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436
New Insights Into Smile, Mispricing and Value At Risk: The Hyperbolic Model
 Journal of Business
, 1998
"... We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical Black ..."
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Cited by 80 (7 self)
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We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical BlackScholes model. We study implicit volatilities, the smile effect and the pricing performance. Exploiting the full power of the hyperbolic model, we construct an option value process from a statistical point of view by estimating the implicit riskneutral density function from option data. Finally we present some new valueat risk calculations leading to new perspectives to cope with model risk. I Introduction There is little doubt that the BlackScholes model has become the standard in the finance industry and is applied on a large scale in everyday trading operations. On the other side its deficiencies have become a standard topic in research. Given the vast literature where refinements a...
Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility
 REVIEW OF ECONOMICS AND STATISTICS, FORTHCOMING
, 2006
"... A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from highfrequency returns coupled with simple modeling procedures. Building on recent theoretical results in BarndorffNi ..."
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Cited by 79 (7 self)
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A rapidly growing literature has documented important improvements in financial return volatility measurement and forecasting via use of realized variation measures constructed from highfrequency returns coupled with simple modeling procedures. Building on recent theoretical results in BarndorffNielsen and Shephard (2004a, 2005) for related bipower variation measures, the present paper provides a practical and robust framework for nonparametrically measuring the jump component in asset return volatility. In an application to the DM/ $ exchange rate, the S&P500 market index, and the 30year U.S. Treasury bond yield, we find that jumps are both highly prevalent and distinctly less persistent than the continuous sample path variation process. Moreover, many jumps appear directly associated with specific macroeconomic news announcements. Separating jump from nonjump movements in a simple but sophisticated volatility forecasting model, we find that almost all of the predictability in daily, weekly, and monthly return volatilities comes from the nonjump component. Our results thus set the stage for a number of interesting future econometric developments and important financial applications by separately modeling, forecasting, and pricing the continuous and jump components of the total return variation process.
Penalty Methods For American Options With Stochastic Volatility
, 1998
"... The American early exercise constraint can be viewed as transforming the two dimensional stochastic volatility option pricing PDE into a differential algebraic equation (DAE). Several methods are described for forcing the algebraic constraint by using a penalty source term in the discrete equations. ..."
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Cited by 62 (18 self)
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The American early exercise constraint can be viewed as transforming the two dimensional stochastic volatility option pricing PDE into a differential algebraic equation (DAE). Several methods are described for forcing the algebraic constraint by using a penalty source term in the discrete equations. The resulting nonlinear algebraic equations are solved using an approximate Newton iteration. The solution of the Jacobian is obtained using an incomplete LU (ILU) preconditioned PCG method. Some example computations are presented for option pricing problems based on a stochastic volatility model, including an exotic American chooser option written on a put and call with discrete double knockout barriers and discrete dividends.
General Properties of Option Prices
, 1996
"... When the underlying price process is a onedimensional diffusion, as well as in certain restricted stochastic volatility settings, a contingent claim's delta is always bounded by the infimum and supremum of its delta at maturity. Further, if the claim's payoff is convex (concave), then the claim's p ..."
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Cited by 62 (0 self)
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When the underlying price process is a onedimensional diffusion, as well as in certain restricted stochastic volatility settings, a contingent claim's delta is always bounded by the infimum and supremum of its delta at maturity. Further, if the claim's payoff is convex (concave), then the claim's price is a convex (concave) function of the underlying asset's value. However when volatility is less specialized, or when the underlying price follows a discontinuous or nonMarkovian process, then call prices can have properties very different from those of the BlackScholes model: a call's price can be a decreasing, concave function of the underlying price over some range; increasing with the passage of time; and decreasing in the level of interest rates. Much of the financial options literature derives precise option prices, when the underlying asset price process is completely specified. Since it is empirically difficult to ascertain what the true underlying process is, another part of t...
The Surprise Element: Jumps in Interest Rates
 Journal of Econometrics
, 2002
"... Abstract. That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of PoissonGaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short ra ..."
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Cited by 61 (2 self)
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Abstract. That information surprises result in discontinuous interest rates is no surprise to participants in the bond markets. We develop a class of PoissonGaussian models of the Fed Funds rate to capture surprise effects, and show that these models offer a good statistical description of short rate behavior, and are useful in understanding many empirical phenomena. Estimators are used based on analytical derivations of the characteristic functions and moments of jumpdiffusion stochastic processes for a range of jump distributions, and are extended to discretetime models. Jump (Poisson) processes capture empirical features of the data which would not be captured by Gaussian models, and there is strong evidence that existing models would be wellenhanced by jump and ARCHtype processes. The analytical and empirical methods in the paper support many applications, such as testing for Fed intervention effects, which are shown to be an important source of surprise jumps in interest rates. The jump model is shown to mitigate the nonlinearity of interest rate drifts, so prevalent in purediffusion models. Dayofweek effects are modelled explicitly, and the jump model provides evidence of bond market overreaction, rejecting the martingale hypothesis for interest rates. Jump models mixed with Markov switching processes predicate that conditioning on regime is important in determining short rate behavior.
The Finite Moment Log Stable Process and Option Pricing
, 2002
"... We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharpl ..."
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Cited by 51 (9 self)
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We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.
Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options
, 2001
"... This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index, and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the riskneutra ..."
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Cited by 51 (9 self)
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This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index, and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the riskneutral density. Third, we derive laws that decompose individual return skewness into a systematic component and an idiosyncratic component. Empirical analysis of OEX options and 30 stocks demonstrates that individual riskneutral distributions differ from that of the market index by being far less negatively skewed. This paper explains the presence and evolution of riskneutral skewness over time and in the crosssection of individual stocks.