The release of RIO 4.0 contains a large number of significant improvements to ScanRate’s valuation model for Danish mortgage backed securities. The changes increase the precision of pricing and return measures and they remove the need for some of the manual corrections done by RIO users today.
RIO 4.0 changes the technology used for term structure modeling. Traditionally RIO has been limited to a Black-Derman-Toy model implemented using binomial trees. In RIO 4.0 we use a finite difference implementation which allows the user to choose from a range of well known models like e.g. Hull & White (extended Vasicek), extended CIR and Black-Karansinsky. Unlike the BDT these models allows for explicit mean reversion, which improves the ability to fit observed volatility structures. The BDT model is still available as a simple special case. All term structure models may be calibrated to observed caps and swaptions quotes as described in Term structure modelling in RIO. [1]
Some of the pricing problems in the current RIO model - especially around the publication date - were caused by the inflexibility of the binomial implementation. With finite difference techniques we are able to match the exact cash flow dates, publication dates, specific levels of interest rates etc., and we have used this flexibility to address and solve a number of pricing problems.
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Price jump around the publication date |
The publication date changes the way an MBB bond is traded in that the buyer no longer participates in the drawing related to for the next term date. Depending on the size of the drawing this will affect the market price. In most cases for high coupon bonds we will expect an upward jump in price. Due to approximations caused by the current binomial implementation of RIO the price jump could deviate somewhat from the jump directly calculated by extracting the present value of the drawing. In the finite difference implementation the price will jump exactly as expected.
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| The chart shows end of period price as well as holding period return for Nykredit 8% 2031. Holding periods start at June 14, 2002, and ends at different dates in the interval from June 2002 to December 2003. The term structure model at the start date - a CIR term structure model calibrated to swaption volatilities - is used at all future periods. The prepayment model is the DMBS Q4, 2002 model. Note how the end-prices jump upwards, when we pass a publication date, while the holding period return accumulates smoothly. End-prices are shown less accrued interest, which explains the slightly irregular pattern around Christmas 2002. |
Similar improvements also affects the holding period returns, which now changes smoothly across the publication date reflecting the fact that a fully forecasted prepayment will have no effect on total return to the bond holder. |
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Improved interpolation of prepayments |
When return forecasts are needed across several cash flow dates the current implementation calculates expected prepayments at the first and last cash flow date while the intermediate prepayment rates are found by linear interpolation. In the new setup we interpolate yield curves at each intermediate publication date while the prepayment rates are found from the prepayment model. This lead to important improvements in the precision and consistency of these estimates across different scenarios. As an example it is thereby ensured, that ad hoc information related to the first prepayment forecast will not affect forecasts for later prepayment dates. |
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Automated updates of forecasted debtor distributions |
Due to large loans having higher prepayment rates the debtor distributions will change across time. The updated debtor distribution leads to new and typically higher option adjusted prices. In the current version these changes in debtor distributions could only be done manually, which is a large undertaking, when one needs to simulate different scenarios across multiple cash flow dates. In the return calculation employed by the new release the debtor distributions are automatically updated reflecting forecasted prepayment behaviour for each individual debtor group and each future cash flow date. The new release even allows the user to monitor the future development of each individual debtor distribution. |
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Interest rate sensitivity and user defined prepayment rates |
RIO user has the ability to define a forecast for the next prepayment date. However, the change from model generated to user defined prepayment rates previously introduced a bias in the interest rate sensitivity – even if the user fixed at a level corresponding to the model estimates. In the new version this bias is removed and the sensitivity measures will seamlessly reflect the user defined forecast. |
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A smooth model for the delivery option |
In the current version of RIO the delivery option is handled by assigning a zero prepayment rate when market prices are below par value. Unfortunately this may lead to somewhat unstable price behaviour around par. The new release uses a logistic function which ensures a smooth behaviour of price, prepayment rates and sensitivity measures. |
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Option adjusted cash flows |
For a list of MBBs a new function, rw_OACashFlow, quickly summarizes the present value of all future cash flow paths at each future cash flow date. This function has a number of uses, including giving an interesting display of the cash flow implication of different interest rate scenarios. |
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BoligX-lån |
We have developed a new pricing model for adjustable-rate mortgage loans with optional caps and floors. The function is designed to price the so-called Bolig-X loans from Totalkredit, but a range of similar loans could be analyzed as well. Prices and sensitivity measures may be compared directly to the similar values for standard callable MBBs. |
All improvements mentioned above are included in the current release of RIO 4.0. A new version of RIO Function Library for Excel (RFL) which supports the same range of models will become available March 2003. Please contact ScanRate if you would like to try the beta release of the upcoming RFL release. [2]
MBB pricing results from the RIO model will change with the introduction of the abovementioned improvements. The size and direction of these changes will differ across bonds.
Mortgage backed bonds are very complex and no model will replace the critical financial analyst. However, RIO now automatically handles a range of problems, which formerly called for careful manual adjustments by the analyst. This represents a totally new level of precision and forecast performance and it allows the analyst to concentrate on the essential issue – to quickly uncover and exploit differences in return and risk across mortgage bond series[3]
[1] Much more analysis and details on the implementation are given in two recent Ph.D. projects by Nicki Rasmussen and Mikkel Svenstrup. The Ph.D. projects have been sponsored by ScanRate and supervised by the Aarhus School of Business. The full text of each thesis may be downloaded from ScanRates web site. Two of the papers have been submitted to Social Science Research Network.
[2] A new technology makes it possible to run RIO spreadsheets across the web with data and calculations at a central server placed at Scanrate. RIO users will there be able to test the new functionality with no need for local installation.
[3] To ease the conversion to the new release RIO still supports every aspect of the current binomial model.