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Volatility from Vega – Why math models can’t predict the future

Guest post by Eric Worrall

How can we predict the climate, when we can’t even predict financial markets?

Subprime Housing Crash

US Subprime House Price Crash

Financial markets are a high stakes battle between teams of skilled traders, armed with powerful computers. [In a perfect market] The factors that affect market prices are well known, and for mathematicians, surprisingly simple to describe. Yet with all this underlying simplicity, traders don’t attempt to predict the future, because they know from bitter experience that predicting the future is futile. Instead, they use their models to gain a deeper understanding of the present.

Say you are trading financial options. Options are a right to buy or sell an underlying commodity (gold, shares in a company, tons of beef, whatever) at a future point in time, for an agreed price. The exact rules vary in different places, but essentially – your option gives you the right to buy an ounce of gold in one month, say,  for $1000.

If so, and the price of gold is $1,200 per ounce, then your option is worth $200, right?

Wrong. In one month, the price of gold might be $800, in which case your option is worthless – there is no point using the option to buy gold at $1,000, when you could simply buy it on the spot market for $800. Or in one month, the price of gold might be $1,400, in which case your option will be worth $400, double the $200 it would be worth if you exercised the option (activated the trade) at the current price of $1,200.

How do you price something based on a future price which you can’t foresee?

The answer is you try to estimate the likelihood of the price shifting significantly from its current value. You add an estimate of gold price volatility to your calculation, based on the current range of prices, how much the price of gold is jumping around in a day’s trade, versus the length of time left on the option (1 month).

Of course, there’s more to it that that. Instead of buying and holding the option, you could have put the money into a high interest bank account. So the interest you could have earned if you put the money into a savings account is part of the cost of owning the option – that has to be factored into the value of the option. And if you want to be really precise, you have to consider counterparty risk (the risk that the issuer of the option will go bust, and won’t honor the deal), market liquidity(whether there are enough buyers and sellers to ensure a “real” market, or whether the scarcity of market participants will allow big players to fix prices to maximise their profits at the expense of other participants), sovereign risk (the risk the government will step in and ruin your trade with hostile new laws), and the cost of making a trade (tax, market fees, your time, etc).

But I just said traders don’t use their models to predict the future, and isn’t what I described sounding an awful lot like predicting the future?

The point is, the model can’t tell you what the price of gold will be – it can only tell you what the price of gold might be, to give a range of outcomes with their probabilities as you see it.

So traders use their models to explore possibilities. To protect themselves from the $800 risk, they cover themselves by buying a complementary option – for example, they might buy the right to sell a large quantity of silver at $20 / ounce – the opposite kind of option to their right to buy gold option. The price of silver more or less tracks the price of gold, so buying a right to sell silver means that if the price of gold drops, rendering their gold option worthless, the price of silver will also most likely drop. If the trader gets the right deal when buying the silver option, the trader can still make a profit if the gold price (and the silver price) falls, by buying silver at a low price, and selling it at the locked in silver option price of $20. If the trader has done their job, in the event of a price drop, they will make enough profit from their silver trade to more than offset their loss on the now worthless gold option.

The skill of the trader is exploring the landscape of possibilities, to use the models to help discover paired complementary deals which can lock in a guaranteed profit, regardless of what happens to market prices.

Of course, real trading strategies are generally a lot more complicated than this simplistic example. With all the competing teams of highly skilled traders crawling over the possibility landscape all hours of the day or night, the opportunity for a profit from a deal that simple should disappear before it properly had a chance to manifest.

My point is, the models are not used to predict the future, they are used to explore the landscape of future possibilities, to discover ways to lock in guaranteed profits, and to provide alerts if the portfolio of options and other instruments has an unexpected weakness – to identify scenarios in which traders’ portfolios become exposed to a serious risk of loss, so they can patch the holes in their positions before they become a problem.

Nobody is daft enough in the financial world to believe they can predict the future. The models are only used to answer “what if” questions, to help close loopholes in their complex web of trades which might lead to dangerous losses.

In addition, traders are acutely aware of the limitations of their models. For example, from the limited viewpoint of mainstream financial models, the subprime mortgage crisis occurred because the boundary conditions of the financial models were breached. One of the underlying assumptions of most financial models is that you can always buy and sell your financial instruments (options, stock, gold, etc), but in times of extreme crisis, the market sometimes freezes up – nobody wants to touch your worthless paper with a barge pole. In these conditions, the model description of reality breaks down, and the door is opened to uncontrolled losses.

The big difference between climate science and financial markets, is that the best PhDs work in financial markets, potentially earning millions of dollars per year in bonuses, helping big banks lock in profits and avoid risk. The financial modellers know the limitations of modelling – most of them know you can’t predict the future with a mathematical model, so they don’t even try. The limits of models is a lesson they have all learned through bitter experience, while watching the occasional delusional colleague take a fall. Even in financial markets, skilled scientists sometimes become seduced by the illusion of model predictive skill, before being wiped out when the markets unexpectedly turn against them.

By contrast, climate modellers claim their models have predictive skill – because there is no reality check to correct this delusion. When the model failure is obvious, such as the growing divergence between model predictions and observed temperatures, there is no penalty for failure. Climate modellers have the freedom to claim their nonsense is still valid, even in the face of overwhelming evidence that it is not. There are no groups of angry shareholders in climate academia, challenging the mistakes of modellers, demanding that failed or delusional modellers be fired from their jobs.

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