Tuesday, April 24, 2007

Structured Products

Just got my hands on Structured Products by Satyajit Das. It consists of two volumes, 2600 pages total. Volume 1 covers applications of derivatives, synthetic assets, exotic options, and interest rate and currency structured products. Volume 2 covers equity linked structures, commodity linked structures, credit derivatives and new markets (e.g., inflation, insurance, weather, etc).

You'd think that such massive tomes, covering such an encyclopedic list of topics, contain a wealth of knowledge. You'd be wrong. The explanations are at such a basic level that they are essentially useless to anybody with even an elementary understanding of structured products. And to top it off, the material is incredibly dated (even though the third "revised" edition was published in 2006). For example, the author dedicates pages to employee stock option plans and how they are not reflected in the financial statements, with references to articles written in the 1990s. He appears completely unaware that IASB and FASB both now require employee stock options to be accounted for in company's financial statements.

A total waste of money.

Saturday, April 21, 2007

WHD Problem 5.9

Calculate the theta, gamma, vega and rho for European call and put options.

Note: I have assumed a non-dividend stock.

Θ = ∂Π/∂t

Θc = - ½S0N'(d1)σ/√T - rKe-rTN(d2)

Θp = - ½S0N'(d1)σ/√T + rKe-rTN(-d2)

Γ = ∂2Π/∂S2

Γc = Γp = N'(d1)/S0σ√T

v = ∂Π/∂σ

vc = vp = S0N'(d1)√T

ρ = ∂Π/∂r

ρc = KTN(d2)e-rT

ρp = -KTN(-d2)e-rT

Thursday, April 19, 2007

Transforming the Black-Scholes equation into the Heat equation

(∂V/∂t) + ½ σ2 S2 (∂2V/∂S2) + r S (∂V/∂S) - rV = 0

First substitution: u = V e-rt

V = u ert

(∂u/∂t) = (∂V/∂t) e-rt - V r e-rt

(∂u/∂t) + V r e-rt = (∂V/∂t) e-rt

(∂V/∂t) = ert (∂u/∂t) + V r = ert (∂u/∂t) + r u ert

(∂u/∂S) = e-rt (∂V/∂S)

(∂V/∂S) = ert (∂u/∂S)

(∂2V/∂S2) = ert (∂2u/∂S2)

And the equation changes to...

ert (∂u/∂t) + r u ert + ½ σ2 S2 ert (∂2u/∂S2) + r S ert (∂u/∂S) - r ert u = 0

(∂u/∂t) + ½ σ2 S2 (∂2u/∂S2) + r S (∂u/∂S) = 0

Second substitution: S = ex

x = ln S

(∂S/∂x) = ex
(∂x/∂S) = 1 / S

(∂u/∂x) = (∂u/∂S) (∂S/∂x) = (∂u/∂S) ex = S (∂u/∂S)

S2 (∂2u/∂S2) = S2 ∂/∂S (∂u/∂S)

= S2 (∂x/∂S) ∂/∂x (∂u/∂S)

= S2 (1/S) ∂/∂x (1/S ∂u/∂x)

= S [ 1/S ∂2u/∂x2 + ∂u/∂x ∂/∂x (1/S) ]

= ∂2u/∂x2 + S (∂u/∂x) (-1/S2 ∂S/∂x)

= ∂2u/∂x2 - (1/S) ex (∂u/∂x)

= ∂2u/∂x2 - ∂u/∂x

And the equation changes to...

(∂u/∂t) + ½ σ2 (∂2u/∂x2 - ∂u/∂x) + r (∂u/∂x) = 0

(∂u/∂t) + ½ σ22u/∂x2 + (r - ½σ2) ∂u/∂x = 0

Third substitution: z = x - (r - ½σ2)t to cancel the first derivative term, and t' = - t to conform to the usual sign convention.

(∂u/∂t) = (∂u/∂z)(∂z/∂t) + (∂u/∂t')(∂t'/∂t) = (∂u/∂z)[-(r - ½σ2)] + (∂u/∂t')(-1)

∂u/∂x = ∂u/∂z

2u/∂x2 = ∂2u/∂z2
And the equation changes to (dropping the ' on the t variable) ...

- (∂u/∂t) - (r - ½σ2) (∂u/∂z) + ½σ2 (∂2u/∂z2) + (r - ½σ2) (∂u/∂z) = 0

- (∂u/∂t) + ½σ2 (∂2u/∂z2) = 0

And finally, voila, we have the heat equation...

∂u/∂t = ½σ2 (∂2u/∂z2)

WHD Problem 3.6b

Find the most general solution of the Black-Scholes equation that has the special form V=A(t)B(S).

(∂V/∂t) + ½ σ2 S2 (∂2V/∂S2) + r S (∂V/∂S) - rV = 0

V = A(t) B(s)

(∂V/∂t) = B (dA/dt)

(∂V/∂S) = A (dB/dS)

(∂2V/∂S2) = A (d2B/dS2)

B (dA/dt) + ½ σ2 S2 A (d2B/dS2) + r S A (dB/dS) - r A B = 0

(1/A) (dA/dt) + ½ σ2 S2 (1/B) (d2B/dS2) + r S (1/B) (dB/dS) - r = 0

½ σ2 S2 (1/B) (d2B/dS2) + r S (1/B) (dB/dS) - r = - (1/A) (dA/dt)

Since the left-hand side depends only on S and the right-hand side depends only on t, the only way the equality can hold is if both sides are equal to a constant K.

- (1/A) (dA/dt) = K

A(t) = c e-Kt

½ σ2 S2 (1/B) (d2B/dS2) + r S (1/B) (dB/dS) - r = K

½ σ2 S2 (d2B/dS2) + r S (dB/dS) - (r + K) B = 0

S2 (d2B/dS2) + (2r/σ2) S (dB/dS) - (2/σ2) (r+K) B = 0

This equation proceeds as in the previous exercise.

λ2 + (2r/σ2 -1)λ + (-2/σ2)(r+K) = 0

λ = { (1 - 2r/σ2) ± [ (2r/σ2 - 1)2 + (8/σ2)(r+K) ]½ } / 2

λ = { (1 - 2r/σ2) ± [ (2r/σ2 - 1)2 + (8/σ2)(r+K) ]½ } / 2

λ = { (1 - 2r/σ2) ± [ (2r/σ2 + 1)2 + (8K/σ2) ]½ } / 2

There are three cases depending on the roots: two real roots, one real root, two complex roots. And to be explicit, we should note that the case of two real roots can come about either with a real value of K (which leaves the form of A(t) above unchanged) or with a complex value of K (which would require rewriting A as we'll see in a minute).

Case 1: λ1 and λ2 are distinct real roots.

B(S) = c1 Sλ1 + c2 Sλ2

V(S,t) = (c1 Sλ1 + c2 Sλ2) e-Kt

Case 1A: K = 0
(Special scenario under case 1)

This reduces to the special case where there is no time dependence V = B(S)

V = c1 S + c2 S (-2r/σ2)

Case 2: λ1 = λ2 = λ is the only real root.

B(S) = Sλ (c1 + c2 ln S)

V(S,t) = Sλ (c1 + c2 ln S) e-Kt

Case 3: λ1 = a+ib and λ2 = a-ib are complex roots (with K real).

B(S) = Sa [ c1 cos (b ln S) + c2 sin (b ln S) ]

V(S,t) = Sa [ c1 cos (b ln S) + c2 sin (b ln S) ] e-Kt

Case 3A: λ1 = a+ib and λ2 = a-ib are complex roots (with complex K = c + id).
(This is not strictly separate from case 3; it's simply a matter of expanding e-Kt for complex K.)

B(S) = Sa [ c1 cos (b ln S) + c2 sin (b ln S) ]

V(S,t) = Sa [ c1 cos (b ln S) + c2 sin (b ln S) ] e-ct (cos dt - i sin dt)

Note that all of these solutions (except Case 1A) have too many degrees of freedom, due to the freedom of choice in choosing K. Normally boundary conditions would restrict the universe of valid values for K, but the problem as stated did not provide any such conditions.

Wednesday, April 18, 2007

WHD Problem 3.6a

Find the most general solution of the Black-Scholes equation that has the special form V=V(S).

(∂V/∂t) + ½ σ2 S2 (∂2V/∂S2) + r S (∂V/∂S) - rV = 0

Substituting V=V(S) reduces the partial differential equation to an ordinary differential equation.

S2 (d2V/dS2) + (2r/σ2) S (dV/dS) - (2r/σ2) V = 0

This is an Euler differential equation x2y'' + axy' - by = 0, the solutions of which can be found with the aid of the characteristic equation.

λ2 + (a-1)λ + b = 0

λ2 + (2r/σ2 -1)λ + (-2r/σ2) = 0

Applying the quadratic equation, one obtains (after a bit of algebra) two roots

λ = 1 and λ = (-2r/σ2)

Using these roots, we determine that the most general solution of the Euler equation is
V(S) = c1 S + c2 S (-2r/σ2)

Saturday, April 14, 2007

WHD Problem 2.5

There are n assets Si,...,Sn satisfying the following stochastic differential equations dSi = σi Si dXi + μi Si dt, for i = 1, ..., n

The Wiener processes dX i satisfy E[dXi] = 0 and E[dXi2] = dt, as usual, but the asset price changes are correlated with E[dXidXj] = ρijdt where -1 ≤ ρij ≤ 1.

Derive Ito's Lemma for a function f(Si,...,Sn) of the n assets.


Actually, I already know most or all of the content of The Mathematics of Financial Derivatives; I am reading it as a review in preparation for more advanced materials I am hoping to get to in the near future.

This exercise is pretty trivial, mostly a matter of keeping track of all the variables.

The Taylor series expansion is
df = (∂f/∂t)dt + Σ(∂f/∂Si)dSi + ½Σ(∂2f/∂Si∂Sj)dSidSj

dSidSj = (σi Si dXi + μi Si dt)(σj Sj dXj + μj Sj dt) = σi σj Si Sj dXi dXj = ρij σi σj Si Sj dt
dropping all higher order terms and then substituting in the correlation assumption.

So finally we obtain
df = [ (∂f/∂t) + Σ μi Si (∂f/∂Si) + ½ Σ ρij σi σj Si Sj (∂2f/∂Si∂Sj) ] dt + Σ σi Si (∂f/∂Si) dXi

Thursday, April 12, 2007

Here we go...

Senator Charles Schumer and other members of the Senate Banking Committee said the federal government should spend "hundreds of millions of dollars'' to bail out subprime mortgage borrowers facing foreclosure. Non-profit groups would distribute the money to help homeowners refinance loans they can't repay, Democratic Senators Schumer of New York, Robert Menendez of New Jersey and Sherrod Brown of Ohio.

So, let me get this straight those of us who did the RESPONSIBLE thing and did not buy more house than we could afford (while watching prices skyrocket out of our reach due to these irresponsible buyers) are now being asked to bend over and take it once more as our tax money goes to subsidize those who did buy more house than they could afford? Why?

And I'm tired of hearing that folks didn't understand what they were getting as a mortgage. Everyone understands adjustable interest. And everyone understands whether or not a payment is more than they can afford. And last of all everyone should understand the consequences of lying about his/her income on a mortgage application. I don't have any sympathy.

These folks took a risk. If it had worked out for them, the profit was all for them. They weren't planning to share it with me. It didn't work out, so I have to share the loss? WTF?

Job Cuts at Citigroup

Citigroup will eliminate about 17,000 jobs as part of a companywide restructuring to reduce costs and improve profit. Overall, the cuts amount to about 5% of the bank's 327,000-strong work force. Citigroup said its plans include "shrinking the size of corporate centers," several of which are in New York. It also expects to move some 9,500 jobs to lower-cost locations. Still, the elimination of the jobs won't reduce the bank's work force, but merely slow its growth, Citi executives said.

Ravings Brands Selling Moe's Southwestern Grill

Moe's Southwest Grill, the crown jewel of Atlanta-based parent Raving Brands, is being sold to Focus Brands, the Atlanta-based owner of Carvel Ice Cream, Schlotzsky's, Cinnabon and international stores of Seattle's Best Coffee. The announcement Wednesday comes on the heels of a lawsuit by franchisees, who among other things said the chain's management was secretly considering a sale. Raving Brands founder Martin Sprock denied that claim as recently as last week.

Tuesday, April 10, 2007

BearingPoint

The Company's continuing failure to timely file certain required periodic reports with the SEC imposes significant risks to the Company's business, including the possible loss of business, delisting from the New York Stock Exchange and defaults under the Company's credit facility. The Company has identified material weaknesses in its internal control over financial reporting, which could materially and adversely affect its business and financial condition. The Company's current cash resources might not be sufficient to meet its expected near-term cash needs, especially to fund intra-quarter operating cash requirements and non-recurring cash requirements (e.g., to settle lawsuits).

Apparently, BearingPoint didn't file its annual reports for fiscal 2004 and 2005 on time, nor will it file its 2006 report on time. It also has failed to file quarterly reports on time for the past six quarters in a row.

Friday, April 06, 2007

MBA Salaries

Came across the following in the WSJ...

The following business schools reported the highest average annual base salaries for full-time graduates, according to "The Wall Street Journal Guide to the Top Business Schools 2006".
  • Stanford University: $100,400
  • Harvard University: $99,848
  • Massachusetts Institute of Technology: $94,131
  • University of Pennsylvania: $92,986
  • Dartmouth College: $91,900
  • Northwestern University: $91,390
  • Tuesday, March 27, 2007

    The Mebert Hoax

    I've always been fascinated by this ultimate example of Dilbert-ism in the real world, but the story due to age (it happened back in 1997) has been getting more difficult to find on the internet. So I've taken a minute to document the story here for posterity.

    Here's the story as originall written in the San Jose Mercury News...

    My goal is to see if a group of executives will allow somebody who has very few credentials, except for good hair, to come into their meeting and get them to write a mission statement which is so impossibly complicated that it has no real content.--Scott Adams, Oct. 8, 1997, 9:30 a.m.

    Two hours later, management consultant Ray Mébert strides through the doors of Logitech International's headquarters in Fremont. Few employees give a second glance at the short, mustached man in a gray suit as he weaves through a maze of cubicles to a conference room in which almost a dozen senior executives have been assembled.

    In a memo distributed to a selected group of Logitech's vice presidents and senior managers, Pierluigi Zappacosta, the company's co-founder and vice chairman, described Mébert as a man with ''special talents as a facilitator'' and ''a very original thinker'' who has collaborated with big-name consultants.

    It's not as if Logitech, the world's largest manufacturer of computer mice and related devices, is in a slump. In Silicon Valley, the 3,000-employee company is considered a strong innovator. But in this fast-paced industry, survival depends in large part on aggressively finding new business opportunities, which is why the gifted Mébert has been summoned. His charge, in the words of Zappacosta's memo, is to help ''crisply define the goals'' of the New Ventures Group. Translation: It's time for that most dreaded of corporate exercises, rewriting the mission statement.

    Mébert (the French pronunciation, please!) carries nothing but a thin manila folder with documents summarizing Logitech's business goals--which he has studiously avoided reading. ''I try not to become too familiar with the companies I'm consulting for,'' Mébert explains. ''I find that, otherwise, generic solutions might not fit as well.''

    If the size of his entourage is a yardstick, Mébert clearly is a success. Does Michael Porter, the celebrated authority on competitive business strategy, arrive with a photographer, a videotaping crew and a personal assistant named Sheena Diamond? Noting all the electronic gear, one exec is heard to mutter, ''Wow, he's got to be expensive.''

    Mébert quickly confirms his stature in the management consulting universe. ''I did the Harvard MBA thing, and then I went to Procter & Gamble where I worked on the Taste Bright Project,'' Mébert says. Taste Bright, he explains, was a top-secret effort his team worked on for years, to boost soap sales by cashing in on not only the olfactory but also the gustatory sense.

    "There actually are some people who admitted in focus groups that they would sometimes taste soap. We found that to get repeat business it was necessary to actually improve the smell as well as the taste of the soap,'' Mébert says. Zappacosta nods empathetically at such a difficult assignment. There follow serious nods--and a few chuckles--around the table.

    Mébert continues with his credentials: He did a stint at Fortune Computer (one of the valley's legendary business failures), then founded Ray Mébert Associates. Apple immediately recruited him to strategize on its much ballyhooed--now beleaguered--handheld computer, the Newton.

    These less-than-proud consulting experiences do not raise an eyebrow. Then again, as any loyal reader of ''Dilbert'' can tell you, consultants play by their own rules. To quote that management guru Dogbert, ''Consultants don't need much experience in an industry in order to be experts. They learn quickly. If your 26-year-old consultant drives past the Egghead software outlet on the way to an assignment, that would qualify as experience in the software industry.'' Mébert, it seems, adheres strictly to the Dogbert doctrine.

    If the Logitech execs were to look closely, they would notice a few signs that Mébert is not exactly who he says. Strands of sandy blond hair peek from under his thick brown locks. His mustache is a little too symmetrical. Not bad, though, given the hasty transformation Mébert underwent two hours earlier at his home in Danville. It's also home to Mébert's alter ego, ''Dilbert'' creator Scott Adams.


    And here's a couple of interviews Scott Adams gave about the incident shortly afterwards.

    I got a call from Tia O'Brien [an independent reporter on assignment] for the San Jose Mercury News. She wanted to do a story that was going to be interesting and different. We brainstormed and came up with the idea that I'd put on a disguise, go to a corporation as a consultant, and see if I could fool people into thinking that I was a high-paid consultant when, in fact, I was just full of crap. Zappacosta thought it would be a fun idea. So we set up the scam. Tia acted as my assistant, and Pierluigi was the only one who was in on it in a room full of business executives at Logitech. For over one hour I took them through an exercise on how to rebuild their mission statement. I actually convinced them that the one they had was woefully inadequate. That's part of the humor of it - all mission statements are quite useless. So to tell them the one they had wasn't doing the job should have raised a red flag to begin with. But people in corporations are so used to two things: First, absurdity - so nothing seems too unusual. And second, there is not enough payoff to rock the boat. It was much easier for everyone to listen to what I had to say than to jump on me at the first sight of absurdity. Certainly everyone in the room had at least a moment where they said, "Man, I'm wasting my time!" But I made sure I always skated just below the level at which somebody would call my bluff and would think it was worth taking the chance of calling me a fraud. I had them thinking, "What if it just turns out that he's just eccentric but the best consultant in the world?"

    See that picture to the left there, by the light switch? Where I'm peering from behind Dilbert? I have a big mustache and fake brown hair on? I was outfitted by a makeup artist and I went into Logitech as a famous consultant. I was brought in by the founder of the company, who was in on it, and he was in on the joke, and a reporter for the San Jose Mercury News, a freelancer who was working there, set it up with me. They had their senior management there and I gave a whole presentation and reworked their mission statement with them. They thought I was there to give them a better mission statement. But, my stated goal was to give them the worst mission statement ever written, convince them it was good, and get them to agree to put it to music. I succeeded in all that. They agreed to put it to music and I didn't actually have them put it to music. But I got volunteers, and people volunteered. It was the worst mission statement ever written. Every person in that meeting was way above average in intelligence and not one bit more gullible than anybody else on Earth. Completely normal gullibility.

    Friday, March 23, 2007

    Private Equity Firm To Go Public

    Blackstone Group is preparing to become the first major private equity firm to go public. The $4 billion IPO values Blackstone at $40 billion. But investors can only buy into Blackstone's management company, not the companies it owns, and they'll have limited voting rights. Blackstone's partners will remain in control, said Martin Mayer at the Brookings Institution.

    [Thanks to CP for bringing this to my attention.]

    Monday, March 19, 2007

    45% of first-time buyers put $0 down

    According to the National Association of Realtors 45% of first-time buyers nationwide put no money down.

    That's up from 42% the last time I posted the statistic back in March 2005.

    Sunday, March 11, 2007

    Collapse of Arthur Andersen LLP

    To those who think that the destruction of Arthur Andersen was an over-reaction, keep in mind that we are not just talking about Enron. Arthur Andersen over its last few years also signed off on the extremely dirty books of Sunbeam, Waste Management, Global Crossing, Qwest, and (most appaling of all) WorldCom. This was clearly not just a few bad apples but a systemic cancer within a company that not that long ago was held up as the paragon of auditing ethics.

    Staff:

    Of course, the jewel of the crown was Arthur Andersen's tax practice, with its approximately 500 US partners, which was won by Deloitte Touche Tohmatsu in April 2002.

    The other big ticket item in the collapse of Arthur Andersen LLP was that Robert Half International established the firm Protiviti by hiring more than 700 professionals from the risk consulting practice including more than 50 partners.

    The rest of the firm was carved up like a Thanksgiving turkey...

    Ernst & Young Acquires Arthur Andersen's Chesapeake Office - 350 employees including 39 partners.

    Ernst & Young Acquires Pittsburgh Offce - 87 employees including 8 partners.

    Ernst & Young Acquires Louisville Office - 45 employees including 3 partners.

    Ernst & Young acquired the Financial and Commodities Risk Consulting and Financial Services practices of Arthur Andersen's Chicago office - 65 employees including 12 partners

    Ernst & Young hired 78 Andersen staffers in Miami, Fort Lauderdale and West Palm Beach.

    Ernst & Young acquired Ann Arbor, Grand Rapids and Toledo offices - 159 employees including 14 partners

    Ernst & Young hires approximately 100 Arthur Andersen professionals including 6 partners from Andersen's Los Angeles, Denver, Phoenix, and San Diego practices.

    Deloitte & Touche acquired about 950 staffers from the Chicago office, far more than any other Big Four firm.

    Deloitte & Touche acquired 225 employees from the Milwaukee office

    Deloitte & Touche acquired 50 employees from the Las Vegas office

    Deloitte & Touche acquired the Minneapolis office - 229 employees including 16 partners

    From the Atlanta office, Deloitte & Touche hired 359 employees including 39 partners, and Ernst & Young hired 51 employees including 5 partners

    The Boston office was divided up between the Big Four - Ernst & Young signed up 15 partners, PricewaterhouseCoopers 5 partners, Deloitte & Touche 11 partners and KPMG 4 partners

    KPMG picked up more than 200 employees and partners from the Seattle office

    Grant Thornton picked up 50 employees including 6 partners from the New York office

    Grant Thornton got 161 employees including 19 partners in Charlotte, Greensboro and Columbia

    Grant Thornton buys Tulsa office with 35 employees

    Huron Consulting Group was formed by 35 Andersen professionals, mostly from the financial consulting practice, in Chicago.

    Keep in mind that this entire process was started in April and was completed by July. I did not think a company with 28,000 US employees (85,000 globally) could collapse in four months. If anybody has information on offices that are not listed here, I'd like to hear from you. In particular, I am interested in learning what happened to the rest of the NYC office.

    Clients:

    This list is entirely too long to reproduce in this blog since Arthur Andersen had almost 2500 clients. In this case, I will rely on internet links and hope they do not die on me.

    http://www.accountingweb.com/cgi-bin/item.cgi?id=74745
    http://www.forbes.com/2002/03/13/0313andersen.html
    http://www.forbes.com/2002/06/28/0627andersen.html

    Collapse of Andersen Worldwide

    Defections of Andersen's global affiliates
    I would normally provide this information via a link, but I wanted the actual text documented here in case the link dies because this information is becoming increasingly difficult to find on the web.

    Argentina 4/16/02 Plans to merge with Ernst & Young
    Australia 3/28/02 Announces plans to merge with Ernst & Young
    Baltic States 4/15/02 Announces plans to merge with Ernst & Young
    Belgium 4/23/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Brazil 4/9/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Bulgaria 4/24/02 Announces plans to merge with Ernst & Young
    Canada 4/12/02 Announces deal to merge with Deloitte Touche Tohmatsu
    Chile 4/9/02 Announces plans to merge with Ernst & Young
    China 3/22/02 Announces plans to merge with PricewaterhouseCoopers
    Colombia 4/23/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Croatia 4/24/02 Announces plans to merge with Ernst & Young
    Czech Republic 4/24/02 Announces plans to merge with Ernst & Young
    France 4/16/02 Plans to merge with Ernst & Young
    Germany 4/24/02 Plans to merge with Ernst & Young
    Holland 4/24/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Hong Kong 3/22/02 Announces plans to merge with PricewaterhouseCoopers
    Hungary 4/24/02 Announces plans to merge with Ernst & Young
    India 5/4/02 Announces plans to merge with Ernst & Young
    Indonesia 4/14/02 Announces plans to merge with Ernst & Young
    Italy 4/23/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Japan 3/28/02 Announces plans to merge with KPMG
    Mexico 4/9/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Middle East 4/22/02 Announces plans to merge with PricewaterhouseCoopers
    Netherlands 4/22/02 Announces plans to merge with Deloitte Touche Tohmatsu
    New Zealand 3/28/02 Announces plans to merge with Ernst & Young
    Norway 4/9/02 Announces plans to merge with Ernst & Young
    Phillipines 4/24/02 Announces plans to merge with Ernst & Young
    Poland 4/9/02 Announces plans to merge with Ernst & Young
    Portugal 4/9/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Romania 4/24/02 Announces plans to merge with Ernst & Young
    Russia 3/22/02 Announces plans to merge with Ernst & Young
    Singapore 4/3/02 Announces plans to merge with Ernst & Young
    Slovakia 4/24/02 Announces plans to merge with Ernst & Young
    Slovenia 4/24/02 Announces plans to merge with Ernst & Young
    South Africa 4/11/02 Announces plans to merge with KPMG
    Spain 4/3/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Sweden 4/22/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Switzerland 4/17/02 Announces plans to merge with Ernst & Young
    Taiwan 4/11/02 Plans to merge with Deloitte,Touche Tohmatsu
    Thailand 4/3/02 Reaffirms plans to merge with KPMG
    United Kingdom 4/10/02 Announces plans to merge with Deloitte Touche Tohmatsu
    Vietnam 5/10/02 In discussions to merge with KPMG

    http://www.accountingweb.com/cgi-bin/item.cgi?id=76820