If you'd like some non-real-time insight into the London Whale, may I highly recommend this oral history, by Edinburgh sociologists Donald MacKenzie and Taylor Spears, of how investment banks came to price and trade and hedge things like the index CDS that the Whale dabbled in? It made me tear up a little. It is let's say somewhat technical but it's not really about math or derivatives, it's about how people experience their lives in derivatives departments of investment banks.
The main discussion is about the relationship between certain derivative pricing formulas and the credit crisis, and in particular about why ratings agencies did a bad job of rating asset-backed CDOs. The authors attribute these mis-ratings to a cultural problem, in which the people building and rather ABS CDOs were credit-analyst banker type rather than quant types who derive their views from market prices and efficient market assumptions:
In the major investment banks, some analysis of ABS CDOs (beyond simply checking desired ratings) was conducted, but in most cases very little by the standards of the culture of no-arbitrage modelling. ABS CDOs often fell outside the remit of the derivatives departments of those banks. ... As noted, no-arbitrage modelling extracts martingale or risk-neutral probabilities from patterns of market prices. Goldman aside, this style of modelling – which is what the interviewee meant by ‘quanting’ – was, as far as we can discover, simply not applied to ABS CDOs. Rating agencies did model ABS CDOs, but rating agencies do not work with martingale probabilities: rather, they seek to estimate actual probabilities of default, and to do so they use the historical records of defaults, not price patterns. In the case of subprime mortgage-backed securities, which dated at most only from the 1990s, such records encompassed only one relatively mild recession and almost continuously rising house prices. Unfortunately – as we now know only too well – when those conditions changed, such securities, and the mortgage borrowers on whom they were based, began to behave quite differently.
Because this is an oral history of quants, it comes from a quant perspective; the quants think that their no-arbitrage random-walk models based on implications of market prices are better than cash flow models based on historical data. Part of that is that their models are disciplined by the market: you can't say "well we think none of our loans will default because none of them have in the past" if the market is pricing your loans as though they'll default (under some mathematically sensible method of translating market prices into implications about default). But part of it is also that quant modelers have an intellectual culture of wanting to get things right rather than a culture of wanting to get a certain result. This tickled me:
Although [correlation modeling] techniques might originally have been proprietary, they quickly became common knowledge amongst investment bank quants. People moved from bank to bank, carrying knowledge of models with them, and quants – typically educated to PhD level or beyond – retained something of an academic habitus, talking about their work to their peers, and seeking opportunities to publish it.
Isn't that sort of cute? They'll happily share formulas with competitors because it's not about the money, it's about doing science. Money science.
Now it's safe to say that JPMorgan's CIO was stuffed with derivatives traders and quants, but it does seem as though some of that culture was missing and might have been useful. The CIO had an ill-tested VaR model that seems to have been specific to it, it marked its positions differently from the rest of the bank, and it kept its positions secret from the investment bank. When you get away from a scientific culture of discussing your theories openly and testing them against reality, you get ... well, in this case, you get losses.
There's more worth reading here; in particular, the paper gives a good sense of how credit derivatives modeling and hedging is at least in part about market convention rather than mathematically provable correct hedges. For instance:
[One] quant, however, went on immediately to ‘other’ the Gaussian copula base correlation model: ‘The bad thing is it’s not a model.’ That statement indicates a second source of dissatisfaction with the Gaussian copula, at least amongst the quants interviewed (traders, etc., typically did not give voice to this second source). All these quants were perfectly well aware of the ad hoc fixes that were necessary to keep practices involving the Black-Scholes-Merton model ‘working’. These, however, were fixes to what they saw as a good model, indeed the paradigmatic good model: one in which prices were imposed by arbitrage, and in which there was a well-defined risk-neutral or martingale measure. The quant who told us that the Gaussian copula was ‘not a model’ went on to explain what he meant: ‘it doesn’t satisfy the law of one price [in other words, the absence of arbitrage opportunities]. It ... can give you inconsistencies and arbitrages very easily. You’re not computing values ... as expectations under some well-defined measure.’
In other words: you can plug market data into your model, and your model will tell you how to hedge the thing that you have. It will tell you how much money you'll make if interest rates change by this much, or credit risk changes by that much, or volatility goes up or correlation goes down or whatever. It's just that those outputs won't necessarily be right: they'll be right under the terms of the model, but the model doesn't provably replicate the real world. Everyone has more or less similar models - what with all their quants talking to each other and whatnot - but that just means that their models replicate a useful convention, not that they replicate reality in all circumstances.
I don't know enough about the Whale's trades to know how relevant that is - most people seem to think he was trading in fairly standardized things and was whacked by liquidity problems, not straight-up mis-hedging - but it's worth throwing into the mix. One thing lots of people and senators like to say is "if you have a hedge, and you lose $2 billion on the hedge, shouldn't you have made $2 billion somewhere else?" And the answer is no, for lots of reasons, but one of them is that you don't know what reality will be until it happens. The Whale maybe - though probably not! - hedged his trades appropriately for his model; he just didn't hedge them appropriately for what actually happened.