Aprecia Technical Documents

Here is the associated technical article published in the Nikkei Financial Daily about Aprecia

Financila frontier on Sep 13th, 1995 Nikkei Financial Daily

new approach on swap management
smooth intergradation from standard to inside with usage of sensitivity

There are standard approach and internal model approach according to market risk measurement of BIS 2 regulation. But there are problems using both of them.It is unweighted to shift standard instumentation to internal model approach as an realistic reciprocation.Hatori Marshall Co.Ltd developed bucketing approach management system according to actual sensitivity measurement which can measure swap market risk efficiently.

It is necessary to reconfigure organizaition along with considerable system investor in order to meet both qualitative and quantitative criteria if accurate risk management is practiced and internal model sholuld be adopted as what the large financial institutions is doing.On the other hand, adoption of standard instumental approach from the view of convenience is barkward from the view of competitie conservation. The most realistic answer is that at first take standard instrumental approach facing BIS2 regulation and then sequencially shift from risk category to internal model after necessory know-how is builtup and systemacllyadapted in situation that both approaches are accompanied by risk.

conversion under regulation

It is essential to introduce standard instrumental approach program then shift to internal model to impliment the theory.As carefully described in the regulation, at first superficial notional should be transformed to substantial notional if they are different.
Complex programming is necessory in case that there are irregular swaps or enormous positions to combine with long/short positions as the common instrumental approch in addition that it is difficult to shift it to internal model later even if it takes time and trouble for grogramming.
Basel Committee admitts the bucketing approach that comprehend plural swap positions as the amount of the basic zero-coupon bond after distributing each cahsflow of the swap to nearest 2 grid-points inside the frame of standard instrumental approach.
It is easy to calculate the equity captial with high speed even if when handling swaps which can not be dealed with easily by common standard approach if the bucketing program is developed.Then it can be smoothly transformed to internal model because VAR can be calculated from the sensitivity of zero-coupon bond,valatility and correlation matrix etc.

Practice of Bucketingr║/b>
1.calculation of grid point DF
Picture 1 is mark-to-market diagram of the cashfloww 1,000,000( called CFn)between the 2 grid points of Aug 28th and Dec 289th and the trade date is 5th Oct.
DF of Aug 28th's grid point can be worked out from 1month interest rate and DF of DEC 28th can be worked out from 5 months interest rate if today is July 28th.We suppose here that 1 month (31 days)interest rate is 3% and 5 month(153 days) interest rate is 2%, DF can be worked as formular1.
fomular 1 ]

2.Acalculation of NPV and the interpolation of DF
DFn at 5th Oct can be got by interpolation of DF1 and DF2,PV of the CFn can be caculated by formular 2.

formula 2]

3.Bcalculation of sensitivity
As CFn is between the grid point of 28th Aug and 28th Dec, PV is effected by the change of interest rates and that can be comprehended by intuition.We call the the PV's movement caused by interest rate interest sensitivity.
Interest rate rises to 3.1% if 1 month interest is increased by 10 basis point and DF of Aug 28th will change.Of course PV of CFn will change to what formular 3 is like because of the movement of DFn. In other words, interest sensitivity comes as in formular 4 with the 10bp increase of 1month interest rate. With the same procedure -128.34835947 yen is the interest sensitivity against 10bp increase of 5months interest rate.

[formula3 ]

[ formula 4]

4.decompsition of cash flows
The attibute of CFn is described by Pic 5 from the calculation result of step1 to step 2.

[ formula 5]

reciprocation to market transactions

Consider CFn=CF1+CF2 on condition that it caters to the two attributes of formular 5 even if CFn is broken into CF1 or CF2.CFn has a sensitivity to the particular grid point because the decomposed cahsFlow such as CF1 & CF2 locate on the grid point although CFn has 2 proportional sensitivities to the movement of 1month rate and 5 month rate as CFn is between Aug 28th grid point and Dec.28th grid point CFn.
So, it comes with formula.

[ formula 6]

From the above we conclude that CFn can be distributed to CF1 and CF2. CF1= 688,524.59 Yen
CF2 = 311,475.41

Then equity captital can be worked out by inputting bucketed cashflow as PV of zero-coupon bont into ladder, the standard instrumental approach.
Hatori Marshall call the procedrue from step1 to step2 bucketing under measured sensitivity. Regular periods are chozen with transactons processed in the market although the decision of the grid point depends on users.

The above bucketing approach is diffrent from the common bucketing which is conducted according to the proportion of cashflow's generated date to the whole term without measuring sensitivity at first.
Hatori Marshall developed Apprecia, a risk management system collaborated with COSMAC CO.LTD, taking this approach of measuring sensitivity with the consideration of system performance and developing cost.
It takes enormors time to conduct term-proportion bucketing because swap portfolio are registered by large amount of trades and there can be hundreds of thousand of orders.
Apreccia configure out DF as functions of yield curve and take the specification that DF interlock the shift of grid point on the curve,achiving a high performance of bucketing according to measuring sensitivity, and the easy expansion on option's gamma risk instrument program with little modificatoin .

Reality beyond text

Although BIS2 tends to focus attention on VAR ,there are lots of problems which should be solved such as instability of correlation matrix in matrix method or abnormal distribution of historical valotility.It is easy for everyone to develop a program ignoring those problems and only carrying out VAR measurement according text, but the significant VAR instrument can not be achieved.
It is a realistic choose by construction with sophistic approach within the frame of standard instrument before the accomplishment of quantitative VAR instrument on target.