Читать книгу FX Option Performance - Peter Billington - Страница 6

Let's be honest, there is no shortage of books on Foreign Exchange (FX) options. There are plenty of places, online and on paper, where you can read about how to value FX options and associated derivatives. You can learn about the history of the market and how different valuation models work. Regular surveys will inform you about the size and liquidity of this vast market, and who trades it.

This is not what this book is about. This is about what happens to an option once it is bought or sold. It is about whether the owner of an option had cause to be happy with their purchase. It is about whether FX options deliver value to their buyers.

In the financial markets, there is huge and detailed effort made to value contracts accurately at the start of their lives. Some decades ago this work was begun in earnest when Black and Scholes published their famous paper [1]. Perhaps indeed we could say it started in 1900 when Bachelier derived a very similar model [2] though this was not followed up on. But, in general, quantitative researchers in the markets and in universities spend long hours to devise ways of correctly valuing complex contingent deals under sets of assumptions which make the mathematics possible.

But are these assumptions right, i.e. over time, do they turn out to have been correct? Bizarrely, they do not have to have been ‘correct’ to continue to be used; later in the book we will give some detailed examples of assumptions that turn out to be manifestly incorrect. For an option, we can say that in an efficient (‘correctly priced’) market, on average, we would expect an option to pay back the money it cost in the first place – less costs, of course.1 In this book we will use terms like ‘mispriced’ or ‘misvalued’ to indicate that the average payoff of the option is significantly different from the average premium paid to own the option.2

That this is not always the case may be surprising. But that options can be systematically ‘cheap’ or ‘expensive’ throughout the history of the market, depending on their precise nature, is even more surprising, and should be of significant interest to many different areas of the finance community.

Why is this not widely known? In part it is simply the focus of the market participants. Most trading desks will operate on a daily mark to market P/L with drawdown and stop-loss limits.3 Another way of putting this is that they will want to make money all or most days, with limited risk. So the timescale and nature of a trading desk dictates that the price of a contract ‘now’ is the focus of the market. Further, depending on the hedging strategy and how the option is traded, different end results can be seen. So pricing the contract ‘now’ is in many ways simpler than trying to model an option's performance. Later, we will discuss in detail how a desk manages its portfolio of options to make money, but we may summarise it now by saying that, ideally, deals are done and hedged so that a small but almost riskless profit is locked in almost immediately. After that, the combination of the deal and its offsetting hedges should be almost immune to market movements – so a systematic tendency for deals to be cheap or expensive over time may well not be noticed on a trading desk, as long as they can be hedged at a profit. The situation is complicated by the fact that a perfect hedge is rarely available, combined with the fact that a trading desk may want to have a ‘position’ – a sensitivity to market movements – when they believe that certain moves are likely to occur.

But the other reason that the long-term mispricing of parts of the FX option markets is not well known is that FX options are a young market! Before one can say that a contract is generally cheap or expensive, one needs to observe it under a variety of circumstances. To say that 12M options bought in 2006, when market confidence was high and volatility low, were cheap because they paid out large sums in 2007, when confidence was greatly shaken and volatilities had begun a very sharp rise, would be to look at a particular case which does not represent the generality of market conditions. It is only really now, with widely available option data available going back to the 1990s, that we can say we have information available for a wide variety of market regimes, and importantly, the transitions between these regimes. We will discuss exactly what data are needed and available in the next chapter, but for now we may say that for most liquid currencies there will be perhaps 20 years of daily data available, with longer time series or higher frequencies available in some cases.

So, we are now in a position to say whether FX options have performed well or badly for their buyers and sellers. We can take a day in the past, collect all the data needed to calculate the cost of the option and look ahead to the payoff of the option at expiry to compare the two. We can tell, on average and for different time periods, whether the options have had the correct price.

If they have not had the correct price – and the fact that there is a book being written on the subject implies that this has been the case at least some of the time! – then the situation becomes much more interesting. Why did the market appear to be inefficient? Was there a good reason? Is it connected to the way options are used, the way they are hedged, differences in demand and supply? We will show that indeed, in different ways, the payoff and the cost of the options have differed significantly throughout the history of the market, and moreover these differences have been systematic, repeated in different currency pairs and market regimes.4