool data Valuation & Monte Carol Models: HJM + Forward Curve Prepayment, Delinquency, Default, Loss The Structured Cashflow Macro-economics Monte Carol Simulations Patented Sorting Algorithm Virtual Table Join Index Distributed Query and Join Inter-UBX Index Operations UBFile Row & Column-wise update KDS Proprietary Information •5 UBX Advantage •Virtual Pocket Sorter • Linear sort • All the housekeeping is done in parallel with the data memory access so the total sort time is the time it takes to access each character of the sorted field one time only. •Patented UBX Sorter • Base on US Patent # 5278987 • O(N) N not N*log N • Superior ability to process large datasets. KDS Proprietary Information 6 On-Demand Services Mortgage POD/DOD: Prepayment/Default On-Demand – A portal service provides slice and dice of Agency prepayment data for MBS analytics VOD: Valuation On-Demand – A portal service provides all asset classes Monte Carlo Simulations (MCS) OAS and Scenarios valuations SOD: SCW On-Demand – A portal service for Structured Cashflow Waterfall (SCW) product issuance, analytics, and surveillance Equity EOD: Equity Derivative On-Demand – A portal service for ETF & its Derivatives via Monte Carlo Simulation 7 Real-time Analysis and Query - Monthly Statistics • About 13,500 query analysis per month • 2.2 trillion dollars MBS trading will be affected per month • Dynamic simulation and price projection of rich/cheap analysis KDS Proprietary Information •8 Real-time Analysis Flash Report IOS Report Servicer -Specpool •High efficiency, real-time •Provide market real-time snapshot to capture market movements. •Customize on-demand •Provide customized services for our clients • Comprehensive, clear •Provide various statistics of market indicators to catch market dynamics. •KDS can provide timely and accurate market information, which serves as the crucial reference for tens of trillion dollars trading within seconds by Wells Fargo and other world's top financial institutions, and make huge profits. KDS Proprietary Information •9 Monte Carlo Workflow Collateral •Collateral (Residential Mortgage Loans) •(Residenti Equity Valuation Equity Pricing + Equity Prepayment & Default Models + + Equity Derivatives Interest Rate and HPA Models: MC simulations or Rep Paths for stress testing Macro Economic Factors & Assumptions: Prepay Delinquency Structured Cashflow Waterfalls (SCW) MSR Risk Mgmt FASB157 Roll Rates IAS 39 Default Loss Severity Pricing Hedging Equity OnDemand Securitization Calculators Applications Rates and HPA Input Models Output 10 Monte Carlo Simulations Model Very fast convergence achieved with the combinations of: High-dimensionality proprietary quasi-random number sequence (3x360 dimensions) Proprietary controlled variate technique Proprietary moment matching technique 11 MCS OAS Pricing Methodology Generate Monte Carlo Simulations (MCS) interest rate and HPA up to 3000 paths at end-of-market, store in binary format to be used by OAS pricing programs. Calibrate OAS spread matrix to Agency TBAs using KDS poollevel agency prepay models Calibrate OAS spread matrix to most recent market surveys of benchmark ABS tranches (BC, ALT-A, JUMBO and Options ARM deals) using KDS loan-level prepay and loss models Calibrate OAS spread matrix to most recent whole-loan transactions (market-driven, excluding distressed liquidations). Run client MBS/ABS portfolios using calibrated OAS matrices on KDS’ proprietary 1024 CPU farm 12 Rich & Cheap Analysis – Monte Carlo Simulation •GNR2013-122, CI •Two graphs show the different dynamic results. The first graph is the better one in which mean is larger than mode. •The second graph has the reverse result. •GNR2013-122, PA •Dynamic rich/cheap price simulation can be conducted by using mean and mode, which can also be used for hedging and risk management. KDS Proprietary Information •13 Rich & Cheap Analysis - Risk Measures •GNR2013-122, CI •GNR2013-122, PA KDS Proprietary Information •14 Rich & Chip Analysis - Cash Flow Holding •Hedging and risk management strategy is based on the analysis of the projected cash flow. KDS Proprietary Information •15 Structured Assets Valuation Engine SAVE integrates the following 5 subsystems: Three-factor LIBOR market interest rate model Prepayment, Delinquency, Default & Loss model Stochastic macro-econometric model Structured Cashflow Waterfalls (SCW) model Monte Carlo Simulations (MCS) OAS model 16 Structured Assets Valuation Engine Post-Issuance Extraction Translation Loading Scripting Waterfall VOD MCS_OAS Econ Scenarios Pool Optimization POD DOD Bond Sizing Rosetta Stone Hedging RA Bond Sizing Pricing/Valuation Issuance Pipeline Management Slice & Dice RA Loan Loss/Credit Model Pre-Issuance Surveillance Tax AssetDatabase 17 Collateral Data ETL Data Extraction, Transformation, and Loading Remittance PDF report -> flash reports 80 ABX deals, 80 PrimeX deals, 125 CBMX deals Custom defined deals remittance flash reports delivered real-time Agency prepayment flash reports delivered real-time Data Center Hosting on behalf of Clients: – Loan level data from LP, Intex, Lewtan – Loan level data from private firms 18 Collateral Data Management Slice and Dice Engine applied in Pooling, Optimization, and Surveillance Complete database for agency (FN, FH, GN) Pass-Through’s – Complete Loan Performance, Lewtan, and Intex loan level database for prepayment and default analysis: – – mapped to groups, bonds, and Intex, Lewtan ground groups Macro-Economic data integrated: HPI’s, unemployment, etc Time Series and Aging Curves: web-based GUI – – – Fully expanded Mega-pools, Giants, Platinum’s, STRIPs, CMO’s Roll rate analysis Various breakout analysis Portfolio feature: simple or with weights S-Curve: pre-defined or user-supplied rate incentives with lag-weights 19 SCW Deal Structuring Collateral CF Engine – Period based (amortization, scheduled payment/coupon, calendar, fee, OPT/ARM, Strips, Interest Reserve, Tax, etc..) Scripting Engine – Python based waterfall programming with Customizable and Modulated Script Command Call – Y/H/SEQ/ProRata/OC/Shifting-Interest – Credit Enhancement – – – – Bond/Pool Insurance Policies Surety Bond Guarantee Derivatives (SWAP, Cap/Floor) Reserve Account Triggers Modules – DLQ, Loss NAS/PAC/TAC RE-REMIC Pricing/Update/Payment Modes 20 SCW Deal Structuring Application – Valuation On-Demand MCS_OAS Econ Scenarios – Payment and performance surveillance & verification – Risk Management Market Risk Hedging MSR – REMIC (Projected) Tax 21 SCW Structuring Scripting Module SetDealParameters(('strike_rate', 5.05), ('index_name', 'LIBOR_1MO'), ('cuc_level_pct', 10), ('sen_enhance_threshold_pct', 40.20), ('stepdown_month', 37), ('oc_floor_pct', 0.50), ('oc_target_pct', 4.25), ('dlq_trigger_threashold_pct', 39.80), ('loss_trigger_threashold_pct', 1.35) # compute and swap flag and swap in/out amount SetSwap() SetTrancheParameters(('A1A','A1B','A2','A3','A4','A5') ('target_paydown_pct',59.80) ) # compute NEC SetNetMonthlyExcessCF() SetTrancheParameters('A1A', ('cuc_multiplier', 2), ('coupon_spread', 0.17) ) SetTrancheParameters('M1', ('cuc_multiplier', 1.5), ('coupon_spread', 0.30), ('target_paydown_pct',66.20) # set bond coupon based CUC multipliers and coupon spread SetCoupon(['A1A','A1B','A2','A3','A4','A5','M1','M2','M3','M4','M 5','M6','M7','M8','M9']) # compute stepdown flag from senior enhancement SetStepDown(['A1A','A1B','A2','A3','A4','A5']) # compute DLQ trigger SetDlqTrigger() # compute loss trigger SetLossTrigger() # compute sequential trigger SetSeqTrigger() # compute principal distributions SetPrincipalDistributions() 22 Example I: GNMA 2010-054 Diagram and KDS Waterfall Programming Total_Int = deal.COLL_TOTAL_INT •BK Total_Prin = deal.COLL_TOTAL_PRIN + deal.TRANCHE['BZ'].TR_ZACCRUAL PayIntDue(['BX','BZ', 'IA', 'IB', 'IC', 'ID', 'PA', 'PB', 'PC', 'PD'], AS=[], FROM= [Total_Int]) •PAC II •I A •PA •PA •IA # PAC I Principal Distribution PAC_I_AMT = GetTotalBalance('PA', 'PB', 'PC', 'PD') - deal.PAC_BAL['PACI'] PayPrin(['PA', 'IA'], FROM= [PAC_I_AMT , Total_Prin]) •PAC I •PC •IB •PAC II Principal •PAC I Principal PayPrin(['PB', 'IB'], FROM= [PAC_I_AMT , Total_Prin]) PayPrin(['PC', 'IC'], FROM= [PAC_I_AMT , Total_Prin]) PayPrin(['PD', 'ID'], FROM= [PAC_I_AMT , Total_Prin]) •IC # PAC II Principal Distribution PAC_II_AMT = GetTotalBalance('BK', 'PA', 'PB', 'PC', 'PD') - deal.PAC_BAL['PACII'] PayPrin(['BK'], FROM= [PAC_II_AMT , Total_Prin]) PayPrin(['PA', 'IA'], FROM= [PAC_II_AMT , Total_Prin]) •PD •ID PayPrin(['PB', 'IB'], FROM= [PAC_II_AMT , Total_Prin]) PayPrin(['PC', 'IC'], FROM= [PAC_II_AMT , Total_Prin]) PayPrin(['PD', 'ID'], FROM= [PAC_II_AMT , Total_Prin]) •BZ # BZ Allocation PayPrin(['BK'] , FROM = [Total_Prin]) •BK •Remaining Principal •Accretion •Principal •PB # Remaining Without Regarding to PACs •PA •IA PayPrin(['BK'] , FROM= [Total_Prin]) •PB •IB PayPrin(['PA', 'IA'] , FROM= [Total_Prin]) •PC •IC •PD •ID PayPrin(['PB', 'IB'] , FROM= [Total_Prin]) PayPrin(['PC', 'IC'] , FROM= [Total_Prin]) PayPrin(['PD', 'ID'] , FROM= [Total_Prin]) Example II: FNMA 07082 Structuring Diagram Dated Date: 07/01/2007 Settlement Date: 07/30/2007 Payment Date: 08/25/2007 Delay Day: 24 GroupII Principal Distribution GroupI Principal Dsitribution GroupIII Principal Distribution Until Planned Bal A VA 78.57% B Until Planned Bal GroupI Classes PK PL PB PC GourpII Classes KP LP 21.43% 85.71% 14.29% FC SC B Until Targeted Bal VA ZAaccrual Until VA/B payoff SQ FA SU ZA (Z) Until 0.0 Until 0.0 SQ GourpII Classes KP LP Until 0.0 GroupI Classes PK PL PB PC SQ MACR Recombination Classes (RCR) PA PM SA 24 Example III: JP MORGAN MORTGAGE TRUST 2007-CH3 Closing Date 5/15/2007 Collateral Type – Subprime Home Equity Capital Structure: – Overcollateralization – SEN/MEZZ/JUN Y Structure – Net SWAP cover OC Deficiency, Interest Shortfall, Realized Loss, NetWAC Carryover – Cross-Collateralization Triggers in – – – – Enhancement Delinquency Cumulative Loss Sequential Trigger OC and Subs Test 25 Example IV: NEW CENTURY HEL TRUST 2006-2 Closing Date 06/29/2006 Collateral – Subprime Home Equity Capital Structure: – Overcollateralization – SEN/JUN Sequential – Net SWAP cover OC Deficiency, Interest Shortfall, Realized Loss, NetWAC Carryover – Cross-Collateralization (on Group I & I Notes Sen) Triggers in – – – – Enhancement Delinquency Cumulative Loss Sequential Trigger OC and Subs Test 26 RMBS Valuation Models Prepay, Default, Severity, Delinquency – Modeling Approach Delinquency Transitions Prepay/Default Competing Risks – Agency and Non-Agency Collateral: Prime Jumbo Alt-A Option ARM Subprime HELOC Fannie/Freddie FHA/VA 27 TBA Analytics – – – – De Facto Standard Pool pricing Worst to Delivery Slice-and-Dice and Priding Absolute value: Yield to Maturity, OAS, Total Return Relative value: return vs. other securities (corporate bonds, swaps, agency debt, etc.), vs. sector benchmark (TBA, current coupon, index), vs. intra-sector alternatives (vs. Gold, vs. GN, vs. 15-year, etc.) – Historical rich/cheap analysis: time series mean reversion 28 CMBS Valuation Models Prepay, Default, Timing of Default, Severity, Extension – Key Inputs: Property Type, LTV, DSCR, NOI, Underwriting, MSA, Cap Rate, Refi Threshold, Call Protection, Tenant Attributes – Subsystems APOLLO: NOI Generator, Scenario/Monte Carlo Simulation HELIOS: Loan Level Prepay/Default Generator Market Calibration – CMBX, TRX – Conversion from TRX to OAS 29 •LARGE •REAL ESTATE DATA •For each CMBS deal in the portfolio, the underlying loans and properties are identified and passed into the loan-level analysis and pricing engine. CMBS PORTFOLIO •DYNAMIC CMBS MODEL •Ex) MSA: New York •OFFICE •Property Analyzer breaks down collateral pools into property types by MSA •RETAIL •MULTI-FAMILY •Property and tenant database tracks and monitors high-risk loans and tenants. •Data source containing latest and historical performance data for CMBS/CRE properties •MARKET DATA •Baseline NOI time-series projected per property type •NOI PROJECTION •INDUSTRIAL •NOI PROJECTION •HEALTH-CARE •NOI PROJECTION •SELF-STORAGE •NOI PROJECTION •DYNAMIC CALIBRATION : Defines initial NOI surface for all properties in portfolio, and utilizes the Baseline NOI feed to define Specific (Absolute) NOI Projections for all properties in portfolio. •DISCOUNT MARGIN: Pricing spreads are determined based on CMBS deal performance, default behavior, and market data. •BASE SEVERITY •BASE SEVERITY •HOTEL •BASE SEVERITY •INDUSTRIAL •BASE SEVERITY •HEALTH-CARE •BASE SEVERITY •SELF-STORAGE •BASE SEVERITY •Loan-level NOI projections translated into loan-level Implied DSCR Projections •PRICING MODEL: Utilizes information and projections from component models to setup pricing scenarios for each CMBS deal in the portfolio, and interacts with KDS cash flow engine to produce price/cash flow projections for the corresponding CMBS tranches. •LEGEND •Main Input/Output File •External data source •KDS low intensity computing module •KDS moderate intensity computing module •KDS high intensity computing module •External pricing engine •Baseline projections/scalars, generated in-house or obtained via subscription (e.g. PPR) •BASE SEVERITY •RETAIL •NOI PROJECTION •NOI PROJECTION •OFFICE •MULTI-FAMILY •NOI PROJECTION •HOTEL •PREPAYMENT MODEL: Prepayment projection curves generated for all loans, based on property details (e.g. type, geography, call protection, etc.) •Baseline SEVERITY (given default) values projected per property type •CMBS PRICING REPORT KDS Proprietary Information 30 •CREDIT MODEL: Projects loan-level defaults, timing of defaults and liquidations, and loss-given-defaults, based on DSCR curves and baseline severities provided. Extensions, work-outs, and loanmodifications are also projected at this step. Manual overrides on defined parameters are possible. •KDS Cashflow Model Index Derivative Analytics Complete coverage in PRIMEX, ABX, CMBX, MBX/IOS/PO Calculate Market Implied Spread(OAS) based on Economic Scenarios and 3000 paths Monte Carlo Simulation Monte Carlo Simulation based risk measures in – – – – – – – Mode Skewness (Pearson's first) Mean Sigma Var 1-dVar Risk Score Daily and Weekly Reports based on Market Close Price 31 Agency Index Daily Report 32 TBA Daily Report 33 Prepay/Default/Severity Overview Projects monthly prepayment, delinquency, default and loss severity rates of new (at purchase) or seasoned (portfolio) loans. Takes into account of loan, borrower and collateral risk characteristics as well as macro economic variables on rates and home prices. Based on a hybrid delinquency transition rate and competing risks survivorship model where the prepay & default risk parameters are estimated from historical loan-level data. 34 Prepay/Default/Severity Overview Based on a proprietary highly non-linear nonparametric methodology with parameters estimated from non-agency loan-level data. Prepay and default are jointly estimated in a competing risk framework. 35 Prepay/Default/Severity Overview Model Inputs – Collateral type (e.g., alt-a, non-conforming balance, no prepay penalty). – Age, Note rate, Mortgage rates, Yield curve slope. – Home price (zip/CBSA-level if used at loan-level, otherwise stateor national-level) – Unemployment rate – Loan size, Documentation, Occupancy, Purpose, State, FICO, LTV, Channel. – Delinquency history and status (past due, bankruptcy, REO) – Negative amortization limit (recast) for option ARM – Modification type, size, and timing – Servicer 36 Prepay/Default/Severity Overview Model Outputs – Prepayment and default probabilities at each time step – Delinquency rates – Loss severity 37 Derivative Hedging On-Demand All forward curves are generated using proprietary nonparametric calibration technique that is guaranteed with maximum smoothness The forward curves are consider “trading quality” and “battle tested” have been by various trading desks for trades in excess of $1T worth of derivatives These should not be compared with forward curves from Bloomberg where they are only for informational purposes, or with many leading Asset/Liability software venders where the forward curves are usually used for monthly portfolio valuation (i.e., accounting purposes) rather than for trading purposes 38 Derivative Hedging On-Demand All flavors of interest rate swaps (including swaps with embedded options, both European and Bermudan) Swaptions (European, Bermudan and/or custom) LIBOR, CMS/CMT caps/floors CMM (constant maturity mortgage) swaps, FRAs (forward rate agreements), and swaptions (this includes our mortgage current model) Mortgage options Treasury note/bond futures and options Other customized derivatives 39 Derivative Hedging On-Demand 40 Equity On-Demand • Hedge-funds and investment banks that develop these type of tools to capture mispricings in equity derivatives markets keep them proprietary and do not share with them anyone. • The KDS option model and trading platform, also known as EOD, tackles all of these challenges and makes the proper tools available for traders so that they can profit from mispricings everyday! • The EOD allows traders to wake up in the morning with trading strategies that are indifferent to whether the market is bullish or bearish. Instead, they can focus on profiting using high probabilities in both up and down markets. This eliminates trading based on human emotion, which is the cause for most financial mistakes! • The Bullish vs. Bearish paradigm was created by the Technical Model mindset. Using volatility based analysis and high-probability trading means that the so-called “Bullish” or “Bearish” trade is no longer meaningful, and profitability does not depend on the direction of the market! • In this presentation, we will cover the different parts of the EOD system, describe how to use the system, and most importantly show how to execute trading strategies and make money consistently using the EOD. 41 EOD Option Pricing EOD platform utilizes advanced option pricing models. Based on trader’s “Risk Appetite,” he or she can use EOD to create trading strategies such as: – High Probability Mean Reversion strategies – Time decay (Theta) strategies – Spread based strategies (vertical/calendar spreads) – Underlying ETF buy/sell strategies “Risk Appetite” is based on confidence levels, or probability ranges, that are used for mean-reversion trades and also allow traders to tweak their risk tolerance using precise metrics. For example, a confidence level gives the trader ability to know the exact probability that a buyer of an option will exercise, at any given time. This is very important for HPMR trades! EOD successfully eliminates subjectivity from options trading by specifying strike price targets and buy/sell thresholds. 42 Pricing Methodologies Our underlying option models use advanced techniques from quantum physics and nonlinear mathematics, applied to financial analysis and trading. The models are applied to finance using fundamental laws of physics and mathematics, and utilize coordinate transformations in Space, Time, Force, Momentum, and Energy. Since option prices have diffusion properties, we can use systems of partial differential equations to model price behavior. We model the randomness observed in prices and volatilities by using stochastic frameworks such as Variance Gamma and Long-Range Stochastic Volatility (discussed later). Since solutions to these stochastic and highly nonlinear system of PDE’s are unsolvable via analytical methods, we must utilize massive parallel-processing computational power to run extremely large numbers of scenarios at infinitesimal (intra-day) time steps. 43 Pricing Methodologies REAL-TIME probability distributions of option prices, as well as REALTIME option chains pricing solutions, are calculated through evaluating the large number of intra-day scenarios. Unlike EOD, most option pricing models in the market-place use BlackScholes-Merton (BSM) framework as the underlying theory. There are many problems with using this BSM framework to do real-time options trading, most importantly: – – – – Probability distributions do not have FAT-TAILS as observed in the markets. Prices utilize a single volatility, which is clearly not true in reality. BSM framework does not have ability to imply a Volatility Skew or Volatility Smile. BSM framework was created for European-style options which can only be exercised at maturity. In reality, most ETFs that trade on exchanges are American-style, which can be exercised any time. – There is no ability to capture and quantify JUMPS (both up and down) in prices of options and underlying Equity Index/ETF. – BSM Equations were designed by professors (not traders) to allow “analytical solutions” for their convenience. In practice, we don’t care about elegant “analytical solutions” if the prices are WRONG! 44 American Short-Range Jump Diffusion Model: 100K Pricing Paths for IWM (iShares Russell 2000 Index) 45 Volatility Surface Smile: TZA vs. TNA • The volatility surface of the inverse 3x leverage TZA compared against the positive 3x leverage TNA indicates an inverse relationship. • However, the relationship is not precisely inverse due to the fact that both TZA and TNA are separate tradable securities, with unique option chain dynamics. • Therefore, we are able to capture not only the intrinsic inverse relationship, but also the individual supply/demand dynamics for each ETF. Volatility of Volatility (VXX Surface) American Short-Range Jump Diffusion Model In addition to Stochastic Volatility, the VGSV based framework enables us to price options using American exercisability. The American exercise feature utilizes a Least-Squares Monte Carlo (LSM) methodology which iteratively quantifies the probability of exercise PER timestep. VGSV framework also allows us to model the Jump up and Jump down impact under a Short-Range (i.e. intra-day) time period. Jump processes are modeled via the sampling of gamma and exponential distribution variates over a large number of paths and trajectories. For these reasons, we also refer to our option pricing model as the American Short-Range Jump diffusion (ASD) model. For the long-range (20+ days) option chains, we utilize the America Long-Range Jump diffusion (ALD) model which allows us to capture the longer term convergence properties of option pricing. 48 Fat-Tail Distributions EOD uses proprietary methods based around Short-Range Variance Gamma stochastic volatility (VGSV) and Long-Range stochastic volatility models. Within our framework, we are able to produce probability distributions that accurately capture the FAT-TAILS (left and right) implied by the market. Since most of the mispricings (i.e. Money-Making Opportunities) exist near the TAILS of the distribution (OTM options), precisely capturing fat-tails is VERY IMPORTANT! The REAL-TIME display of the probability distributions (“Histograms”) allows traders to not only see the fat-tails, but also track how the area under the fattails is shifting in REAL-TIME. Having this fat-tail probability distribution framework allows us to effectively DISCOVER the market inefficiencies throughout the trading day. 49 Interest Rate Model Three-Factor BGM/Libor Market Model (LMM) Forward curve calibrated to a daily mixture of Libor, Euro$ Futures, Euro$ futures options, and intermediate to long term swap rates Volatility calibrated to daily end-of-market swaption volatility surface The “battle tested” forward curves for trading & valuations are guaranteed with the maximum smoothness. 50 Libor Market Model Also known as the BGM (Brace-Gatare-Musiela) model. It is the “modern” implementation of the well-known Heath-Jarrow-Morton Model Considered the “second-generation” of interest rate models. The “first-generation” being the Hull-White family of short-rate models 51 Key Features of Libor Market Model Model construction is automatically arbitrage free. No need for yield curve calibration. Avoided the problem of convergence when calibrating most type of short rate models. Intuitive volatility and correlation calibration. Can accommodate arbitrary number of factors in a straight forward way. 52 Libor Market Model vs. Traditional Short Rate Models No need to iteratively search for a set of calibration parameters in order to match the yield curve. E.g., Hull-White model is calibrated to the firstderivative of the forward curve, which can be oscillatory sometimes. LMM does not suffer from this problem. For most short-rate models, rates would have to be sampled from some simple lattice (either binomial or trinomial). I.e., rates can only go up or down, but not from a normal distribution. 53 Libor Market Model vs. Traditional Short Rate Models Can sample from short rate model equations using normal distribution, but since the model parameters are calibrated on the lattice, “equation sampling” will not be arbitrage free, i.e, incorrect in most cases. No need for mean-reversion parameter in LMM, which has no true economic meaning (see “Interest Rate Option Models”, R. Rebonato). Therefore no need to calibrate the model to this artificial parameter. Volatility calibration is more intuitive in LMM vs. short rate models (see papers by the author of LMM, and John Hull). 54 Libor Market Model vs. Traditional Short Rate Models Multifactor version of the short rate models are limited to two-factor models. Calibrating these models to market instruments are extremely difficult (see “Interest Rate Option Models”, R. Rebonato). Because of this difficulty, virtually no software vendors offers this functionality except a select few such as Numerix (expensive…) and some Wall Street trading desks. QRM has a “place holder” for a two-factor model, but I was told it’s essentially useless and no client uses it. 55 Libor Market Model vs. Traditional Short Rate Models LMM/HJM models have been adopted by more Wall Street MBS trading desks recently, as they “upgrade” from the older short rate models. Quote from J. Hull’s book (the author of most short-rate models): “because they are heavily path dependent, mortgage-backed securities usually have to be valued using Monte Carlo simulation. These are therefore ideal candidates for applications of the HJM model and Libor market models”. 56 Competitor I Interest Rate Models Single-Factor Black-Karasinski (BK) Single-Factor Hull-White (HW) Better suited for lattice-based pricing applications, such as Bermudan Swaptions, CMS cap/floors, etc. ; issues with arbitragefree in a simulation setting because parameters are calibrated on the lattice but Monte Carlo rates are generated from the stochastic equation (see J Hull book on this issue). Volatility and mean-reversion parameters in Competitor I’s versions of BK & HW are “user inputs”, instead of optimized to fit a series of market option prices (see extensive discussion on this issue in J. Hull’s book); this could problematic because the mean reversion parameter does not have intuitive true economic meaning. Interest rate models are not truly arbitrage-free by design (this is separate from the sampling error issue of Monte Carlo), and the mean-reversion and volatility parameters are not calibrated to market vols. 57 Competitor II Interest Rate Models Prepayment model is not up to standard. The turnover and refi components are not handled well. The refi component is part of prepayment model deals with interest rate sensitivity. Burnout/season component part of the model is also not handled well. Duration result is off from market expectation. This most likely has to do with its prepayment model and it's interest rate model. OAS/interest rate model uses its own version of the lognormal model. It is quite different than either the HJM class of the HULL White class of models. Besides prepayment models, duration calculation can also be sensitive to one's implementation of the OAS/interest rate model. 58 Interest Rate Model Matching discount bond prices from simulated paths and those from the yield curve. Expect some small mismatch due to the nature of Monte Carlo sampling A three-factor model, better pricing for RMBS/REMIC/CMO type of assets that depends on both long and short rates. 59 Interest Rate Model KDS’s LMM can be calibrated to most volatility term structure shapes Typical volatility calibration Interest rate paths from KDS’s interest rate model are completely “open” - can be tested by any user on any given day for pricing any benchmark or custom fixed income assets. 60 Interest Rate Model Summary Interest rate modeling is at the center of interest rate risk management. Sophisticated interest rate risk management demands state-of-the art interest rate models. Libor Market/HJM models are current state-of-the art and ideally suited for pricing and risk managing mortgage securities. 61 Home Price Model Mean-reverting Targets long-term HPA using a historical “mean”. Mean-reversion parameters tunable for faster or slower reversion. HPA Projection 250 HPA (%) 200 150 100 50 0 1989 1994 1999 2004 2009 2014 2019 62 Personal Income & HPI Forecast 63 HPA Scenarios 64 Unemployment Scenarios 65 Technology KDS Proprietary Information •66 UBX Architecture •FTPServer Server •FTP •ClientBrowser/Apps Browser •Client •Internet, Intranet, Extranet, IP Packet IP Network, •Internet, Intranet, Extranet, Packet •OLTP Database Network, •Optical Network •Optical Network •N •1 •1 •Super •SysGovernor •Web •Web Engine •SysGovernor •Index ••1 •Data Set •Existing •ComputeNode •Index •1 •8 CPU •64GB RAM •SSD Cache •HAV CPU Node ••1 •1 •8 CPU •64GB RAM •SSD Cache •Data Set •1 •Network Attached HAS: High Availability Storage Complex Engine •Existing •Existing •ComputeNode •HAS: N+3 redundancy, SSD buffer, High Availability Storage •N •1 •HAV CPU Node •ComputeNode •Index ••1 •1 •8 CPU •64GB RAM •SSD Cache •Data Set •CPU + GPU •64GB RAM •SSD•CPU Cache+ GPU •64GB RAM •SSD Cache •Fiberoptic Switching Complex •Gigbit Ethernet Switch •1 •HAV CPU Node •GPU Enhanced Compute Nodes •HAV: High-Availability Virtualization based on Xen Cloud Platform (XCP) KDS Proprietary Information 67 UBX Advantage Index: Index all the data by UBX sorter. – Index take only 40% storage – Randomly search abilities – Easy maintenance Parallel Model: several parallel optimization methods can be carried on in UBX: – Local Optimization: NLIN, SLSQP, LSBFGS, COBYLA, BOBYQA, etc – Global Optimization: DIRECT, CRS, StoGO, ISRES, etc – Used to calibrate the QED Pricing Model Flexibility: new business rules and definitions can be implemented within minutes using high performance scripting languages Efficiently take advantage of open source module KDS Proprietary Information •68 UBX Advantage High-speed data acquisition: Use core system function to reduce unnecessary cost. High Volume Data: Overlapping I/O tasks with computation tasks. Parallelism: Large datasets are partitioned into smaller portions and processed in parallel on multiple computational nodes. Expansibility: As a result of the inherent parallelism of our model, as more nodes are added, larger datasets can be processed at reduced time. Streaming: Multivariate solution is done in a scan. KDS Proprietary Information 69 UBX Advantage SPMD: Single Process Multiple Data, data mining, VOD MPMD: Multiple Process Multiple Data, model calibration, MCS Virtual fields: fields can be mathematical formula to save storage and extend the usage Table Join: table can be joined to re-use existing fields Table can be combined horizontally and vertically to extend the usage KDS Proprietary Information 70 UBX Advantage Virtual Tables: tables can be combined to form virtual logical tables •Combined Table •Vertical File: •UBFile1 Horizontal File: •UBFile1 •UBFile2 •UBFileN •UBFile2 •UBFileN KDS Proprietary Information 71 •Processing Time UBX: The Sweet Spot •Traditional System •UBX Advantage •UBX •Data Storage/Analysis Complexity For larger datasets and complex situations, UBX advantage is obvious, compared with traditional data processing system. 72 KDS Proprietary Information Nonlinear Least Square Regression Benchmark Performance 800 •Traditional System 700 •UBX Time in seconds 600 500 400 300 200 100 0 0 5,000,000 10,000,000 15,000,000 20,000,000 25,000,000 Num be r of r e cor ds No. of Record Date Size (MB) 45,889 Number Node Nonlinear Cycles Time (s) 3.15 1 6 9 5 4,254,142 09/00 - 08/01 896.61 12 6 8 288 8,243,801 09/99 – 08/01 1,737.48 24 6 8 353 12,606,708 09/98 – 08/01 2,657.02 36 6 8 456 19,953,262 09/96 – 08/01 4,205.39 60 6 8 682 24,621,612 09/94 – 12/00 5,189.30 83 6 8 709 KDS Proprietary Information 73 Embedded System Crossbar Switch •PCI Interface 74 Field Programmable Gate Array(FPGA) •64 bit 66 MHz PCI KDS Proprietary Information 64 GB ECC DRAM Very Long Word Instruction SRAM Embedded System Pipeline Case: calculation of cash flow void OAS2Price::GetCF() { double c0 = loan_.cash0_, c1; double sBal; for(int i = 1; i <= pIntRatePaths_->nTimes_; ++i) { int WAM = pIntRatePaths_->nTimes_ - (i - 1); sBal = c0 * (1. - pow(1. + loan_.coupon_ / 1200., 1 - WAM)) / (1. - pow(1. + loan_.coupon_ / 1200., - WAM)); c1 = (1. - .01 * GetSMM(i)) * sBal; 1,641 clock ticks for each Iteration of the for loop pCashFlow_[i - 1] = c1 * loan_.sfee_ / 1200.; c0 = c1; } } 75 The time quanta for the FPGA is equal to 10 clocks of a 1GHZ processor. For this example the embedded system is about 160 times faster then the C++ open environment. The rate of completed calculations is independent of the analysis complexity and the data size. KDS Proprietary Information Embedded System Pipeline Case: calculation of cash flow C++ void OAS2Price::GetCF() { double c0 = loan_.cash0_, c1; double sBal; for(int i = 1; i <= pIntRatePaths_->nTimes_; ++i) { int WAM = pIntRatePaths_->nTimes_ - (i - 1); sBal = c0 * (1. - pow(1. + loan_.coupon_ / 1200., 1 - WAM)) / (1. - pow(1. + loan_.coupon_ / 1200., - WAM)); c1 = (1. - .01 * GetSMM(i)) * sBal; pCashFlow_[i - 1] = c1 * loan_.sfee_ / 1200.; c0 = c1; } WAM } c b Loan_Coupon a WAM f g d e sBAL calculation as quanta a = loan_.coupon_ / 1200 b=1+a c = 1 – WAM d = bc e=1–d f = 1+ a g = -WAM h = fg k=1–h m=e/k sBal = c0 * m •c0 m h sBAL k Each quanta is implemented in FPGA reconfigurable resources. 76 KDS Proprietary Information Embedded System Pipeline Case: calculation of cash flow CLOCK TICK 1 Loan_Coupon WAM a b WAM f WAM CLOCK TICK 2 Loan_Coupon a b WAM f CLOCK TICK 3 Loan_Coupon WAM a b WAM f c g c g c g d e m h d e c0 m h d KDS Proprietary Information sBAL k e c0 m h sBAL k k At each time tick the data moves to the next calculation. A data calculation is completed for each time tick. 77 c0 sBAL Competitive Expertise KDS Proprietary Information •78 Expertise on Marketable Securities • Marketable securities • • • • U.S. agency mortgage backed securities (Fannie, Freddie, Ginnie) Non agency mortgage backed securities (private label) Collateralized debt obligations (CDOs) Securitization of assets • Valuation on demand platform • • • • Massive database on U.S. securities Real time feed of market information Advanced interest rate model and forward curve Multiple variable credit and prepayment models KDS Proprietary Information 79 Expertise on Consumer Lending • Lending products • Residential mortgage loans • Consumer and small business credit card loans • Peer-to-peer installation loans • Extensive in-depth management experience • • • • • • • Marketing solicitation Credit underwriting Portfolio management Collection strategies Basel II implementation Credit risk scoring Credit bureau management KDS Proprietary Information 80 Expertise on Derivative Valuation • Derivative instruments • • • • • • Swap European Swaption American Swaption Floating rate bond Fixed rate bond Cap floor • Valuation on demand platform • • • • Advanced interest rate model Market calibrated forward curve New quantum field pricing model Counterparty Valuation Adjustment (CVA) KDS Proprietary Information 81