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.