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"A derivative is like a razor, you can use it to shave
yourself, or you can use you it to commit suicide."
James Morgan - Financial Times
Today's derivative products differ from their Jurassic ancestors by virtue of the fact that they are far more complex and valued mathematically using advanced computers instead of the back of the envelope approach. The derivatives industry has revolutionized the financial word, examples of some of the latest trends and developments being:
Exotic derivative products are now becoming the fastest growing area within the derivative markets. This has had a profound impact on the derivatives industry and is one of the main reasons why derivative pricing models have become a hotbed of research and development.
The discovery of new risks in areas long considered stable has triggered a search for more effective tools in the management of risk, allowing institutions to calculate Value at risk (VaR) and more recently, credit VaR more accurately.
The dissemination of more real-time generated theoretical derivative prices by global exchanges and more recently real-time generated theoretical implied volatility values by some quote vendors are empowering investors with a greater degree of price transparency within the derivative markets. In addition, dissemination of stock futures and sector based derivatives are helping to increase the profile of exchange traded derivatives.
The interdisciplinary subject of financial engineering has had a profound impact on the derivative industry, and for this reason most of issues above are discussed from a financial engineering perspective.
More sophisticated derivative pricing models
"A trader who slavishly uses a model to make every trading
decision is heading for disaster. Only a trader who fully
understands what a model can and cannot do will be able to make the
model his servant rather than his master. "
Sheldon Natenberg - Derivatives Trader
Many complex derivative products such as over the counter (OTC) exotics, tailored specifically for financial institutions to meet the needs of their clients, have complex payoff profiles that can not be accurately valued by traditional models. In addition vanilla and OTC-style derivatives on listed exchanges, perceived to be high volume and low margin, need to be priced accurately, as many exchanges are utilizing pricing models to generate and disseminate real-time theoretical values.
More realistic assumptions
Traditional pricing models are based on simplified assumptions, such as no transaction costs, prices are assumed to follow a geometric random walk, that there is infinite liquidity. In the real world however, some of these assumptions are seriously challenged, and theoretical evaluation using such models can be grossly inaccurate. Financial engineers affectionately known as 'rocket scientists' are developing model algorithms encompassing new methodologies, in an attempt to model the price changes of the underlying asset in a more realistic way. As a consequence, derivative models are becoming increasingly more sophisticated, and more complex mathematically. In a generalized Black and Scholes world, one of the key arguments leading to their pricing formulas is based on the idea that a portfolio needs to be rebalanced frequently in order to remain riskless. However recent theories considers option pricing when dynamic portfolios are discretely rebalanced, and is based on the idea that traders in practice hedge their portfolios at random times, and more specifically at each time the underlying asset has changed by a given percentage amount.
The new generation
OTC derivatives, especially exotics and interest rate derivative products, have been the catalyst for many of the advances in derivative pricing. The modeling of the term structure has become increasingly popular, and for this reason both equilibrium and no-arbitrage term structure consistent models are proving to be very popular. In particular the no-arbitrage single-factor Black, Derman and Toy (BDT) is properly the most widely used model to price interest rate and bond derivatives, by virtue that it is designed to be exactly consistent with the observed term structure of interest rates.
Financial engineers are developing a host of advanced analytical derivative pricing models offering fast, closed-form evaluation of many complex derivatives. Analytic models are popular with practitioners for a variety of reasons: they are computationally efficient, offer reasonable analytical tractability and can be calibrated to a wide set of derivative prices with relative ease. Unfortunately they are not as versatile as their numerical based relatives, by virtue of the fact that many complex derivatives such as American-style exercise options or options whose payoff depend on multiple stochastic factors (e.g. multiple asset options) have no analytical formula, and can only be priced using numerical based models.
The rapid evolution of financial engineering now encompassing many more aspects of numerical analysis, and computer science, together with increased optimization of both old and new numerical techniques has paved the way for the development of a new generation of numerical models/algorithms providing quicker, more accurate and robust derivative pricing. Indeed they model the term structure very accurately, allow the stochastic modeling of interest rates and volatility, and provide in general better analytical tractability than analytical models. This is by virtue of the fact that analytical models assume that the underlying price is monitored on a continuous basis whereas in real life, observation frequency is observed at discrete points.
In particular, improvements in the efficiency of numerical techniques such as generalized Monte Carlo simulation (MCS), using quasi-random numbers and hedge based control variates resulting in faster convergence and variance reduction, have made MCS methods very popular amongst practitioners and academics by virtue of their flexibility in pricing many types of complex derivatives, especially option derivatives under multiple stochastic factors such as stochastic interest rate/volatility, and options whose payoff depends on both the path followed and final value of the underlying asset. MCS methods are still computationally intensive, but generally prove to be more efficient than other numerical methods for an increased number of stochastic variables.
Another numerical method receiving much attention and gaining widespread popularity is implied trees. Essentially the idea behind the implied tree model is to extract important information (the market consensus regarding future expectations) from liquid options with different strikes and maturities, to build an arbitrage-free model. Implied trees are really a generalization of binomial and trinomial trees; in addition they assume that the volatility measure is a function of both asset price and time.
The new generation of derivative models do provide better pricing. However, both market practitioners and academics are well aware that these models can be highly sensitive, and in the absence of reasonably accurate input information can indeed be known to generate less accurate results than traditional models. As a consequence methods of extracting and generating more accurate input information are being examined. In the case of no-arbitrage models the term structure observed is an input, thus it is crucial to have accurate zero-coupon volatilities when using for example the BDT model to price bond derivatives.
All pricing models are based on probability theory. They cannot be expected to explain everything, nor can the values they generate be taken to be definitive. At best they provide good benchmarks. Indeed we should never forget that so-called 'model arbitrage' resulted in mammoth losses by some of the giants in the investment banking world during the last decade. Peter L. Bernstein, author of the worldwide bestseller 'Against The Gods' says, "It is one thing to set up a mathematical model that appears to explain everything. But when we face the struggle of daily life, of constant trial and error, the ambiguity of the facts as well as the power of the human heartbeat can obliterate the model in short order."
Better risk systems
"The optimal number of bank failures is not
zero."
Alan Greenspan - Federal Reserve Board Chairman
The need for more sophisticated risk systems providing for better financial risk management has been increasingly recognized over the last several years. Derivative products are complex, making their risk management and thus their regulation far more difficult than other financial instruments. After the debacle of LTCM, there has been a drive by central banks globally for greater transparency of market participant's risk. Banks have internal value at risk (VaR) calculators to evaluate regulatory capital to support their trading books. All pricing models used for VaR calculations require approval by an approved regulating body, prior to their official status of being licensed to capture risk.
Stressed market scenarios, such as the current Latin American crisis where the Argentine currency has come under severe pressure due to political instability, compounded by weak economic activity or the failure by Japan's government, corporations and banks in measuring and managing their risk, present new challenges. Risk systems are catering for more worst-case scenarios than ever before, as catastrophic losses are not as rare as once thought, forcing institutions to perform what is known as 'stress testing'- an estimated measure of the performance of the portfolio under extreme market conditions.
The discovery of new techniques and use of sophisticated pricing models for evaluating risk has provided institutions with better insight in identifying the sources of market risk, leading to a better understanding and analysis of how their own risk profiles may evolve over time in terms of profit and loss variations.
Although new methodologies provide new insights, it is very difficult to establish how accurate they will be, as one can not prove this by mathematics. As a consequence risk managers can only assess the impact of implementing new methodologies by examining the results generated by their risk systems over time. Hopefully, valuable lessons learnt from previous trading disasters will result in better risk systems been developed encompassing modern portfolio risk management techniques such as stress testing, VaR and more recently credit VaR.
Many institutions are ensuring that their front, middle, and back offices are utilizing the same pricing models, as this is the only way to accurately assess both the economic value and risk of the trades. In particular, firms are giving serious consideration to the applicability of using various modeling techniques and pricing models in risk management. As a consequence, numerical techniques such as Monte Carlo simulation are being used in assessing estimates of the possible 'model error' in using a particular modeling approach to analyse certain types of risk, Monte Carlo simulation seems to be the preferred choice for many institutions due to the flexibility of the method for pricing many types of derivatives, as it allows for the incorporation of more realistic underlying price processes, such as jumps in asset prices.
As with all areas of financial engineering, faster computers have helped to escalate the development of computational methods providing many of today's tools required for sophisticated risk analysis. The benefits are clearly visible, one example of this being how risk systems are able to perform large-scale data compression of complex portfolios for quicker VaR calculations.
Stochastic programming, concerned with optimal portfolio selection and the generation of future risk factors based on a set of risk attitudes, and linear programming, a highly developed area of constrained optimization, are two areas of research that have contributed significantly to the development of the new generation of advanced risk systems offering quicker and more sophisticated evaluation of portfolio risk.
These include advanced portfolio stress testing techniques, which help institutions to calculate portfolio risk measures under extreme conditions more easily. Bayesian probability simulation and extreme value theory are two areas of current research attracting much attention. They are helping financial engineers to perform sophisticated modeling of portfolio risk under stressed market scenarios, catering even for catastrophic events.
More interaction between all parties involved In the risk management process (i.e. traders, risk managers, financial engineers and regulators) has resulted in the more effective management of risk and in the development of more robust risk systems, which can mean lower regulatory capital for the bank. The better risk systems are in capturing, monitoring and analyzing the risk of the firm, the better the firm will gauge its risk capital requirements. Although risk management systems are continuously been enhanced, one should never forget however that the mathematically driven apparatus of modern risk management is based on probability theory, and thus risk is never fully removed. New techniques provide new insights, not guarantees. However, firms that have good management systems in place are deemed less likely to fail or become a regulatory embarrassment.
More global dissemination of derivative prices
Global exchanges and some quote vendors are using price generation systems, LIFFE autoquote being an example, to generate and disseminate up-to-date indicative derivative theoretical prices, offering all users a price discovery mechanism to better evaluate the risk-reward profiles of a particular trade.
Helping market liquidity & efficiency
"Markets look a lot less efficient from the banks of the
Hudson than the banks of the Charles."
The late Fisher Black
Price generation systems are helping to increase liquidity and efficiency in some markets for a number of reasons, some of these being:
- Enabling up-to-date option prices to be disseminated globally throughout the business day, regardless of whether the derivative instrument has traded.
- Bid/offer spreads generated being centered around a theoretical fair value for most strikes of an option series, helping to police some of the ridiculous ('leg-me-over') prices that small traders sometimes get quoted by the market.
- Ability to generate new bid/ask prices in response to market changes, providing an indication of the price level at which a trade is likely to be executed.
- Offering independent validation and thereby increasing price transparency.
- Monitoring electronic exchange traded systems
Some derivative exchanges are using theoretical derivative price generation functionality within their own electronic automated trading systems (e.g. LIFFE Connect) allowing for more price transparency, flexibility, and better price execution. System generated bid/ask spreads help to alert exchange officials to any sudden changes in the market. If the market receives an order outside the inner spread the automated system alerts the trader to this fact, if however an order is entered into the market breaching the outer bid/ask spread, then the order can either be rejected and/or the exchange officials notified of possible changing market conditions, and maybe to adjust some of the system inputs e.g. the market may be using a different volatility skew.
Dissemination off implied volatilities
Using option market prices, some quote vendors are calculating and disseminating real-time option implied volatilities, offering users important information regarding the market consensus of future underlying asset price volatility, providing a good basis for strategy selection. Problems can arise however when there are no market prices, or if implied volatility has been generated from a minimum spread, not centered around a theoretical fair value. Concentration is normally centered around the 'at the money' (ATM) strikes, as these are more in line with what the market consensus perceives to be the 'real' volatility. The fact that both exchanges and some quote vendors are publishing implied volatility values allows institutions to create robust data sets enabling them to measure risk independently to that provided by the front office.
Dissemination of stock futures & sector based derivative values
Stock futures and sector based derivatives are becoming one of the fastest growing areas in the derivative industry, providing investors and fund managers with greater flexibility by helping to increase and decrease exposure in underlying equities markets. The current boom means that mandates are now focusing on managing sectors rather than regions, as recent studies have shown there is greater volatility looking at sectors in comparison to country factors, This should strike us as intuitive with the integration that the world economy has seen over recent decades. The current trend seems to indicate that more trading desks are being transformed to sector desks rather than regional desks, as financial institutions seem to be in the process of rotating their traders so that they have for example, a global technology trading group, rather than a Japan, EU and US trading group. Exchange traded funds (ETFs) are enjoying rapid growth, helping investors build diversified portfolios with relatively low tracking error. Sector based futures and ETFs will extend the risk manager's arsenal of available tools that will allow more efficient hedging of the portfolio's unsystematic risk. Asset allocations and portfolio managers will be able to quickly create an overlay strategy that enables the repositioning of portfolios so that they tilt on sectors.
The recent launch of universal stock futures by the LIFFE exchange in response to substantial member demand will provide many trading opportunities for investors. In addition LIFFE is planning to disseminate theoretical stock future prices in the not so distant future.
Peach International is a software consultancy based in Henley-On-Thames specialising in derivative pricing software.
