Thorsten Lehnert

Explaining smiles: GARCH option pricing with conditional leptokurtosis and skewness

Implied volatilities from equity options invariably show patterns that are inconsistent with lognormality. Time variation in volatility is an obvious, and widely explored, potential explanation. One approach has been to assume an explicit model of the volatility dynamics, typically a GARCH process. Another has been to compute an implied volatility smile/skew from option prices and then to model its behavior. This article presents a comparison of three such approaches using a large set of DAX option prices to imply out the model parameters. The “ad hoc Black-Scholes” technique of Dumas, Fleming, and Whaley fits an empirical volatility smile, and the model of Heston and Nandi produces GARCH volatilities in a closed-form framework. The third model is a very flexible GARCH variant: an EGARCH model with disturbances drawn from a GED process. This last model allows an asymmetric volatility response to positive and negative return shocks, plus additional skewness and kurtosis beyond that of standard GARCH, coming from the non-normal distribution of return shocks. In both in-sample and out-of-sample analysis, the EGARCH-GED model produced the best fit to observed option prices.

Measuring Financial Contagion Using Time-Aligned Data : The Importance of the Speed of Transmission of Shocks

This paper presents a new empirical approach to address the problem of trading time differences between markets in studies of financial contagion. In contrast to end‐of‐business‐day data common to most contagion studies, we employ price observations, which are exactly aligned in time to correct for time‐zone and end‐of‐business‐day differences between markets. Additionally, we allow for time lags between price observations in order to test the assumption that the shock is not immediately transmitted from one market to the other. Our analysis of the financial turmoil surrounding the Asian crisis reveals that such corrections have an important bearing on the evidence for contagion, independent of the methodology employed. Using a correlation‐based test, we find more contagion the faster we assume the shock to be transmitted.

Loss Functions in Option Valuation: A Framework for Selection

In this paper, we investigate the importance of different loss functions when estimating and evaluating option pricing models. Our analysis shows that it is important to take into account parameter uncertainty, because this leads to uncertainty in the predicted option price. We illustrate the effect on the out-of-sample pricing errors in an application of the ad hoc Black-Scholes model to DAX index options. We confirm the empirical results of Christoffersen and Jacobs (Christoffersen, P., K. Jacobs. 2004. The importance of the loss function in option valuation. J. Financial Econom.72 291--318) and find strong evidence for their conjecture that the squared pricing error criterion may serve as a general-purpose loss function in option valuation applications. At the same time, we provide a first yardstick to evaluate the adequacy of the loss function. This is accomplished through a data-driven method to deliver not just a point estimate of the root mean squared pricing error, but a distribution.

On the Relationship between Credit Rating Announcements and Credit Default Swap Spreads for European Reference Entities

Previous research suggests that credit rating announcements by Moody’s are anticipated by participants in the credit default swap market. In particular, it is argued that downgrades and negative outlook reports do not contain significant information, but there seems to be anticipation of both types of ratings announcements. In this paper, we examine credit default swap spread changes conditional on a ratings announcement for European reference entities. For our sample of J.P. Morgan Trak-X Europe companies, we find evidence that downgrades and negative outlooks do contain significant information, but find no evidence that announcements are anticipated by participants in the credit default swap market. Additionally, we find evidence that CDS spreads initially do not fully adjust to the information in positive or stable outlook reports resulting in significant post-announcement day effects.

Investor sentiment, mutual fund flows and its impact on returns and volatility

Purpose – The purpose of this paper is to investigate the impact of individual investor sentiment on the return process and conditional volatility of three main US market indices (Dow Jones Industrial Average, S&P500 and Nasdaq100). Individual investor sentiment is measured by aggregate money flows in and out of domestically oriented US mutual funds.Design/methodology/approach – A generalised autoregressive conditional heteroscedasticity (GARCH)‐in‐mean specification is used, where our measure for individual sentiment enters the mean and conditional volatility equation.Findings – For a sample period of six years (February 1998 until December 2004), we find that sentiment has a significant and asymmetric impact on volatility, increasing it more when sentiment is bearish. Using terminology of De Long et al., we find evidence for the “hold more” effect, which states that when noise traders hold more of the asset, they also see their returns increase, and the “create space” effect, which states that noise tra...

On style momentum strategies

Barberis and Shleifer (2003) suggest that US investors classify assets into different styles based on, for example, market capitalization or B/M ratios. They find that prices can deviate substantially from fundamental values as a styles popularity changes over time. In this paper, we discuss implications of this prediction and empirically investigate the profitability of style momentum strategies for the UK stock market. Results suggest that a simple trading rule can generate significant positive returns, but for our sample of FTSE 350 stocks those strategies are less profitable and more risky compared to regular momentum strategies.

A Cumulative Prospect Theory Approach to Option Pricing

It is a well known empirical fact that actual option prices show persistent and systematic deviations from Black-Scholes option values. While a substantial number of enhancements have been proposed in the literature, these approaches typically leave investors’ preferences towards risk unmodified. In this paper we study option prices in an economy where investors are valuing call options according to the cumulative prospect theory of Kahneman and Tversky. We distinguish two prospect option pricing models, based on whether cash flows are either considered to be segregated or aggregated over time. These models are compared with the Black-Scholes model and the stochastic volatility model of Heston. Empirical analysis of European call options on the S&P 500 index shows that prospect option pricing models significantly improve the fitting performance compared with the Black-Scholes model and that especially the aggregated version’s performance is at least equivalent to the Heston model.

TIPS, Inflation Expectations, and the Financial Crisis

The authors show that inefficiencies in the U.S. market for inflation-linked bonds can be exploited by informed traders who include survey estimates or inflation model forecasts in trades on breakeven inflation. The Treasury Inflation-Protected Securities market has yet to fulfill investors’ expectations as a low-risk, efficient, and liquid financial instrument. Index-linked government bonds eliminate not only default risk but also inflation risk because they adjust cash flows for accrued inflation over time. In the past, the governments of many developed countries (e.g., the United Kingdom, Canada, and Sweden) issued inflation-linked bonds. In 1997, the U.S. Department of the Treasury followed suit by issuing Treasury Inflation-Protected Securities (TIPS). We investigated the TIPS market to improve our understanding of the major factors that drive risk and returns in that asset class. Although earlier studies identified liquidity premiums as one possible if not major factor driving TIPS returns, the financial crisis of 2008 allowed us to examine how risk premiums related to index-linked government bonds are affected by changes in the perception and pricing of risk. Previous research indicated that the TIPS market is inefficient and that market inefficiencies can be exploited by informed traders who include survey estimations or inflation model forecasts in trades on breakeven inflation. Our results—over a period in which the TIPS market matured and increased in depth while the volatility of real yields and inflation also increased—confirm that TIPS market inefficiency was not temporary but persisted from 1997 to 2009. Using estimations generated by the Survey of Professional Forecasters or forecasts based on an inflation-forecasting model to construct a breakeven trading strategy leads to excess returns over a static buy-and-hold strategy. These excess returns remain substantial even after accounting for trading costs. A more detailed analysis of trading strategy–related excess returns suggests that the breakeven strategy performs well during periods of high macroeconomic volatility. This finding can be explained by an enhanced attractiveness of TIPS as uncertainty around future inflation increases. Thus, in general, TIPS market participants’ predictions of future inflation rates during periods of macroeconomic uncertainty are rather poor. Using a systematic approach to forecast inflation is, therefore, especially useful during times of economic uncertainty. Furthermore, our results suggest that the TIPS market has yet to fulfill investors’ expectations of being a low-risk, efficient, and liquid financial instrument. In particular, TIPS returns include a substantial liquidity premium, which, in addition to exposure to changes in real yields, may increase, rather than eliminate, risks in investors’ portfolios. With respect to the financial crisis between the last quarter of 2008 and the second quarter of 2009, our observations further point to inefficiencies in the TIPS market. The most striking evidence from our results is that breakeven inflation turns negative. This finding implies that TIPS are not considered equivalent to government bonds, which leads to the requirement of a substantial liquidity premium for holding TIPS. Moreover, the liquidity premium appears to change significantly over time and to vary with such factors as perceived financial market stability. Note: The views and opinions expressed in this article are the authors’ own and do not necessarily reflect the views and opinions of BlackRock.

European Inflation-Indexed Government Debt Security Markets

The U.K. was the first industrialized country to issue index-linked government bonds. France has joined this group of issuers recently with two series indexed either to French inflation or to inflation in the euro area. This investigation of the efficiency of these markets tests the information content of inflation forecasts to develop trading strategies speculating on the movement of break-even inflation. The results indicate that the market for the French OATi offers the possibility of excess returns, a result that is fairly consistent regardless of market frictions introduced in the return calculation. These trading strategies are beneficial for practitioners tracking index-linked bond indexes in the particular markets.

TIPS, Break-Even Inflation, and Inflation Forecasts

This study investigates the efficiency of the U.S. market for inflation-indexed government bonds using a signal based on inflation forecasts and evaluating the effectiveness of several trading strategies to provide abnormal returns. The market for U.S. TIPS offers the possibility to obtain excess returns if information about future inflation is combined with a trading strategy speculating on the movement of break-even inflation. These results are fairly consistent over time for the shorter maturity. Index-linked government bonds can be considered an asset class with idiosyncratic characteristics that make them an important part of an investment portfolio.