As Josh Rosner, an expert on mortgage securities at Graham Fisher in New York noted in a research piece last week, the leverage used to put such securities pools together can amplify losses. For example, a 4 percent loss in a mortgage-backed security held by collateralized debt obligations can turn into almost a 40 percent loss to the holder of the C.D.O. itself.
Continue reading "Josh Rosner, Graham Fisher: leverage amplifies losses" »
Option Volatility & Pricing: Advanced Trading Strategies and Techniques, second edition (1994, Hardcover) by Sheldon Natenberg.
Natenberg not only takes great pains to explain the concept of volatility, in addition to other inputs into an option pricing model, but clearly shows that option pricing isn't the exact science many seem to believe, for the simple reason that we never know if our volatility estimate is correct.
A way to measure the effects of problems in the sub-prime mortgage
sector is to look at Credit Default Swaps (CDS). Remember that these
CDS contracts effectively work as a kind of insurance policy for banks
or other holders of bad mortgages. If the mortgage goes bad, then
the seller of the CDS must pay the bank for the lost mortgage payments
(alternatively ... if the mortgage stays good then the seller makes a lot
of money).
The index that measures the CDS market for home equity is called
the ABX.HE index. The sub-variation of this index that refers to risky
sub-prime loans is called the ABX.HE BBB index.
Markit's ABX catalog.
SIFMA, the Securities Industry and Financial Markets Association
represents the industry (eponymously)..
Born of the merger between The Securities Industry Association and
The Bond Market Association, SIFMA is a 'single powerful voice'.
Example publication: Mortgage Prepayment Projection Tables,
PSA Median, CPR average, etc.
More in Quant Finance, mortgage.
Interest Rate Risk - Models Similarities and differences
By comparing three different approaches to interest rate modelling, namely
* spot,
* forward and
* market models,
Han Lee of Commerzbank Securities finds that each has a different method
of constructing the effective volatility function, which determines its use.
Han H Lee is head of fixed-income derivatives research at Commerzbank
Securities in London.
See also Basel on Interest Rae risk, OCC / Treasury on interest rate risk,
and the FDIC on interest rate risk management.
epicureandealmaker on fat tails.
Derivatives: Transfering risk or reducing risk ?
Review Paper. Interest-rate term-structure pricing models: a review
Riccardo Rebonato
Interest-rate term structure modelling from the early short-rate-based
models to the current developments; use models for pricing complex
derivatives or for relative-value option trading. Therefore, relative-pricing
models are given a greater emphasis than equilibrium models.
The current state of modelling owes a lot to how models have
historically developed in the industry, and stresses the importance
of 'technological' developments (such as faster computers or more
efficient Monte Carlo techniques) in guiding the direction of theoretical
research.
The importance of the joint practices of vega hedging and daily
model-recalibration is analysed in detail. The relevance of market
incompleteness and of the possible informational inefficiency of
derivatives markets for calibration and pricing is also discussed.
Continue reading "Interest-rate term-structure pricing models: Riccardo Rebonato" »
Accrued Interest aka accruedint, smart about finance and economics.
Why Home Depot should borrow more.
Effect of Mortgage Refinancing on Interest-Rate Volatility
and not vice versa, by Duarte at UW.
Continue reading "Effect of Mortgage Refinancing on Interest-Rate Volatility, Duarte" »
AllAboutAlpha, example:
value premium, value pricing.
return = alpha + beta * (market return)
Nassim Nicholas Taleb, Fooled By Randomness (and black swans), with
bloglike-notebook.
Black Swan discussion: MeFi, Telergraph
Trilogy by Andrew Davidson and Co (AdCo)
1. Active Passive Decomposition
2. Prepay risk and option adjusted valuation concept
3. prOAS Valuation model with refinancing and turnover risk
TBMA Mortgage Prepayment Projection Tables: Questions and Answers
TBMA = The Bond Market Association.
Continue reading "TBMA Mortgage Prepayment Projection Tables" »
Hedging beyond duration and convexity.
By considering a representation using a Fourier-like harmonic,
empirical evidence that such a series provides our hedging
strategy on a mortgage-backed security (MBS) with the first
four principal components of yield curve.
An Empirical Test of a Two-Factor Mortgage Valuation Model:
How Much Do House Prices Matter?
Mortgage-backed securities, with their relative structural simplicity
and their lack of recovery rate uncertainty if default occurs, are
particularly suitable for developing and testing risky debt valuation
models. A two-factor structural mortgage pricing model in which
rational mortgage-holders endogenously choose when to prepay
and default subject to
i. explicit frictions (transaction costs) payable when terminating
their mortgages,
ii. exogenous background terminations, and
iii. a credit related impact of the loan-to-value ratio (LTV) on
prepayment.
We estimate the model using pool-level mortgage termination data
for Freddie Mac Participation Certificates, and find that the effect of
the house price factor on the results is both statistically and
economically significant. Out-of-sample estimates of MBS prices
produce option adjusted spreads of between 5 and 25 basis
points, well within quoted values for these securities.
SUGGESTED CITATION:
Chris Downing, Richard Stanton, and Nancy E. Wallace,
An Empirical Test of a Two-Factor Mortgage Valuation Model:
How Much Do House Prices Matter ? (link to 406 K, PDF file)
Chris Downing, Federal Reserve Board, Washington, DC
Richard Stanton, Haas School of Business, University of California, Berkeley
Nancy E. Wallace, Haas School of Business, University of California, Berkeley
Continue reading "Two-Factor Mortgage Valuation Model: How Much Do House Prices Matter?" »
An equilibrium valuation of fixed-rate mortgage contracts in
discrete time -- the mortgagor’s prepayment behavior
described by intensity process and with exogenous mortgage
rates, the value of the contract is derived in an explicit form
that can be interpreted as the principal balance plus the
value of a certain swap.
A nonlinear equation for what the mortgage rate in a
competitive market, and thus mortgage rates are endogenous
and depend upon the mortgagor’s prepayment behavior.
The complementary problem, where mortgage rates are
exogenous and the mortgagor seeks the optimal refinancing
strategy, is then solved via a Markov decision chain.
Finally, the equilibrium problem, where the mortgagor
is a representative agent in the economy who seeks the
optimal refinancing strategy and where the mortgage
rates are endogenous, is developed, solved, and analysed.
Mortgage Valuation and Optimal Refinancing, Stanley R. Pliska:
shorter and longer versions.
Continue reading "Mortgage Valuation and Optimal Refinancing, Pliska" »
Andrew Kalotay research on mortgage theory.
Valuation and optimal exercise of options, calling and refunding.
Previously: Option-Theoretic Prepayment Model for Mortgages by
Fabozzi , Kalotay and Yang.
Journal of Fized Income (JFI) by Institutional Investor.
Related:
Fixed Income Analysts Society (FIASI);
Fixed Income Securities: Tools for Today's Markets, Second Edition by Bruce Tuckman;
The Handbook of Fixed Income Securities, Edited by Frank Fabozzi.
Mortgage option prices behave quite differently than the prices of
options on underlying securities that do not exhibit significant
convexity. As a result, the intuition of many market participants
about option risk characteristics does not typically apply to
mortgage options.
The risk characteristics of these options: negative convexity of
the underlying mortgage and the positive gamma of the option
impact call option convexity in opposing directions. As a result,
call option convexity can be either positive or negative,
depending on the interest rate scenario and option specification.
On the other hand, a mortgage put option is always positively convex.
A quantitative understanding of these risk characteristics is critical
for money managers and broker/dealers who use mortgage options.
The Complexities of Mortgage Options
Prendergast, Joseph R.
THE JOURNAL OF FIXED INCOME
March 2003
Cointegration and Error Correction Mechanism Approaches:
Estimating a Capital Asset Pricing Model (CAPM) for House
Price Index Returns with SAS
Many researchers erroneously use the framework of linear
regression models to analyze time series data when predicting
changes over time or when extrapolating from present conditions
to future conditions. Caution is needed when interpreting the results
of these regression models. Granger and Newbold (1974) discovered
the existence of ‘spurious regressions’ that can occur when the
variables in a regression are nonstationary. While these regressions
appear to look good in terms of having a high R2 and significant
t-statistics, the results are meaningless. Both analysis and modeling
of time series data require knowledge about the mathematical model
of the process.
This paper introduces a methodology that utilizes the power
of the SAS DATA STEP, and PROC X12
and REG procedures. The DATA STEP uses the SAS LAG and
DIF functions to manipulate the data and create an additional
set of variables including Home Price Index Returns (HPI_R1), first
differenced, and lagged first differenced. PROC X12 seasonally
adjusts the time series. Resulting variables are manipulated
further (1) to create additional variables that are tested for
stationarity, (2) to develop a cointegration model, and (3) to
develop an error correction mechanism modeled to determine
the short-run deviations from long-run equilibrium. The relevancy
of each variable created in the data step to time series analysis is
discussed. Of particular interest is the coefficient of the error
correction term that can be modeled in an error correction mechanism
to determine the speed at which the series returns to equilibrium. The
main finding is that Metropolitan Statistical Areas (MSAs) with very
slow shortrun acceleration paths to the equilibrium have higher
returns and risk associated with house price returns than
MSAs with very rapid speed-of-adjustment coefficients.
-- Ismail Mohamed and Theresa R. DiVenti, PDF.
THE QUANT by Richard Booth: about the intersections of law, business, finance,
economics, and statistics. A law Professor.
Credit Risk Models II: Structural Models
July 2005
The structural approach for modelling credit risk considers both
the case of a single firm and the case with default dependences
between firms.
In the single firm case, we review the Merton (1974) model and
first passage models, based on Black & Cox (1976), examining
their main characteristics and extensions. The issue of estimating
structural models is also addressed, covering the different ways
proposed in the literature.
The issue of estimating structural models is also addressed,
covering the different ways proposed in the literature.
Secondly, we model default dependences among firms, which account
for two types of default correlations: cyclical default correlation
and contagion effects. We close with a brief mention of factor models.
The paper guides readers throught the literature, providing a
comprehensive list of references and, along the way, suggesting
different possible extensions for its future development.
[PDF]
Continue reading "Credit Risk Models II: Structural Models. (Elizalde)" »
Traditionally, economists have thought that big up-and-down
fluctuations in returns indicated risky investments, so many hedge
fund investors have hoped to see a pattern of smooth and even returns.
Andrew Lo quickly saw that lots of hedge funds were posting returns
that were just too smooth to be realistic. Digging deeper, he found
that funds with hard-to-appraise, illiquid investments - like real
estate or esoteric interest rate swaps - showed returns that were
particularly even. In those cases, he concluded, managers had no way
to measure their fluctuations, and simply assumed that their value was
going up steadily. The problem, unfortunately, is that those are
exactly the kinds of investments that can be subject to big losses in
a crisis. In 1998, investors retreated en masse from such investments.
Mr. Lo came to a disturbing conclusion: that smooth returns,
far from proving that hedge funds are safe, may be a warning
sign for the industry.
We model 1980--2003 rating and cohort specific cumulative default
frequencies. The data is decomposed into systematic and firm-specific
risk components. We have to cope with
(i) the shared exposure of each cohort and rating class to the same
systematic risk factor;
(ii) strongly non-Gaussian features of the individual time series;
(iii) possible dynamics of the unobserved common risk factor;
(iv) changing default probabilities per rating cohort over time
(ageing effects), and
(v) missing observations. We propose a non-Gaussian multivariate state
space model that simultaneously deals with all of this issues.
The model is estimated using importance sampling techniques.
Continue reading "Non-Gaussian Panel Time Series Model Decomposing Default Risk" »
Macroeconomic variables besides inflation and real activity drive the
yield curve in the framework of no-arbitrage affine term structure
models. We construct model-based projection of all the latent factors
onto the observable macro factors, which are real activity and
inflation.
As a result, the factors are decomposed into the “macro” part: a
linear function of the macro variables and their lags; and the truly
novel part which is orthogonal to the entire history of the macro
variables. We are able to relate the unexplained part of the short
rate to such measures of liquidity as the AAA credit spread and MZM
growth rate. The unexplained part of the slope is highly correlated
with the budget deficit.
Continue reading "Macroeconomic determinants of the yield curve" »
LMM Calibrator Estimation of volatility and correlation parameters in
the sense of (Brigo and Mercurio 2001), (Brigo and Morini 2004) and
(Brigo, Mercurio, and Morini 2005)
Alternative strategies and implementation issues, Thomas Weber, .
In 1976 Black and Cox proposed a structural model where an obligor
defaults when the value of its assets hits a certain barrier. In 2001
Zhou showed how the model can be extended to two obligors whose assets
are correlated. In this paper we show how the model can be extended to
a large number of different obligors. The correlations between the
assets of the obligors are determined by one or more factors.
We examine the dynamics for credit spreads implied by the model and
explore how the model price tranches of collateralized debt
obligations (CDOs). We compare the model with the widely used Gaussian
copula model of survival time and test how well the model fits market
data on the prices of CDO tranches.
We consider two extensions of the model. The first reflects empirical
research showing that default correlations are positively dependent on
default rates. The second reflects empirical research showing that
recovery rates are negatively dependent on default rates.
Continue reading "Correlation-dependent Credit Structural Model" »
The optimal recursive refinancing problem where a borrower minimizes
his lifetime mortgage costs by repeatedly refinancing when rates
drop. Key factors affecting the optimal decision are the cost of
refinancing and the possibility that the mortgagor may have to
refinance at a premium rate because of his credit.
The optimal recursive strategy often results in prepayment being
delayed significantly relative to traditional models. Furthermore,
mortgage values can exceed par by much more than the cost of
refinancing. Applying the recursive model to an extensive sample of
mortgage-backed security prices, we find that the implied credit
spreads that match these prices closely parallel borrowers’ actual
spreads at the origination of the mortgage. These results suggest
that optimal recursive models may provide a promising alternative
to the reduced-form prepayment models widely used in practice.
Francis A. Longstaff, Anderson School of Management.
Modelling of dependence is one of the most rucial issues in risk
management. Whereas classically independence was equated to linear
correlation, more recently, mainly due to extremal market moves,
the limitations of the linear correlation concept were strongly felt.
In order to stress test dependence in a financial or insurance
portfolio, the notion of copula offers a versatile tool.
* Basic properties of copulas,
* The underlying simulation and numerical issues,
* Use of copula based techniques in integrated risk management.
[*]
* Simulation of dependent risks,
* Statistical estimation of correlation in the static case,
* Dependence and correlation in a dynamically changing environment
* Extremes for heavy-tailed random vectors and multivariate stochastic processes.
Crucial to questions of risk aggregation, the project aims to
establish the fundamentals of dependence and correlation modelling.
Default models and asset pricing models at Enricode Giorgi's resource,
some with correlated defaults.
OAS measure of yield has been introduced to accurately price callable
bonds but is also used now as a measure for bullets' yield.
1. For bullets, it is more accurate than yield to maturity (YTM) as
a. You use implied forward rates instead of the yield to maturity as
a reinvestment rate.
b. You discount using the zero cpn curve instead of the YTM
Even more, you calibrate your forward rates so that the PV of yor
coupons match the market values.
2. For callable bonds and MBS, the YTM measure also assumes holding
till maturity which is obviously inaccurate so the OAS uses binomial
tree which takes into account the contingency of the future coupons.
The OAS is a constant spread to the whole discount curve you use
( e.g. treasury) which would result in a PV equal to the market price.
Kay Giesecke (of Cornell's School of Operations Research and Industrial Engineering)
research interests (Credit Risk, Default Correlation, Credit Derivatives, Systemic Risk)
match his research.
The Handbook of Fixed Income Securities
Edited by Frank Fabozzi
Hardcover: 1500 pages
Publisher: McGraw-Hill; 7 edition (April 1, 2005)
ISBN: 0071440992
Part 1. Background.
1. Overview of the Types and Features of Fixed Income Securities.
2. Risks Associated with Investing in Fixed Income Securities.
3. A Review of the Time Value of Money.
4. Bond Pricing and Return Measures.
5. Measuring Interest Rate Risk.
6. The Sturcture of Interest Rates.
7. Bond Market Indexes.
Part 2. Government and Private Debt Obligations.
8. U.S. Treasury and Agency Securities.
9. Municipal Bonds.
10. Private Money Market Instruments.
11. Corporate Bonds.
12. Medium-Term Notes.
13. Inflation-Indexed Bonds (Tips).
14. Floating-Rate Securities.
15. Nonconvertible Preferred Stock.
16. International Bond Markets and Instruments.
17. Brady Bonds.
18. Stable Value Investments.
Part 3. Credit Analysis.
19. Credit Analysis for Corporate Bonds.
20. Credit Considerations in Evaluating High-yield Bonds.
21. Investing in 11 and Other Distressed Companies.
22. Guidelines in the Credit Analysis of General Obligation and Revenue Municipal Bonds.
23. High-Yield Analysis of Emerging Markets Debt.
Part 4. Mortgage-Backed and Asset-Backed Securities.
24. Mortgages and Overview of Mortgage-Backed Securities.
25. Mortgage Pass-Throughs.
26. Collateralized Mortgage Obligations.
27. Nonagency CMOs.
28. Commercial Mortgage-Backed Securities.
29. Securities Backed by Automobile Loans.
30. Securities Backed by Closed-End Home Equity Loans.
31. Securities Backed by Manufactured Housing Loans.
32. Securities Backed by Credit Card Receivables.
Part 5. Fixed Income Analytics and Modeling.
33. Characteristics of and Strategies with Callable Securities.
34. Valuation of Bonds with Embedded Options.
35. Valuation of CMOs.
36. Fixed Income Risk Modeling.
37. OAS and Effective Duration.
38. Evaluation Amortizing ABS. A Primer on Static Spread.
Part 6. Portfolio Management.
39. Bond Management. Past, Current, and Future.
40. The Active Decisions in the Selection of Passive Management and Performance Bogeys.
41. Managing Indexed and Enhanced Indexed Bond Portfolios.
42. Global Corporate Bond Portfolio Management.
43. Management of a High-Yield Bond Portfolio.
44. Bond Immunization. An Asset/Liability Optimization Strategy.
45. Dedicated Bond Portfolios.
46. Managing Market Risk Proactively at Long-Term Investment Funds.
47. Improving Insurance company Portfolio Returns.
48. International Bond Investing and Portfolio Management.
49. International Fixed Income Investing. Theory and Practice.
Part 7. Equity-Linked Securities and Their Valuation.
50. Convertible Securities and Their Investment Characterics.
51. Convertible Securities and Their Valuation.
Part 8. Derivative Instruments and Their Portfolio Management Applications.
52. Introduction to Interest-Rate Futures and Options Contracts.
53. Pricing Futures and Portfolio Applications.
54. Treasury Bond Futures Mechanics and Basis Valuation.
55. The Basics of Interest-Rate Options.
56. Controlling Interest Rate Risk and Futures and Options.
57. Interest-Rate Swaps.
58. Interest-Rate Caps and Floors and Compound Options.
Fixed Income Securities: Tools for Today's Markets,
Second Edition by Bruce Tuckman.
1. THE RELATIVE PRICING OF FIXED INCOME SECURITIES WITH FIXED CASH FLOWS.
# Bond Prices, Discount Factors, and Arbitrage.
# Bond Prices, Spot Rates, and Forward Rates.
# Yield to Maturity.
# Generalizations and Curve Fitting.
2. MEASURES OF SENSITIVITY AND HEDGING.
# One-Factor Measures of Sensitivity.
# Measures of Price Sensitivity Based on Parallel Yield Shifts.
# Key Rate and Bucket Exposures.
# Regression-Based Hedging.
3. TERM STRUCTURE THEORY AND MODELS.
# The Science of Term Structure Models.
# The Short-Rate Process and the Shape of the Term Structure.
# The Art of Term Structure Models: Drift.
# The Art of Term Structure Models: Volatility and Distribution.
# Multi-Factor Term Structure Models.
# Trading with Term Structure Models.
4. ANALYSIS OF SELECTED SECURITIES.
# Repo.
# Forward Markets.
# Eurodollar and Fed Fund Futures.
# Interest Rate Swaps.
# Fixed Income Options.
# Note and Bond Futures.
# Mortgage-Backed Securities.
Derivatives Portal risk and finance papers, journals, books, conferences.
More background than trade press touts.
Recommended.
financialbulls by JW O'Brien looks at financial engineering
and risk management in real life.
Modeling Residential Mortgage Termination and Severity
Using Loan Level Data
Three essays on modeling residential mortgages.
Chapter 1 presents and estimates a new model of loss given
default using a new dataset of prime and subprime mortgages. The
model combines option theory proxies with information on the loan
contract and the cash flow position of the borrower. The results
suggest that severity on subprime and adjustable rate mortgages are
similar to losses on fixed rate prime loans, but that investor owned
properties have significantly higher losses than owner occupied
houses. The results also suggest systemic overappraisals on refinanced
loans.
Chapter 2 uses option pricing methodology to value the prepayment and
default options associated with a residential mortgage, if house
prices are mean reverting.
Numerical solutions compare the results from the mean reverting house
price model to the results from a model where house prices follow a
geometric Brownian motion process.
The main contributions are:
(1) the value of the implicit rent (service flow) is derived as a
function of the house price process instead of assumed to be constant,
as in prior research;
(2) the mean reverting model has additional factors that may help
forecast mortgage termination; and
(3) the house price process is shown to have a significant effect on
the value of a mortgage over a wide range of parameter values.
Chapter 3 presents a modeling framework for residential mortgages that
has separate models for each loan payment status (Current, 30 Days
Late, 60 Days Late, 90+ Days Late, in Foreclosure, in REO, or Paid
Off). It is shown that several classes of traditional mortgage
prepayment and default models are restricted forms of this model, and
that the restrictions are rejected empirically.
Continue reading "Residential Mortgage Termination and Severity, De Franco" »
A new approach for modeling the prepayments of a mortgage pool
shows how to value mortgage pools and agency mortgage-backed
securities. A notion of refinancing efficiency describes the
full spectrum of refinancing behavior.
The approach has two distinguishing features:
(1) The primary focus is on understanding the market value of a
mortgage, in contrast with standard models that strive (often
unsuccessfully) to predict future cash flows, and
(2) we use two separate yield curves, one for discounting mortgage
cash flows and the other for MBS cash flows.
An Option-Theoretic Prepayment Model for Mortgages and Mortgage-
Backed Securities
To appear in International Journal of Theoretical and Applied Finance
Dec 2004, jrg 7, nr 8, december 2004, pages 949-978.
[PDF]
Riskmetrics journals and old (1999-2002) Working Papers.
In 2003 November, the Fixed Income Analysts Society tipped its hat to
three leading lights in the fixed-income arena, inducting Frank J.
Fabozzi, Abner D. Goldstine and Oldrich A. Vasicek into its Hall of
Fame. The eighth annual awards ceremony recognized the trio for their
contributions to the advancement of fixed-income analysis and
portfolio management. Previous Hall of Famers include Martin
Leibowitz, Fischer Black, John C. Bogle and William H. Gross.
Fabozzi, of course, is a name on everyone’s lips. He single-handedly
created and stocked a library of books on fixed-income education
where nothing of the kind existed, helping school many thousands of
individuals in the theory and business of the debt markets. Goldstine
is an innovator in the creation of bond portfolios for investors.
Vasicek is a fixed-income modeler who opened up new avenues in
interest rate derivatives and credit modeling.
