| Chapter (Issue) |
Description |
| 2012 |
| Time Dependent Mean Reversion (p. 21) |
2012 Q2
A specific extended Hull-White model with time dependent mean reversion rate is presented and evaluated in different variants. The new model is capable of improving the simultaneous fit to several swaption strips significantly, and it even seems to do so with retained stability and without over-fitting the parameters. |
| Pricing Curves for Mortgage Bonds (p. 21) |
2012 Q1
In the last theme of SPV we described the use of two curves in valuation of floating rate bonds - a pricing curve for discounting and a fixing curve for calculating reset rates. Attention was mostly given to how the fixing curve was estimated and used. In this theme we will focus on the choice of the pricing curve and see what impact it has on calculations of Danish fixed-rate mortgage-backed bonds. We will construct four curves - SWAP, government, segment, and OIS - and see the impact on loan yield spreads, option-adjusted spreads, and model prices. |
| 2011 |
| Estimation of fixing rate curves (p. 21) |
2011 Q4
Since the beginning of the debt crisis back in 2008 focus has shifted towards using more than a single yield curve when valuating floating rate bonds. This is the subject of the theme. First a yield curve is chosen to discount future payments. This yield curve is called the pricing curve and should reflect the risk of the bond issuer. A second yield curve is used to match the interest rates used when fixing the floating rate payments, e.g. EURIBOR3M, EURIBOR6M, etc. This curve is called the fixing curve. As we observe that credit risk has entered deposit rates during the debt crises a fixing curve should be constructed for each deposit rate. We look at and compare estimation procedures for pricing and fixing curves. Finally, we con-struct an example showing the impact of the different curves in valuation of a floating rate bond. |
| Modelling of High-coupon Bonds (p.21) |
2011 Q3
The theme investigates fair value pricing for high coupon bonds (8% - 12%). The analysis is commenced using two index based models within the DMBS calculation framework; continuing the work from the theme in SPV 09Q2. The DMBS model is found to be overly sensitive to highly burned out bonds which is true for almost all of the bonds in this segment, leaving almost identical bonds with quite different fair values. In an effort to handle this issue the analysis is extended by simplifying the model and introducing two constant prepayment models based on the implied prepayment rate and another OA Spread index respectively. In order to achieve stability in fair values across time and to obtain a model that fits observed quotes, experiments with subdivisions of coupon rate segments to improve behavior are conducted. This results in another problem as most of the high coupon bonds are not only illiquid; they also seem to jump between bid and ask quotes. As a consequence, carefulness is needed when creating subdivisions of the bonds used for averaging. The conclusion is that it is not unambiguous which model has the best performance. However, the new models seem to produce more stable results, and the results are more comparable for bonds with similar characteristics. |
| Estimating Fixed-to-Float Prepayments (p.21) |
2011 Q2
In the theme of this release we try to estimate a prepayment model, which has been extended to model Fixed-to-Float prepayments. We investigate two explaining variables; the slop of the yield curve and the difference between the coupon rate and a short interest rate. We introduce a Threshold level to the new variables to get more control over where and when we want the model to exhibit Fixed-to-Float prepayment. The estimation sample consisting of the last 9 years of prepayment observations do unfortunately not hold enough information to distinguish Fixed-to-Float prepayment from traditional prepayments. This is mainly due to a very high correlation between the new variables and the NPVGain variable in the estimation sample. We do still believe the model is a good explanation of the prepayment behavior of the borrowers, but we are unable to estimate usable parameter values from the prepayment history. |
| Modeling Fixed-to-Float Prepayments (p.23) |
2011 Q1
As was the case in the previous release of SPV, the subject of the theme of this release is prepayments originating from borrowers switching from fixed rate loans to adjustable rate loans, referred to as Fixed-to-Float prepayments. Continuing the data analysis of the previous release we make a preliminary extension to the current prepayment model in order to incorporate Fixed-to-Float prepayment. The proposed extension to the prepayment model uses information on the slope of the yield curve to forecast Fixed-to-Float prepayment. The resulting prepayment model gives us a clear indication on how Fixed-to-Float prepayment can be incorporated in the existing model. However, further investigations are needed before the model can be included among the standard SPV models. |
| 2010 |
| Data survey on Fixed-to-float prepayments (p.21) |
2010 Q4
The subject of the theme is prepayments originating from borrowers switching from fixed rate loans to adjustable rate loans, referred to as Fixed-to-Float prepayment. We analyze data on total outstanding nominal amounts in different loan types to identify when and why borrowers switch loan types. We find that borrowers do indeed switch between loan types and that the primary reason is increases in the immediate payment reduction associated with the switch. We hope to use this knowledge to extend the current prepayment model to include Fixed-to-Float prepayment. |
Analysis of Option Adjusted Spreads (p.21) |
2010 Q3
In the theme of this release we analyse the recent decrease in the weighted spread calculated by the Danish FSA (Finanstilsynet) in the DMBS model. The considerable decrease is primarily caused by the DMBS model tending to overestimate prepayment rates. It seems as if the model has difficulties explaining the quite low levels of actual prepayment rates despite large gains. We introduce a new model with a different specification of the prepayment function in order to incorporate a more ag-gressive burnout effect into the model. The conclusion is that prepayment rates generated in the new model are generally more in line with actual prepayments. Considering a two year period the new model generates higher and more stable option adjusted spreads and option adjusted key figures than the current model. |
The preliminary Redemption Model (p.21) |
2010 Q2
This theme proposes an extension of the current preliminary redemption model. Once a week the Danish mortgage institutions publish the preliminary redemptions due for prepayment on the next unpublished payment date. These data are utilised by the preliminary redemption model in RIO to improve the forecasting abilities of the mortgage model. Data indicates that the arrival pattern of preliminary redemptions does not only depend on time, but also on the level of prepayment. The relative prepayment intensity, which is currently only time-dependent, is therefore extended to de-pend on the level of prepayment as well. The current and extended models are estimated historically with one and five years rolling windows of estimation data, and their forecasting abilities are com-pared. It is concluded that one year of estimation data results in quite unstable parameter estimates over time. Furthermore, the extended model is slightly better at forecasting the prepayment rate on the next unpublished payment date. |
Prepayment Modelling for Interest Only Bonds (p.23) |
2010 Q1
In the theme of this release we address the subject of prepayment modelling for interest only bonds. Our first analysis shows that the DMBS model performs equally well for bonds with and without interest only periods when performance is measured by the difference between the estimated and actual prepayment rates. The same conclusion is reached if we estimate the DMBS model based on an extended sample where we include 55 interest only bonds. In the next analysis we extend the prepayment function with a dummy variable for delayed amortization. The resulting model is termed DMBSext. We find that this model slightly outperforms the DMBS model for bonds with interest only periods while the two models perform equally well for the remaining bonds. A similar conclusion is reached in the last analysis where we replace the maturity variable with a non-callable duration instead of extending the prepayment function with an extra variable. |
| 2009 |
Dividing Mortgage Loans by Bond Type (p.21) | 2009 Q4
In the theme of this release we revise the procedure used to assess the development in the amounts of mortgage loans within different bond types. The objective is to gen-erate a procedure for assessing the nominal amount on a daily basis. The basis for the calculations is the nominal outstanding amounts delivered daily by OMX. On each trade day we calculate the change in the outstanding amount for each bond. Positive changes are categorised as issues and negative changes as withdrawals. Summing across bonds this leads to a simple assessment of the development in the different bond types. However, the resulting time series are not very precise as they display several spikes and jags. We analyse these issues one at a time and outline ways to han-dle them. This leads to a number of data corrections and imposing all of these we end up having very smooth time series for all bond types. |
Revision of the Prepayment Model for Bonds with Semi-Annual Payments (p.21) | 2009 Q3
In the theme of this release we evaluate the performance of the model for bonds with semi-annual payments, M0. This model differs from the other SPV models in that it uses a simplified version of the prepayment function which does not incorporate the delivery option or any bur-nout measure. Moreover, the model is estimated based on a sample comprised solely of semi-annual bonds. The model has been included as one of the standard SPV models since January 2009.We start by introducing an alternative version of the M1 model which is estimated on the basis of a larger estimation sample than the regular M0 model. We term this model M0_Ext. A com-parison of this model to the regular M0 model leads to the conclusion that the regular M0 model slightly outperforms the extended. Moreover, we find that the best prepayment estimates from the M0 model are obtained by assuming that all loans are concentrated in the group consisting of the smallest loans – group 12. Next the M0 model is compared to the DMBS model. As for the M0 model we establish that the best results for DMBS model are obtained by concentrating all loans in loan group 12. Compar-ing the single loan group versions of the two models we reach the following conclusion. Both models perform equally well for the in-sample bonds, i.e. the bond that are in the estimation sample of the M0 model, while the DMBS model outperforms the M0 model out-of-sample. |
Spread Models (p.19) | 2009 Q2
In the theme of this release we adress the subject of fair value pricing. We introduce and analyze four different models which may be used as basis for fair value pricing. Performance is measured by average price variation and average difference between model and market prices. Our conclusion is that a model using a coupon/cap rate dependent spread performs well when we calculate the spreads on basis of a sample comprised of liquid bonds. We also obtain quite good results with a model using the same sample but where we further divide the bonds by end year. |
Analysis of prepayment Function Specifications (p.23) | 2009 Q1
In the theme of this release of SPV we introduce three modifications to the DMBS model set-up. Since none of the examinations result in significant differences in the estimated prepayment rates or key figures we conclude that the current specification is quite robust. However, we do find that it might be beneficial to drop the weighting in connection with the estimation, as this gives rise to slightly better results for the bonds with the smallest weights/nominals without compromising the results for the remaining bonds. Moreover, we also obtain reasonable results if we estimate both the mean and standard deviation of the logit distribution. |
| 2008 | 2008 |
Mean Reverting Loan Yield Spreads (p.21) | 2008 Q4
The theme of this release introduces an extension of the pricing model, in which the current loan spread reverts to a long term level. The extension is motivated by the high prepayment rates estimated by the DMBS model of the 7% coupon bonds, while no prepayment have been observed in the market. The mismatch is primarily due to the recent large increase in the loan spread, which the DMBS model does not directly incor-porate. The mean reverting loan spread extension has the desirable effect of bringing the models on track for the 7% coupons bonds with almost no change to the segment of lower coupon bonds. The theme discusses the calculation of loan spreads and describes the extension of the pricing model. The theme additionally in-cludes calculations on a sample of benchmark bonds and a detailed analysis of the key figure properties of the 7% coupon bonds in four different model setups |
Selecting Data for Estimation of Danish Yield Curves (p.21) | 2008 Q3
In the theme of this SPV release we take a look at the estimation of Danish yield curves with main focus on the selection of input data. The theme is divided into three chapters. In the first chapter we investigate the effects of using overnight index swaps (OIS) in the estimation of the swap based interest rate curve instead of deposits. We find that the OIS based swap curve gives rise to more stable bond key-figures. In the second chapter alternative quote sources for the estimation of the government yield curve are investigated. This study is highly relevant since there has been a reduction in the number of daily prices from OMX during the past months. In the last chapter we try to locate the best time during a trade date to snap quotes for yield curve estimation. |
Prepayment Modelling for Newly Opened Series (p.25) | 2008 Q2
In the theme of this release of SPV we take a look at modeling the composition of borrowers for newly opened bond series. This information is typically published for the first time a few weeks after the opening of the bond series. As a consequence an assumption must be applied in order to use debtor information in the prepayment modeling. One of the methods which we investigate is the use of the debtor information from the corresponding closed series. For instance we use the infor-mation from the 5-38 series in the modeling of the 5-41 series. We also take look at a single group model which is estimated to a market sample of bonds without considering the grouping in loan sizes. Moreover we investigate several models based on weighted averages of debtor information stemming from different market samples grouped by coupon, interest only period or open/closed series. Finally, we take a look at a model with debtor information based on a weighted average of the 10 series which have the highest issuance activity at the moment measured in number of new loans. The models are evaluated by comparing their option adjusted key figures to corresponding key figures calculated with the actual debtor information and by use of statistical tests. |
A Prepayment Function for Bonds with No Debtor Information (p.23) | 2008 Q1
In this release of SPV we have developed a prepayment model for bonds without published debtor information.
We start out by creating a sample consisting of such bonds which we term the Test sample. Besides this we also create another sample, termed the Reference sample, which is comprised of bonds with similar characteristics, but for which we do have debtor information.
Examination of the samples reveals that most of the bonds are small burned out series with prepay-ments that are hard to model. Not surprisingly we find that the usual DMBS prepayment function does not work properly for these bonds, and thus we define a simplified version of it which we term DMBSred.
Using this prepayment function and the bonds from the Reference sample, we estimate two models, one where we use the debtor information, Debtor, and one where we do not, NoDebtor. The Debtor estimation results in three group level prepayment functions while the NoDebtor estimation only result in one prepayment function which thus apply for the whole series. Based on the results from these estimations we find that a one loan group model seems appropriate for the bonds in the Reference sample.
Next we test each of our four estimated prepayment functions on the bonds in the Test sample. We conclude that it is the prepayment function for loan group 12, the group consisting of the smallest loans, that has the best performance. We term this model Debtor(12).
In the last section we use the Debtor(12) model to calculate risk measures. As expected inclusion of a prepayment function leads to option-adjusted durations that are lower than the Fischer Weil dura-tions, especially for the longer high coupon bonds. |
| 2007 | 2007 |
The Preliminary Redemption Model (p.27) | 2007 Q4
The theme of the October 2007 SPV features a new preliminary redemption model. Preliminary redemptions are published once a week by the mortgage institutions and are used in RIO for forecasting of actual redemptions at the next unpublished term date. Currently we use a model containing two time-dependent functions. The model is not very intuitive, as it is hard to determine exactly how large an impact the preliminary redemption observation has on the final prepayment rate estimate. The new model is built around one time-dependent function alone. This makes the model very intuitive and easy to interpret, which is exemplified in the theme. The current and new models are estimated based on five years of data, and afterwards the estimated models are compared in several different ways. It turns out that the new model performs quite well, and as a consequence it has been implemented in RIO. |
ASW and OAS - Close, But Not Equal (p.21) | 2007 Q3
In the theme of this release of SPV we look at the difference between the Option Adjusted Spread (OAS) and the Asset Swap Spread (ASW) both theoretically and in practice. The OAS is introduced in connection with a pricing model for a mortgage bond, whereas the ASW is defined in the context of an asset swap package, which in its simplest form is a transaction where the investor receives the mortgage bond and a swap. In the swap, the investor swaps the coupon payment of the bond for a variable rate plus a spread, the ASW. After fixing concepts we look at the effects of embedded options in relation to the asset swap package, and we do a case-study of the actual difference between the OAS and ASW for a capped floater over a period of more than a year. The conclusion is that if the OAS is of moderate size, and if care is paid to closely replicate the capped floater in the construction of the asset swap package, the difference between the two measures is small. |
LIBOR Market Models (p.21) | 2007 Q2
In the theme of this release of SPV, we introduce LIBOR market models. A LIBOR market model has a rich correlation specification, and allows for modelling of volatility smiles. These attributes may be useful in the pricing of mortgage bonds with rather complex coupon structures. We present a simple LIBOR market model with a volatility skew for caps and a parametric correlation structure. The model is calibrated to OTM caps and ATM caps and swaptions, and is then used to price a non-callable capped floater. |
Group Level Prepayment Rates (p.21) | 2007 Q1
In the theme of this release we examine the non-trivial procedure used to generate prepayment rates on borrower group level. These rates are used in the estimation of the parameters for the prepay-ment functions, and it is thus important that they are as accurate as possible. We examine the essential data problems connected with generating group level prepayment rates, and try to explain how we cope with these. The explanations are in many cases supported by exam-ples which we hope will help visualize both the problems and the solutions. |
| 2006 | 2006 |
Revision of the Preliminary Redemption Model (p.21) | 2006 Q4
In the theme of this release we make a revision of the preliminary redemption model. We end up with three alternatives to the current model. Each of the alternative models is quite intuitive, and they all have a good performance considering our 5 year estimation window. However, only one of the alternative models also performs well in the 2nd quarter 2006. |
Performance Attribution: Valuing the Preliminary Redemption model (p.21) | 2006 Q3
In the theme of this release we revise an earlier theme concerning Fixed Income Performance Attribution (FIPA). We especially focus on how FIPA can be used to value the use of a First Prepay Model.We look at FIPA in relatively general terms, but we also give a description of how the FIPA set-up that we use in the analysis is constructed. Moreover we give a short introduction to the First Prepay Model. Finally we cooment on the results. |
Group Level Poolfactors (p.21) | 2006 Q2
In the theme of this release we revise the theme from the 03Q2 release concerning the use of group level poolfactors instead of the series level poolfactor. The motivation for this has been that lately we have experienced some problems with the burnout function especially for the group consisting of the larger loans. We introduce a plausible definition of group level poolfactors and look at some examples. After this we estimate a model similar to the DMBS model with the exception being that this model, M9, uses group level poolfactors. We examine the resulting burnout functions and compare them to the burnout functions from the DMBS model. Moreover we comment on the estimation results relatively to the results from the DMBS model. In order to obtain a full comparison of the two models we also include some valuation results. |
Seasonality and seasoning in the prepayment function (p.66) | 2006 Q1
The theme of this release deals with two different extensions to the prepayment function for the DMBS model. First we examine whether prepayment seem to be seasonality dependent and second we examine whether there seem to be any connection between the age of the bond and prepayment. This last concept is in the litterature known as seasoning. |
| 2005 | 2005 |
Calibration of one factor term structure models (p.4) | 2005 Q4
The theme of this release deals with calibration of term structure models with focus on calibrating to different samples. We consider CIR and Vasicek models with different volatility specifications and we examine calibration to two samples, one consisting of ATM caps and swaptions and one consisting of caps only, both ATM and OTM. |
Vega: Factor Analysis and Pricing Effects (p.15) | 2005 Q3
The theme of this release discusses Vega calculations in the context of mortgage backed securities. Vega measures the price sensitivity in change in the volatility. This quantity is important, especially for the new generation of capped floaters and float-to-fixed loans which contains caps and triggers. |
| Asset Swaps (p. 19) | 2005 Q2
The theme in this issue of SPV is asset swaps. In the light of the introduction of the FlexGaranti and RenteMax products, we try to explain and analyze one possible asset swap strategy used to repackage these products. In addition to this, the "fair" asset swap spread is esitmated and compared using a calibrated interest rate termstructure model. |
| Market Effects From the Introduction of Float-to-Fix Type Loans (p. 23) | 2005 Q1
In this chapter the effect from the introduction of the new types of loans are treated. The news and subsequent announcements from competitors made market participants expect large prepayments on fixed rate mortgage backed securities and following their prices declined. |
Pricing ARMs With Cap and Float-to-Fix Features
(p. 15) | 2005 Q1
Various details of the Adjustable Rate Mortgage Bonds introduced in the Danish market are discussed in this issue. |
| 2004 | 2004 |
Performance Attribution
(p. 15) | 2004 Q4
This theme concerns performance attribution which is a tool used for analysing why a given return, positive or negative, has been genereated. The analysis decomposes return into casues of changes in volatility, changes in interest rates, or simply the passage of time. |
Computationally Feasible Modelling of Burnout
(p. 19) | 2004 Q3
The theme in this issue concerns the efficiency in modelling burnout used in the model. The concept is to introduce an artificial group of idle borrowers that models burnout in model. This enables the calculations to be done without introducing path dependency which increases the calculation time. |
Hedging Performance using Factor Duration
(p. 13) | 2004 Q2
This theme concerns the performance of a hedging strategy based on factor durations where the hedge portfolio is a set of par swaps. We examine realized monthly returns on the mortgages and their hedge portfolios. |
Empirical Duration
(p. 19) | 2004 Q1
In this chapter we examine the relation between empirical and model durations. We propose three possible reasons for the upward bias of the model duration and by a clinical experiment we find that the presence of negative convexity in MBBs is most likely not a significant reason, while the main cause could be that the actual yield curve changes are not parallel as assumed when calculating OA durations. |
| 2003 | 2003 |
Refinancing Bonds
(p. 17) | 2003 Q4
The typical piece of advice that mortgagors receive from mortgage credit institutions is that prepayment is beneficial when it is possible to issue a new mortgage with a coupon rate 2 percent lower than the original at a price above 95. If this piece of advice is followed we should include information on the refinancing bond into the modelling of the prepayment behavior. |
A Preview of the New DMBS Model
(p. 19) | 2003 Q3
A preview of the DMBS model that will be launched in the spring 2004. The new model includes: New delivery option, new swap curve, CIR model is used instead of the BDT model, state dependent burnout and inclusion of data on preliminary redemptions. |
Group Level Poolfactors
(p. 15) | 2003 Q2
It is evident that as some groups prepay faster, the poolfactor in these groups will be lower, in turn making prepayments in the future less likely. The series poolfactor does not capture this phenomena. |
The Implied Gain Factor
(p. 23) | 2003 Q2
This note considers a completely new way of merging an external prepayment rate model and the prepayment model inside a mortgage backed security valuation model. More specifically this is another way of addressing the problem of forcing the first prepayment rate in the mortgage valuation model to match a given aggregate prepayment rate. In the last release we discussed some problems related to correcting for model residuals by operating outside the prepayment function. For example, doing the correction directly on prepayment rates will result in prepayments that are not between 0 and 1 for many interest rate states. The basic idea here is to make the correction on one of the primary explanatory variables instead of the prepayment rate itself. |
Scaling of Group Level CPR
(p. 19) | 2003 Q1
In this chapter the first results of a change in the engine for generating group level prepayments are presented. Specifically, we analyze how the generated group level prepayments can be modified in such a way as to yield a series level prepayment identical to the observed prepayment. At first, this seems to be a natural requirement, but due to the timing and definition errors (see the Technical Document chapter 3) present in Danish mortgage data, this cannot be ensured. |
Fixing of prepayments
(p. 29) | 2003 Q1
The question is how to incorporate information about the aggregate prepayment rate for the next publication date in a way that does not alter the basic dynamics of the model, but still force the aggregate prepayment rate to match the observed. |
| 2002 | 2002 |
Swap curve revisited
(p. 17) | 2002 Q4
If bootstrapped yield curves are used in a finite difference setup the forward rates will not become smooth which causes problems in the calibration of the term structure model. In this chapter we discuss the estimation of a swap curve solving this problem. |
Calibration of The Term Structure Models
(p. 23) | 2002 Q4
In this chapter we consider the calibration of the CIR term structure model to volatility input. First, we compare two different parameterizations of the model. Secondly, we expand the sample of swaptions used in the calibration to include swaptions with longer time to expiry and longer underlying swaps. |
Pitfalls when integrating prepayment- and valuation models
(p. 33) | 2002 Q4
In this section we illustrate problems arising when an exogenous prepayment estimate is enforced on the next publication date in the valuation model. In particular it is standard to incorporate the information from CK93 as a forecast of the total prepayment rate. |
State Dependent option Adjusted Spreads
(p. 17) | 2002 Q3
In this section we present some preliminary results for a simple model for the development of option adjusted spreads. It is a fact that traditional option adjusted spreads (OAS) are correlated with the moneyness of the bond in a non-trivial way. |
Delivery option and approximate price
(p. 25) | 2002 Q3
Prior attempts have used either a binary or a logit model to determine if there was going to be prepayment and the results have been acceptable. Both of these models are based on the theoretical value in the focused node and this introduces an error which size so far has not been analyzed. The model for the delivery option introduced in this chapter is an attempt to quantify this error. |
Preliminary Redemption
(p. 15) | 2002 Q2
Together with the data on preliminary redemptions we investigate using the CPR dictated by the prepayment model to forecast the actual CPR. Furthermore we will make attempts to use the prepayment at the prior term date as an explanatory variable as well. |
First Year Savings
(p. 31) | 2002 Q2
In short, for a given bond we define FYS as the first year payment (FYP) for this bond minus the FYP of a refinancing bond. With this variable we try to capture prepayments from borrowers focusing on short term profit. The section contains an outline of the calculation procedure. |
Poolfactors
(p. 17) | 2002 Q1
A known phenomenon of prepayment behavior is Burnout, which captures that prepayments tends to be lower if a series has been through periods of prepayments. All models estimated in the SPV service include a Burnout variable, the Poolfactor, which summarize the prepayment history of a given series. There is little doubt that the inclusion of the burnout variable improves the performance of the prepayment model, but there is no clear choice for how to define the variable. In the theme an alternative PoolFactor variable is presented and compared to the one used in prior SPV releases. |
| 2001 | 2001 |
Price dependent CPR correction
(p. 17) | 2001 Q4
we introduce a price dependent CPR correction (PDC). In the prior release of SPV we introduced the end notice price correction (ENPC) where the CPR we dictated to be zero of the end notice price was under 100. This methodology had the desired effect and greatly increased the model performance, especially for the DMBS model. It suffered from two problems however which are fixed in this release. |
Evaluation of the Constant PoolFactor Approximation
(p. 21) | 2001 Q4
In this chapter of SPV we quantify the approximation error in a theoretically consistent extension of the standard RIO pricing model. We start out by giving a short introduction to the method and gives a few examples on the model performance. |
Time Series of Calibrated Term Structure Models
(p. 31) | 2001 Q4
In the prior release of SPV we presented numerical results based on time series of various term structure models calibrated to swaption data. The results indicated some stability problems with respect to the calibration to swaption data. We have elaborated on this stability problem along two dimensions: The smoothness of the forward yield curve and the inclusion/exclusion of swaptions with very short swaption expiry. In this chapter we present updated calibration results and option adjusted measures for the following models of Black-Derman-Toy (BDT), Cox-Ingersoll-Ross (CIR) and Vasicek, and Black-Karasinski. |
Preliminary Redemption
(p. 14) | 2001 Q3
In this release of SPV we estimate a functional form which establishes a link between the observed preliminary redemptions and the debtor distribution, where the debtors are divided into homogeneous groups. |
Early Redemption data
(p. 13) | 2001 Q2
In the latest release of SPV we presented pricing results for models in which preliminary redemptions (publised in CK93) were incorporated. In order to use the preliminary redemptions a functional form linking the published preliminary redemptions with the actual prepayments were estimated. In this chapter we present results from further analysis of the relation between preliminary redemptions and actual published prepayments. |
Holding Period Return
(p. 23) | 2001 Q2
The theme compares realised returns to the returns predicted by our MBB model. |
Preliminary Redemption data
(p. 19) | 2001 Q1
This theme describes how information in CK93 can be used for pricing MBBs. We estimate a functional form for the relation between the preliminary early redemptions and the final early redemption. Furthermore we incorporate the information from CK93 in the price calculations by using a time-dependent average of the model estimate of CPR and the CPR predicted by the CK93. |
MBB Curve
(p. 26) | 2001 Q1
Instead of valuing the debt of the borrower using a spread over the default free term structure or using the swap curve we investigate the use of a term structure estimated on MBBs and swaps. |
| 2000 | 2000 |
General model update
(p. 14) | 2000 Q2
In this chapter we go through the new features that have been added to the SPV service since the last release. New explanatory variables have been analysed. Furthermore a swap yield curve has been introduced, in order to use the models that are not based on the government yield curve. Introduces a alternative definitions of the Gain Measure. |
| 1999 | 1999 |
| Definitions of OAD and OAS | 1999 Q4
The theme discusses the various definitions of Option Adjusted Duration and the use of Yield Spreads. |