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Risk Kit
How do you value and hedge an interest rate sensitive security if you don't know which interest rate model you should use? How would you calibrate an interest rate model so that model parameters corresponds to the real world? The Inductive Solutions Risk Kit is a package of analytics and models for quantitative risk assessment simulations and interest rate model calibrations.
Risk Kit Features
- Different Spot and Forward Interest Rate Models
- A Fully Integrated Credit Model
- Advanced Simulation Technology for Fast Computation
- Incorporates A Full Spectrum of Fixed Income Securities
- Computes Hedge Ratios for Rate Changes in Interest, Exchange, and Credit
- Portfolio Replication Utilities
- Integrated Value at Risk Computations
Risk Kit Benefits
- Two Easy-to-Use Excel Workbooks for Simulation and Calibration
- Automatic Data Validation for Models and Product Specifications
- Multiple Models Provide Model Risk Assessment
- Flexible Computational Architecture
Risk Kit is a software system of fixed-income analytics for risk management and trading. It integrates interest rate risk, credit risk, and foreign exchange rate risk in an easy-to-use extensible platform.
Risk Kit computes prices, hedge parameters, and price histograms for bonds, swaps, caps and their derivatives.
Hedge parameters (delta, gamma, vega) for each product are computed for changes in interest rates, foreign exchange rates, default probabilities, and recovery rates.
Risk Kit supports several spot and forward interest rate models. The Risk Kit package has model calibration utilities that can derive model parameters from interest rate markets. The Risk Kit credit model is based on data that is available from ratings agencies.
Risk Kit computes Value at Risk over various time horizons in two ways. The first method uses hedge parameters and knowledge of unusually adverse interest rate, foreign exchange, and credit movements. The second method computes value at risk directly by building histograms from simulated price movements.
The engines underlying Risk Kit consists of several fast C/C++ libraries that interface to two Microsoft Excel workbooks. The QRA Workbook is responsible for pricing, hedging, Value at Risk, and rate simulations; the QES Workbook is responsible for model calibration.
Risk Kit implements 15 different multi-factor interest rate models for either spot or forward interest rates.
Multiple interest rate models are supported within a portfolio of multiple currencies. Risk Kit also provides its own generalized non-parametric multi-factor model, called QES. The QES model calibration engine uses multivariate kernel density estimation, principal components analysis, and polynomial regression techniques to estimate and provide efficient representations for drift, diffusion, and market at risk parameters.
Risk Kit can simulate versions of models due to Vasicek; Cox, Ingersoll, Ross; Black, Derman, Toy, Karasinski; Rendelman, Bartter; Chan, Karoly, Longstaff, Sanders; Sandmann, Sondermann; Heath, Jarrow, Morton; Goldys, Musiela, Sondermann.
Portfolios of products based on up to 10 different interest rates (corresponding to 10 currencies and exchange rates), having of at most 3 factors can be modeled by Risk Kit. (Depending on the platform, these can be extended.) The Risk Kit interest rate models and calibration techniques are discussed in more detail in
Risk Kit models the probability distribution for the time of default (given a particular credit rating) by a discrete time, time-homogeneous finite state space Markov chain, with transition probability table. Transition probabilities are available from credit agencies.
Up to 5 different transition probability tables, each having at most 18 credit ratings can be modeled by Risk Kit. The techniques used in integrating the credit model with the interest rate models are discussed in
Risk Kit uses simulation to generate an interest rate path given a particular interest rate model based on several pseudo random and quasi random algorithms.
Risk Kit implements versions of random number generators due to: L'Ecuyer; Knuth; Faure, Niederreiter; Sobol'-Niederreiter; Faure, Niederreiter, Tezuka; Richtmeyer.
Risk Kit can generate random vectors up to 5000 dimensions. The techniques used in generating random numbers are discussed in
- Bonds (fixed rate and floating rate)
- Different Credit Ratings
- Different Countries
- Basis (Actual/Actual, Actual/360, Actual/365)
- Coupon Rate (Monthly, Quarterly, Semi-Annual, Annual)
- Swaps (Fixed-Float, Fixed-Fixed, Float-Float, Float-Fixed)
- Different Credit Ratings for each Leg
- Different Countries for each Leg
- Caps
- Different Credit Ratings
- Different Countries
- Derivatives of the these securities including:
- Futures (or Forwards)
- Amortizing or Non-Amortizing Principal
- Options (path independent and path dependent)
Hedge ratios are determined by comparing the change in value under small changes in an underlying factor. Risk Kit determines hedge ratios for individual securities in portfolios (consisting of up to 85 fixed income products) as well as for portfolio itself. Risk Kit computes deltas, gammas, and vegas in different ways (See
One of the uses of hedge ratios is to replicate the behavior of one security by a replicating portfolio of other securities. The replicated behavior is defined in terms of hedge ratios. For example, if the portfolio is delta neutral, then the delta of the replicating portfolio is the same as the delta of the security. It has an interactive utility that builds and solves a system of relationships in order to derive the correct weights of a replicating portfolio. (See
Risk Kit computes VaR (see
The Risk Kit QRA Workbook provides an easy-to-use Excel-based tool for specifying and analyzing fixed income portfolios based on multi-currency, multi-credit, and multi-factor interest rate models. Workbooks and macros can be customized.
The QRA Workbook is controls execution and supports full input error checking and formatting for all fixed income products and model parameters. It interfaces transparently to the QRA simulation engine. The results of a Risk Kit simulation — security and portfolio prices, hedges, value at risk, histograms, charts, and portfolio replication weights — are saved in different worksheets in the Risk Kit QRA Workbook.
The Risk Kit QRA Workbook workbook includes the following spreadsheets:
Input for specifying the simulation, interest rate models, hedges, and currencies.
- Model
Spot Input for specifying parameters in multi-factor spot interest rate models. Forward Input for specifying parameters in multi-factor forward interest rate models. Credit Specifies credit ratings, transition probabilities, default preobabilities, and recovery rates. Portfolio Specifies portfolio of fixed income products (dates, cashflows, prices, etc.); on output displays prices, hedge ratios, and Value at Risk at current date. VAR Input specifications for Value at Risk computations; on output shows all VaR hedge ratios at the specified future time horizon. HISTO Shows over 30 Value at Risk statistics and histograms for all individual securities and the portfolio. Replicate An interactive worksheet calculator that computes replicating portfolios from hedge ratios. The Risk Kit QES Workbook provides an easy-to-use Excel-based tool for calibrating non-parametric multi-factor interest rate models. It helps specify files of interest rate data and other econometric factors and files containing bond returns. The results of a Risk Kit QES calibration can also be viewed with the QES Workbook.
The Risk Kit QES Workbook consists of one worksheet:
QES An interactive worksheet set of tools for calibrating interest rate models.
Risk Kit consists of 11 static libraries and 1 Microsoft Windows® 32-bit dynamic link library (DLL).
The Risk Kit QRA engine reads fixed-income product specifications and model parameters either from files or from the Risk Kit Microsoft Excel QRA Workbook. The results of a Risk Kit QRA simulation — security and portfolio prices, hedges, value at risk, histograms, charts, and portfolio replication weights — are also saved in different worksheets in the Risk Kit QRA Workbook.
The Risk Kit QES engine reads files consisting of interest rate data and other econometric factors and computes non-parametric multivariate representations of drifts, diffusions, and instantaneous covariances. It also reads files containing bond returns that it uses to compute the market price of risk for each factor. The results of a Risk Kit QES calibration are files that automatically interface to the QRA engine. The QES engine may also be controlled by the Risk Kit Microsoft Excel QES Workbook.
These libraries provide a full spectrum of fixed income analytics, interest rate and credit models, and statistical model calibration. See the RISK Kit Library Map for a brief summary of each library and a view on how each library is integrated into the Risk Kit system.
The libraries, implemented in C/C++, were designed to be portable to many platforms. The input files that the libraries require and the output files that they build for presenting their results are both summarized in the Risk Kit Directory Map. The Risk Kit QRA and QES Workbooks interface with these files.
(c) 2001 Inductive Solutions, Inc. All rights reserved.