Principal Component Analysis (PCA) is a common and popular tool for the analysis of financial market data, such as implied volatility smiles, interest rate curves and commodity future curves. We provide a critical view on PCA analysis and the corresponding results from empirical literature. In particular, it will be shown how PCA can produce patterned loading vectors if the correlation matrix just happens to belong to a particular matrix class. We will also provide evidence why the level factor is the dominating factor in virtually all empirical PCA analyses and question whether this reflects the true dynamics. In addition, we show how artifacts can be generated by PCA and how problematic the interpretation of PCA results can be, if a system is indeed driven by level, slope and curvature dynamics.

It is well known that prices of foreign exchange options systematically diverge from those consistent with the Garman-Kohlhagen and Black option-pricing models. The implied volatilities of options on the same underlying foreign exchange rate differ across strike prices and terms to expiration. When implied volatilities for the same expiration are plotted versus strike prices and a corresponding function relationship is determined, the result is a convex pattern, which is commonly known as a smile. A logical first step in formulating a theory to explain this phenomenon would be to better understand the empirical record of implied volatility smiles. If time invariant regularities are discovered, this will provide a benchmark to compare implied volatility smiles associated with alternative models. In this article, we summarize the empirical record of implied volatility smiles for four alternative currency pairs: British pound, Swiss franc, Deutsche mark, and Japanese yen all versus the US dollar. The time period of analysis is from 1985 to 2000 and it considers options on futures traded at the Chicago Mercantile Exchange. This article then considers models that have been proposed to explain the existence of implied volatility smiles. Neither stochastic volatility model nor jump-diffusion models are able to generate similar implied volatility smile dynamics. An alternative model that combines both stochastic volatility and jump processes appears to explain the smile surfaces better. While the dynamics are matched, the smiles are not as extreme (in curvature) as the empirical smiles. The differences between the empirical and model generated smile patterns suggest a systematic and substantive negative risk premium. Finally, transaction costs are added to the best fitting theoretical model and the risk premium is substantially reduced. We conclude that both an alternative process for foreign exchange returns and transaction costs explain why implied volatility smiles for options on foreign exchange exist. Keywords: implied volatility smiles; stochastic volatility; jump diffusion; transaction costs

We find an anomaly for traded and non-traded period returns for major non-US stock markets. Returns were significantly negative over trading periods and positive over non-traded periods, while for US stock markets, both non-traded and traded period returns were positive. This anomaly appears to be due to differences in regulatory risk management requirements for equity derivative market-makers. The introduction of Basle I based capital requirements appears to have amplified the anomaly.

This paper examines whether the favorite/long-shot bias that has been found in gambling markets (particularly horse racing) applies to options markets. We investigate this for the S&P 500 futures, the FTSE 100 futures and the British Pound/US Dollar futures for the seventeen plus years from March 1985 to September 2002. Calls on the FTSE 100 with three months to expiration display a relationship between probabilities and average returns that are very similar to the favorite/long-shot bias in horse racing markets pointed out by Ali (1979), Snyder (1978) and Ziemba & Hausch (1986). There are slight profits from deep in-the-money calls on the S&P 500 futures and increasingly greater losses as the call options are out-of-the-money. For 3 month calls on the FTSE 100 futures, the favorite bias is not found, but a significant long-shot bias has existed for the deepest out of the money options. For call options in both markets, for the one month horizon, only a longshot bias is found. For the put options on both markets, and for both 3 month and 1 month horizons, we find evidence consistent with the hypothesis that investors tend to overpay for all put options as an expected cost of insurance. The patterns of average returns is analogous to the favorite/longshot bias in racing markets. For options on the British Pound/US Dollar, there does not appear to be any systematic favorite/long-shot bias for either calls or puts.

Prices of foreign exchange options systematically diverge from those consistent with several previous option pricing models. This paper examines whether alternative models better explaining the empirical dynamics of the foreign exchange futures markets can yield implied volatility surfaces similar to those observed for options on Foreign Exchange futures. The most suitable alternative models include jumps and stochastic volatility. The inclusion of both these factors introduces unspanned sources of risk and therefore, the martingale measure will not necessarily be unique. However, it is not the objective of this research to propose which martingale measure is optimal; the aim, instead, is to gain a deeper understanding of the properties (and particularly the order of magnitude) of the risk premium. This is done by choosing a feasible martingale measure (based upon the no arbitrage condition), assuming no market price of jump or stochastic volatility risks, and price options under this measure. The implied volatility biases from model-based option prices are then compared to the actual implied volatility surfaces for options on these markets. The systematic and substantive differences that are found suggest a negative risk premium, which is a relatively more important (and universal) component in FX option pricing than previously reported. Furthermore, it appears that the relative risk premium across strike price and time is similar across four foreign exchange options markets. This may imply that some systematic mechanism causes the risk premium in these markets.

The introduction of unspanned sources of risk (and frictions) implies that option prices include a risk premium. Prima facie evidence of the existence of risk premia in option prices is contained in the implied volatility smile patterns reported in the literature. This article isolates the risk premium (defined as the simple difference between estimated and observed option prices) on options on U.K. Gilts, German Bunds, and U.S. Treasury bond futures using models that include price jumps and stochastic volatility. This study finds that single and multi‐factor stochastic volatility models with jumps may explain the empirical regularities observed in bond futures. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:169–215, 2003

A number of financial regulators have suggested that risk neutral densities associated with options markets could provide useful indicators of future market turbulence. Critical to this assumption is that such RNDs should provide an unbiased forecast of realised probability density functions. To date, this assumption has not been fully examined. In this research, we test the ability of RNDs for options on the S&P 500 and the British Pound / US Dollar to predict future probability densities. We consider four approaches to estimate the RNDs, which are consistent with approaches proposed and used by financial regulators. We also provide a number of new testing procedures to assess the efficiency and unbiasedness of the forecasts. These tests provide more power than the usual Komolgorov/Smirnov tests. Using non-overlapping quarterly data from the mid 1980s to 2001, we find that we can reject the hypothesis that the RNDs for both the S&P 500 and British Pounds are unbiased forecasts. Even with a limited number of observations, the tests are powerful enough to allow rejection. However, when an adjustment for the risk premium is made, the results become more controversial. Depending on the nature of the adjustment, we can or cannot reject the accuracy of the adjusted implied densities. When a power utility adjustment is made, like Bliss and Panigirtzoglou (2001), we are unable to reject the hypothesis that RNDs are unbiased forecasts of realised densities. Overall, our results tend to support the conclusions of Shiratsuka (2001), that unadjusted RNDs should not be used by financial regulators as financial indicators, and that such use could prove counterproductive; actually increasing future market turbulence rather than alleviating it.

Determining the volatility of the underlying asset is perhaps the single most important issue in practical option pricing. Many forecasting techniques exist, using historical returns data, implied volatility parameters from observed option prices, normal and non-normal probability distributions and more complex stochastic processes, non-market information, and more. But one of the most important aspects of the problem is seldom formally examined: estimation error. Even under ideal conditions, both measured volatility in a historical sample of returns and future realized volatility over an option's lifetime are subject to sampling error. Shorter samples have larger estimation error. A “volatility cone” is a plot of the range of volatilities within a fixed probability band around the true parameter, as a function of sample length. In this article, Hodges and Tompkins examine volatility cones under different assumptions about the true returns process. One important contribution is a bias correction for estimation using an overlapping data sample that produces unbiased estimates and a substantial gain in efficiency. They then apply the analysis empirically to S&P 500 index futures returns and conclude that the observed volatility behavior is consistent with a stochastic volatility process that has fat-tailed innovations.

The depth and breadth of the market for contingent claims, including exotic options, has expanded dramatically. Regulators have expressed concern regarding the risks of exotics to the financial system, due to the difficulty of hedging these instruments. Recent literature focuses on the difficulties in hedging exotic options, e.g., liquidity risk and other violations of the standard Black‐Scholes model. This article provides insight into hedging problems associated with exotic options: 1) hedging in discrete versus continuous time, 2) transaction costs, 3) stochastic volatility, and 4) non‐constant correlation. The author applies simulation analysis of these problems to a variety of exotics, including Asian options, barrier options, look‐back options, and quanto options.

An installment option is a European option in which the premium, instead of being paid up-front, is paid in a series of installments. If all installments are paid the holder receives the exercise value, but the holder has the right to terminate payments on any payment date, in which case the option lapses with no further payments on either side. We discuss pricing and risk management for these options, in particular the use of static hedges to obtain both no-arbitrage pricing bounds and very effective hedging strategies with almost no vega risk.

It is well known that the implied volatilities of options on the same underlying asset differ across strike prices and terms to expiration. However, the reason for this remains unclear. Before the development of theory to explain this phenomenon, it may be helpful to better understand the empirical record of implied volatility surfaces. If regularities are discovered which are stable over time, this may aid the development of theories to explain implied volatility surfaces and provide a means to test alternative models. This paper identifies these regularities and subsequent research will examine the implications of these results. While a number of papers have examined individual option markets and identified smile patterns, it is not clear whether the conclusions found are based upon idiosyncrasies of a particular market or more generally apply to options in other markets. This research fills this gap in the literature by examining sixteen options markets on financial futures (comprising four asset classes) and compares the smile patterns across markets. Furthermore, this analysis considers a longer period of analysis than previously examined in the literature. This allows assessment of the stability of the implied volatility patterns for a variety of subperiods and testing of models outside of sample.

This study examined whether the inclusion of an appropriate stochastic volatility that captures key distributional and volatility facets of stock. index futures is sufficient to explain implied volatility smiles for options on these markets. I considered two variants of stochastic volatility models related to Heston (1993). These models are differentiated by alternative normal or nonnormal processes driving log-price increments. For four stock index futures markets examined, models including a negatively correlated stochastic volatility process with nonnormal price innovations performed best within the total sample period and for subperiods, Using these optimal stochastic volatility models, I determined the prices of European options. When comparing simulated and actual options prices for these markets, I found substantial differences. This suggests that the inclusion of a stochastic volatility process consistent with the objective process alone is insufficient to explain the existence of smiles. (C) 2001 John Wiley & Sons, Inc.

An instalment option is a European option in which the premium, instead of being paid up-front, is paid in a series of instalments. If all instalments are paid the holder receives the exercise value, but the holder has the right to terminate payments on any payment date, in which case the option lapses with no further payments on either side. We discuss pricing and risk management for these options, in particular the use of static hedges, and also study a continuous-time limit in which premium is paid at a certain rate per unit time.

Kirklin, John W. M.D.; Openshaw, Calvin R. M.D.; Tompkins, Robert G. M.D Author Information