On a completely scalable platform, Kamakura's market risk solution provides total integration of credit risk, market risk, asset and liability management, and performance measurement. 

Kamakura's market valuation solution dates from 1993, when we introduced the world's first option-adjusted valuation package featuring a full suite of term structure model analytics and fixed income options technology. 

The quality of the numbers produced by a risk management system is the single most important measure of the system's ability to help organizations improve shareholder value. Kamakura boasts a 100% installation success rate and has never failed to produce high quality risk management results for Kamakura clients using client data on the client site.

Kamakura Market Valuation

Many risk management experts rely on valuation and stress testing in addition to value at risk techniques. Thus accurate market values are even more critical than they are in a VAR context. Kamakura's valuation technology is unique in the following ways:

• Seven VaR Models with user defined confidence levels
• Default adjusted multi-period VaR methods
• Seven yield curve smoothing methods including an unpublished maximum smoothness credit spread technology
• A wide variety of fixed income data input formats 
• Interest rate probability distributions for any rate level and time horizon 
• Automated forward rate curve generation 
• Fixed and floating rate instrument valuation  
• All common principal amortization conventions  
• Arbitrary interest and principal payment schedules  
• Multiple day count conventions  
• Payment in advance or arrears  
• Customizable holiday tables  
• All common derivatives (see Kamakura software overview for partial list)  
• CMO valuation via a link to the Index libraries  
• Complex mathematical functions for floating rate indices, including lags and moving averages, minimum of two rates, maximum of two rates, etc.  
• Five term structure models  
• Fixed length and variable length lattice technology for options valuation  
• User control over number of steps in lattices  
• Multi-factor credit model capability  
• Common Monte Carlo simulation engine for valuation, VAR and net income simulation  
• Three methods of prepayment analysis (transactions cost approach, prepayment table approach and prepayment function approach)  
• Arbitrary definition of risk factors  
• Stress testing with respect to any risk factor  
• Transaction-level processing  
• Proprietary published valuation formula for non-maturity deposit valuation  
• Built in linear and non-linear regression  
• Reduced form credit risk and default models by Robert Jarrow  
• Exact default adjusted valuation
• Back testing

Kamakura Value-At-Risk

When it comes to value-at-risk, Kamakura Risk Manager (KRM) includes three popular methodologies:

• Variance-covariance (matrix) value-at-risk, as popularized by JP Morgan
• Historical value-at-risk, using historical market values 
• Full option-adjusted, credit adjusted Monte Carlo simulation driven value-at-risk

 Variance-Covariance Value-At-Risk

• KRM can generate a variance-covariance matrix internally from historical risk factor data
• KRM can also acquire third-party sources of variance-covariance matrix data on a fully automated basis using standard data mapping tools 
• KRM can process risk factor shifts of any user-desired magnitude 
• KRM allows rich web-based or Excel-based reporting using KRM's standard third party reporting tool Crystal Reports 
• KRM supports a single enterprise-wide portfolio VAR run, while simultaneously producing fully consistent VAR for one or more "cuts" of the portfolio by organizational unit, customer category, product category 
• KRM processes the entire portfolio on a transaction by transaction basis, even if it includes millions of transactions

Historical Value-At-Risk

• KRM produces historical value-at-risk measures both for use in their own right and as a back-testing methodology
• KRM can produce historical volatilities and covariances automatically in KRM format for processing 
• KRM supports a single enterprise-wide portfolio VAR run, while simultaneously producing fully consistent VAR for one or more "cuts" of the portfolio by organizational unit, customer category, product category 
• KRM processes the entire portfolio on a transaction by transaction basis, even if it includes millions of transactions

Credit-adjusted and Option-adjusted Value-At-Risk in KRM

Market participants are well aware that both variance-covariance VAR and historical VAR grossly underestimate the risk in almost every portfolio. There are many common sense and analytical reasons why this is true:

• Portfolio value changes are not normally distributed. As bankers know, lenders have almost no "upside" and and 100% downside. Historical and variance-covariance VAR ignore this simple truth, assuming symmetrical gains and losses
• Both historical and variance-covariance VAR methods ignore cash flows between now and the value at risk date 
• Both methods ignore embedded optionality and other financial options that may be exercisable between now and the value at risk date. When value at risk is being used to determine loan loss reserves, capital adequacy, and internal capital allocations, the value at risk date is commonly many months in advance. That leads to a value at risk calculation on the portfolio the firm has now, not the portfolio the firm will have on the value at risk date 
• Both methods tend to ignore the risk of default, modeling at best variations in credit spreads. This ignores the fact that a default the day before maturity can still result in the loss of 20 or 30% of the principal on the bond. Moving credit spread in a simulation from 5% to 30% on the day before maturity only reduces the bond's present value (5% coupon, 100 principal) from 104.99 to 104.92. Explicitly modeling the loss given default would recognize the real possibility of a major reduction in value from default. Historical value at risk and variance co-variance value at risk ignore this risk and dramatically understate credit risk 
• Both methods suffer from "survival bias." They use historical data on the risk of counterparties that the firm has now, none of which (by definition) would be in the portfolio if they had gone bankrupt during the historical period - the "special asset division" has the bad credits! Again, this results in the dramatic understatement of measured risk

Kamakura Risk Manager has been carefully designed to avoid these pitfalls. Full credit-adjusted and options-adjusted Monte Carlo driven VAR is the only methodology for doing this successfully.

Advantages of KRM's Option-adjusted and Credit-adjusted Value-At-Risk

Kamakura Risk Manager has a number of very significant advantages which we believe result in the most accurate value at risk technology in the industry:

• KRM features explicit transaction by transaction valuation in every scenario using derivatives analytics by Dr. Robert Jarrow.
• KRM explicitly models all cash flows between now and the value at risk date and reinvests them in user-specified investment vehicles 
• KRM explicitly models the impact of default, not just movements in credit spreads, using state of the art credit models developed by Dr. Robert Jarrow and others. 
• KRM's random number generation is completely consistent and fully integrated whether the purpose is valuation and value at risk or net income and balance sheet projection on a financial accounting basis. The risk factor engine is the same. 
• Kamakura can provide credit risk and risk factor data in a KRM compatible format via Kamakura Risk Information Services 
• Kamakura can provide full value at risk processing via Kamakura On-Line Processing Services