hazard rate – online resources

is decent —

Average failure rate is the fraction of the number of units that fail during an interval, divided by the number of units alive at the beginning of the interval. In the limit of smaller time intervals, the average failure rate measures the rate of failure in the next instant for those units surviving to time t, known as instantaneous failure rate.

is more mathematical.

http://www.omdec.com/articles/reliability/TimeToFailure.html has short list of jargon


hazard rate – my first lesson

Imagine credit default is caused only by a natural disaster (say hurricane or tsunami). For a brief duration ΔT (measured in Years), we assume the chance of disaster hitting is λ*ΔT, with a constant [1] λ .

Pr(no hit during    A N Y   5-year period)
= Pr (surviving 5 years)
= Pr (no default for the next 5 years from now)
= Pr (T > 5) = exp(-5λ) , denoted V(5) on P522 [[Hull]]

, where T :=  # of years from now to next hit.

This is an exponential distribution. This λ is called the hazard rate, to be estimated from market data. Therefore it has a term structure, just like the term structure of vol.

More generally,  λ could be assumed a function of t, i.e. time-varying variable, but a slow-moving variable, just like the instantaneous vol. In a noisegen, λ  and vol function as configurable parameters.

In http://www.financial-risk-manager.com/risks/credit/edf.html, λ is denoted “h”, which is assumed constant over each 12-month interval.

“Hazard rate” is the standard terminology, and also known as “default intensity” or “failure rate”.

I feel hazard rate is perhaps the #1 or among top 3 applications of
conditional probability,
conditional distribution,
conditional expectation

So the big effort in studying the conditional probability is largely to help understand credit risk.

mortgage is like a callable bond, briefly

The mortgage you take on can be, for educational purpose, compared to a personally issued bond (you as issuer) with a predefined monthly repayment and a fixed interest rate. (The floating interest mortgage is comparable to a floating-interest bond.)

When you refinance at a lower interest, it's similar to a callable-bond issuer exercising the call option and then refinance.

The call option is embedded in the “bond”. The call option allows the issuer/borrower to “buy” back the bond from the lender, thereby ending the contract.

credit e-trading – basics

2 “external” venues —
$ (ECN) interdealer electronic brokers — Bloomberg, Marketaxess, TradeWeb, BondDesk, NYSE, TMC. These are like the exchange-connectivity interface.
$ Retail-facing Distributors – Fidelity, Charles Schwab etc. These are often the retail-oriented portfolio/wealth managers. These portfolio managers are like the “client connectivity” interface.
* Each external connectivity above can have a customized FIX protocol.

Volume — 300 trades/day, 1000 RFQ(client inquiries)/day, but 4000 price updates/SECOND at peak! Probably incoming quotes. These would update internal cache within the bank. These “incoming” updates must be synchronized with other updates initiated from “within” the bank. Probably the trickiest technical challenge in this platform.

Most trades are institutional (often from wealth management firms) but there are retail trades as small as $5000/trade.

The treasury work-up process also takes place on some of these ECN’s.

Most important products — corporate bonds, CDS, CDX.

(Based on a major credit trading sell-side.)

CDS pricing #hearsay

See also http://www.financial-risk-manager.com/risks/credit/edf.html

Use bid/ask from market to derive the insurer’s (not insurance buyer’s) cash flow including premium received and the “disaster” compensation amount[1]. This gives an implied hazard rate (or default density (?).

[1] related to recovery value. For physical settlement, the insurer pays the buyer the face value, i.e. the sum assured.

I was told this (implied) hazard rate is the key soft mkt data just like implied vol and implied yield. Calibration of hazard rates to CDS market quotes (spreads or upfront points with running coupons)

Plot the hazard rate along maturity. You get a credit spread curve (just like yield curve and the term structure of vol). I guess this is the term structure of hazard rate.

Using this curve you can price all other credit instruments.

Just like vol, there’s a realized default rate (default intensity), whose value is very different from the implied hazard rates backed out from the market quotes.

credit business vs rates business


You asked about credit business vs rates business. Here’s a simple difference —

A bank’s credit department are interested in and monitors individual bond issuers including corporations and municipalities.

Interest rate department are interested in national economies. The issuers in this contexts are national governments, with the ultimate power to print money. Usually these issuers have no credit default risk.

Now is special time. I feel Greece doesn’t t have the power to print money which is euro, but the European Central Bank feels reluctant to print money for Greece.

MBS is a separate PnL from Mortgage lending

MBS is a completely separate PnL from Mortgage lending business. As explained in http://bigblog.tanbin.com/2011/11/buy-sidesell-side-business-units-in.html, a universal bank has commercial banking + security dealing business units. Such a bank often has a mortgage business and a MBS business. Citigroup is an example, where MBS is probably part of Institutional Client Group. It's important to realize the mortgage and MBS businesses have different books and don't necessarily depend on each other.

The mortgage lending business is older and simpler, much like a loan with collateral. The business starts with initial capital and profits by lending at an interest.
– It has realized PnL
– It has a lot of unrealized PnL
– It has significant risk in terms of default
– When housing prices tumble, all hell breaks loose. Borrowers default. Collateral devalues…

MBS business is more like a dealing desk in corp bonds. MBS business starts with its own capital, and profits by buying/selling “assets”. Holding a mortgage “asset” is like holding a coupon-bearing bond with collateral. We need to very clear about the meaning of “asset” before we understand the MBS securitization process, which I will not discuss.
– MBS business can create MBS security from regular mortgage assets (raw material), and sell them
– MBS business can use as raw material mortgage assets by other mortgage lenders, and therefore decoupled from the mortgage department of the parent bank.
– MBS business can buy or sell existing MBS securities, possibly created by other MBS houses.
** Any trader can buy or sell existing MBS securities, but the MBS business probably does it with more purpose.
– MBS business probably should never create a mortgage by lending directly. That's the responsibility of the mortgage department of the parent bank.

MBS can profit while Mortgage business loses money – if the MBS trader is smart
MBS can lose while Mortgage business profits – if the mortgage lending officer is prudent.

CDS trading platform – IV

%%Q: how is JNI used here?
A: some calculation module is in C; some external API is in C. It’s a pain to rewrite things into java, but “we do want to”.

%%Q3: how does a CDS dealer hedge its exposure after it does a deal with a client?
A: It creates an offsetting deal with someone else

%%Q3b: but the dealer can’t disappear from the scene, right?
A: right. Consider an original mtg lender who sells the mtg off to Fannie. The mtg is completely off its books, but every month it still collects the installment. Similarly in the CDS case, the dealer still collects the quarterly premium, with or without the hedge.

Q: personal experience with MOM tuning?
%%A: message rate; subscriber population (RV handles this gracefully); message size and depth
%%A: one slow subscriber can cause message build-up in the broker, but TTL can help.

Q: how is quick sort used on array list and linked list?
%%A: random access needed. In STL, the sort function template is usable on only selected containers, whereas linked list (and other containers) has its own sort() method because the standard sort function is inapplicable.

CDS basics

Background: Many speculators trade “credit products [1]” for a quick profit. In terms of hedgers, I guess bond underwriters may keep some of the new bonds during the bond issue, in which case they would later trade these bonds as part and parcel of the investment banking (underwriting) business.

At the lowest level of the product hierarchy, the underlying product is probably a corporate bond. Since there’s default risk, a common hedge is a CDS.

In fact, CDS is about the only hedge there is. You can also trade the issuer’s preferred stock, commercial papers etc as these are correlated to the bond in your portfolio. I feel shorting the stock is practical only if you intend to hold the bond for a few days.

[1] corporate bonds, CDS etc

Exchanges bring bids and offers together – price discovery through the open order book. In contrast, a pure-play clearing house leaves buyer/sellers alone negotiating trade price over phone/email, but once trade executes, real money is maintained at the margin accounts in clearing house. Clearing house recalculates mark-to-market (not PnL) and margin ratio.

If a counterparty (like Lehman) collapses, clearing house acts as a shock buffer, to break the chain reaction of defaults.

Someone said CDS is like an insurance on a corporate bond.

I guess counterparties leave their security deposit in the clearing house for the duration of the CDS.

Margin risk in CDS is tricky. Scenario testing is required. Concentration risk is the most obvious risk — if an account holds most of the securities about a particular issuer, and the issuer defaults, then no one wants to buy those securities.

credit risk in trading vs commercial banking

Hi Rob,

I feel there are 2 major users of credit risk data.

* traders use it as part of market risk data
* lenders use it to decide on interest rate and perhaps collateral

Everyday thousands of individuals and organizations borrow money from banks, from corporate/muni bond markets, from repo market, from swap market … The interest rate they pay is calculated based on their credit score or credit rating. Essentially it boils down to default risk. For example, Treasuries have the lowest interest because these issuers have the maximum credit rating, even though the Greece government can default just as any issuer.

It's impossible to “guess” how much interest to charge a borrower. It has to be calculated. Therefore, Credit risk is an indispensable system for lending institutions. Not for traders. I feel traders generally look at market risk numbers after executing a trade. That's the all-important concept of VaR.

Credit risk (and market risk) data help traders get a better idea of their risk exposure, and may prompt them to set up hedges or trade less/more aggressively going forward. However, a trader could choose to trust her intuition more than the risk numbers.

Please correct my understanding. You can simply put “no” after any incorrect observation. If you can explain it's even better. Thanks.

credit risk analysis in Singapore

(a blog post. Your comments are appreciated.)

To me, credit risk is all about default risk. There's a whole industry around the rating, measurement/analysis, monitoring, hedging and control of default risk. As such, Credit risk is relevant to both investment banking (buy/sell, underwriting, M&A etc) and commercial banking (ie lending), but how relevant? I feel credit risk is one of many components of market risk in investment-banking, but credit risk is absolutely central to commercial banking.

For the Singapore financial industry, commercial banking generates (much) larger revenue than i-banking, and is a far more important industry to the national economy. Most S'pore businesses need to borrow from banks.

I guess credit risk analysis is more important than market risk analysis in S'pore.

credit risk analytics important to trading desks?

Now I realize the entire credit business (all those credit desks) in any trading firm operates around credit risk or “default risk” of individual issuing companies. I guess credit risk is at the center of all the securitization, CDS trading and straight buying ans selling of corporate bonds.

Am still unsure how precise a mathematician can be about calculating, predicting, measuring default probability. They probably take in tons of reported company financial data and feed them into some complex model.

Muni bonds have non-zero credit risk. In fact many muni bonds are below AAA rating. However, I don’t hear about credit risk analytics in the muni business. In fact, one high yield muni trader I know always prices his offers by hand, without any automatic calculation.

High yield means low rating, right? So credit risk is higher and should be factored into the pricing logic. The trader seems to go by gut feelings?

Q: I know credit risk modeling is used in consumer and corporate loan pricing, but is it also used in fixed income trading? In such areas as interest rate swap, credit default swap, corporate bond trading?
A (from a practitioner): yes

Q: people tell me market risk and credit risk are 2 main focus areas for any bank, but if a bank holds lots of credit instruments (high yield bonds, IRS, CDS securities…) then i feel market risk measurement must depend on credit risk measurement. Right?
A (from a practitioner): yes

buying a mortgage, buying an income generator

In MBS/ABS/CommercialPaper trading, people talk about selling and buying a mortgage. Let’s get comfortable with the concepts.

A bond is an *asset* because it generates (stable) income. What if i want to “buy” the movie revenue of a cinema? I buy it by lending money to the cinema.

If you see a student loan as an income generator, you can buy it from a bank as a “bond”. Think of it as a “personal bond”, issued by the student. Most students we assume are credit worthy so this income is
reliable, like treasuries.

When you sell a loan to an investor, you are selling an income-generator. Mortgage is special because it’s collateralized.

y are munis so popular in wealth-management

…early this year I went out on a limb to say it dominates the fixed-income space, in terms of trade volume. Now I see a Barron’s article estimating 70% of total muni market is retail; with insurance companies taking 16%, and 8% by commercial banks etc. Due to the retail nature, muni desk gets higher volume than other FI desks.

– Citi muni desk has a dedicated HighNetWorth business unit;
– GS pwm clients do more muni trades than other FI trades combined;
– ML muni desk gets more trades from the retail MLBM conduit than all institutional conduits combined.

I think “Most” private wealth accounts invest primarily in 1) eq, 2) fixed income with a very smaller [3] number of (perhaps large) trades in alternative investment such as illiquid funds and private equity. In general, the more illiquid, the lower trade volume. Munis have high bid/ask spread, therefore volume is much lower than equities. In my GS PWM experience, eq trades outnumber fixed income trades every single day.

[3] eq and bond trading can be done by yourself.

Asset-allocation wise, a common pattern is 35 – 50% eq, 25-35% FI. I am no expert in the large and important field of asset allocation, but I guess FI instruments have many wealth-preserving advantages over eq instruments. Many of the equity trades in private wealth accounts aren’t wealth-preserving — they book to brokerage accounts.

Further, I believe fixed income derivatives aren’t particularly popular for wealth preservation. These instruments are created and used by enterprises, and for different purposes.

MBS? no expert here but I don’t feel it has all the advantages of investment-grade bonds.

A bond can cover 20 years — compare equities. Among regular bonds,
– munis offer unique tax advantages
– munis are generally safer than corporate bonds
– minimum quantity is $5000 or lower for muni. Not sure about other bonds.
– munis target retail investors.
– muni is the only fixed-income segment where retail investors can move a market, according to a Barron’s interview.

My own interview questions on credit (or market) risk system

Q: how is your system related to Credit Valuation Adjustment?

Q: what trading desks do you support?
A: many desks. Could be a firm-wide system.

Q: who are the most important users of the reports generated? Traders? Management of the trading desk? Sales teams? Product control?
R: I know Trader, Desk manager are using that.

Q: what asset classes are rated by the system — corporate bonds? other bonds? swaptions? CDS? Mortgage-backed-securities?
R: Bonds, Swaps, Special purpose vehicles.

Q: how many positions in each product?

Q: What kind of traders hold those positions? Holding for how many days?

Q: what’s a typical position size?

Q: What are the major risks to those positions?

Q: What sensitivities are monitored?

Q: I was told CDS is the main credit product on the market. Many banks use CDS to cover and hedge their credit risk. Is CDS covered by your system?

Q: Since you said it’s a reporting system, give me a good idea of the most important pieces of information in your report? To be specific,name at least 3 pieces. Exclude product attributes such as bond name, issuer name, coupon rate, last payment coupon date etc.

Q: give me a good idea of the most important input data to the credit rating system, besides issuer, coupon rate, call dates.

Q: how does the credit risk output from your system affect the trading operation or other businesses? What businesses? Security lending business?

Q: Specifically, what business decisions do these users make after reading your data?
R: user will base on the report to request borrowers to increase collateral.

Q: who are the downstream systems?

Q: does your output data enter the trade “flow” before ORDERS are sent out (ie pre-trade) or after trades are confirmed and become a POSITION (ie post-trade)?
R: Has nothing to do with orders.

Q: if it only affects collateral, then is it part of the buy/sell life cycle? Is it part of security lending life cycle? or some other business life cycle? What businesses? Loan business? Repo business? OTC derivative business that needs collateral?

Q: what are the underlying credit risk methodologies used? Is there a name for that methodology?

Q: how many issuers are covered?
R: Less than 7 hundreds.

Q: do you cover corporate issuers only? If not then who else? Governments? Agencies? Municipalities?

Q: what are the database table sizes in terms of rows and GB? How do you cope with the size?

Q: How large is the largest table you have to query? What kind of data does it hold?
R: my table are small, 80 columns, 100k records. Use ISIN instead of cusip.

Q: is this the largest? What kind of data does it hold? Product data keyed by ISIN?

Q: how long is the batch job? What are the techniques to shorten it?
R: from minutes to several hours. Techniques? none

Q: do you know if the system use a rule engine for the credit risk calculations?

baml hedging in muni desk

* only tr and tr futures are used. These are liquid instruments and have good correlation to muni
* VaR is the standard risk measurement.
* valuation/marking is based on ….take your breath… last exec price for tr, but less standardized and less formalized for muni

how does a mortgage creditor sell off the mortgage?

Q: If a mortgage is a bad thing to a bank, why would anyone want to buy it from the bank?

Underlying asset is the building. Creditorship of the mortgage is a good thing as it generates an income stream. It’s an interest-bearing instrument.

In the worst case, you still get the house — collatelized.

If a mortage pays $2000/month and the house has a (albeit fallen) value of $300k, someone will be willing to pay $1 to become the creditor.

So there’s a fair value even if the borrower has poor credit.

hedging muni long positions

Short muni positions might be similarly hedged, but I feel long muni positions are more common across muni trading desks, so that’s our focus here.

The simplest hedge is a Treasury, followed by Treasury futures (a basket) as the 2nd simplest. If you long a muni bond, you short a treasury, matching dv01.

Q: What if there’s not an exact matching maturity date?
A:  I guess the futures bucketing (Stirt) calc could help traders decide how many futures contracts needed

Q: Why do I need to hedge? What’s the risk in having the long, assuming 0 credit risk?

A: interest rate delta risk. Interest rate can rise, hurting my long market value. By shorting a treasury, i preserve my net market value of long and short

Treasury (futures) is popular because it’s the most liquid hedging instrument.

Q: Why T-futures if there’s treasury? I was told T-futures are similar to treasury in this case.
A: http://finance.zacks.com/guide-hedging-treasury-bond-futures-5786.html I guess cash outlay is smaller with T-fut

How about swaptions? Since a swaption is an option, there’s an insurance premium cost, so some traders avoid it.