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137
TimeChanged Lévy Processes and Option Pricing
, 2002
"... As is well known, the classic BlackScholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to nonnormal return innovations. Second, return ..."
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Cited by 182 (22 self)
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As is well known, the classic BlackScholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to nonnormal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. We propose that timechanged Lévy processes be used to simultaneously address these three facets of the underlying asset return process. We show that our framework encompasses almost all of the models proposed in the option pricing literature. Despite the generality of our approach, we show that it is straightforward to select and test a particular option pricing model through the use of characteristic function technology.
Variance risk premiums
 Review of Financial Studies 000
, 2008
"... We propose a direct and robust method for quantifying the variance risk premium on financial assets. We show that the riskneutral expected value of return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. We propose to use the di ..."
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Cited by 88 (6 self)
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We propose a direct and robust method for quantifying the variance risk premium on financial assets. We show that the riskneutral expected value of return variance, also known as the variance swap rate, is well approximated by the value of a particular portfolio of options. We propose to use the difference between the realized variance and this synthetic variance swap rate to quantify the variance risk premium. Using a large options data set, we synthesize variance swap rates and investigate the historical behavior of variance risk premiums on five stock indexes and 35 individual stocks. (JEL G10, G12, G13) It has been well documented that return variance is stochastic. When investing in a security, an investor faces at least two sources of uncertainty, namely the uncertainty about the return as captured by the return variance, and the uncertainty about the return variance itself. It is important to know how investors deal with the uncertainty in return variance to effectively manage risk and allocate assets, to accurately price and hedge derivative securities, and to understand the behavior of financial asset prices in general. We develop a direct and robust method for quantifying the return variance
Maximum likelihood estimation of latent affine processes, Working paper
 Processes, forthcoming, Review of Financial Studies
, 2006
"... This article develops a direct filtrationbased maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. Filtration is conducted in the transform space of characteristic functions, using a version of Bayes ’ rule for recursively updating the joint cha ..."
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Cited by 47 (2 self)
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This article develops a direct filtrationbased maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. Filtration is conducted in the transform space of characteristic functions, using a version of Bayes ’ rule for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. An application to daily stock market returns over 195396 reveals substantial divergences from EMMbased estimates; in particular, more substantial and timevarying jump risk. The implications for pricing stock index options are examined. 3 “The Lion in Affrik and the Bear in Sarmatia are Fierce, but Translated into a Contrary Heaven, are of less Strength and Courage.” Jacob Ziegler; translated by Richard Eden (1555) While models proposing timevarying volatility of asset returns have been around for thirty years, it has proven extraordinarily difficult to estimate the parameters of the underlying volatility process,
Explaining the level of credit spreads: optionimplied jump risk premia in a firm value model
, 2005
"... Prices of equity index put options contain information on the price of systematic downward jump risk. We use a structural jumpdiffusion firm value model to assess the level of credit spreads that is generated by optionimplied jump risk premia. In our compound option pricing model, an equity index ..."
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Cited by 43 (2 self)
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Prices of equity index put options contain information on the price of systematic downward jump risk. We use a structural jumpdiffusion firm value model to assess the level of credit spreads that is generated by optionimplied jump risk premia. In our compound option pricing model, an equity index option is an option on a portfolio of call options on the underlying firm values. We calibrate the model parameters to historical information on default risk, the equity premium and equity return distribution, and S&P 500 index option prices. Our results show that a model without jumps fails to fit the equity return distribution and option prices, and generates a low outofsample prediction for credit spreads. Adding jumps and jump risk premia improves the fitofthe model in terms of equity and option characteristics considerably and brings predicted credit spread levels much closer to observed levels.
Risk in Dynamic Arbitrage: Price Effects of Convergence Trading ∗
, 2006
"... This paper studies the adverse price effects of convergence trading. I assume two assets with identical cash flows traded in segmented markets. Initially, there is gap between the prices of the assets, because local traders face asymmetric temporary shocks. In the absence of arbitrageurs, the gap re ..."
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Cited by 40 (2 self)
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This paper studies the adverse price effects of convergence trading. I assume two assets with identical cash flows traded in segmented markets. Initially, there is gap between the prices of the assets, because local traders face asymmetric temporary shocks. In the absence of arbitrageurs, the gap remains constant until a random time when the difference across local markets disappears. While arbitrageurs ’ activity reduces the price gap, it also generates potential losses: the price gap widens with positive probability at each time instant. With the increase of arbitrage capital on the market, the predictability of the dynamics of the gap decreases, and the arbitrage opportunity turns into a risky speculative bet. In a calibrated example I show that the endogenously created losses alone can explain episodes when arbitrageurs lose most of their capital in a relatively short time.
Economic catastrophe bonds
 American Economic Review
"... The central insight of asset pricing is that a security’s value depends on both its distribution of payo¤s across economic states and state prices. In …xed income markets, many investors focus exclusively on estimates of expected payo¤s, such as credit ratings, without considering the state of the e ..."
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Cited by 38 (1 self)
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The central insight of asset pricing is that a security’s value depends on both its distribution of payo¤s across economic states and state prices. In …xed income markets, many investors focus exclusively on estimates of expected payo¤s, such as credit ratings, without considering the state of the economy in which default is likely to occur. Such investors are likely to be attracted to securities whose payo¤s resemble those of economic catastrophe bonds–bonds that default only under severe economic conditions. We show that many structured …nance instruments can be characterized as economic catastrophe bonds, but o¤er far less compensation than alternatives with comparable payo ¤ pro…les. We argue that this di¤erence arises from the willingness of rating agencies to certify structured products with a low default likelihood as “safe ” and from a large supply of investors who view them as such.
Stochastic risk premiums, stochastic skewness in currency options, and stochastic discount factors in international economies
 Journal of Financial Economics
, 2007
"... We develop models of stochastic discount factors in international economies that produce stochastic risk premiums and stochastic skewness in currency options. We estimate the models using timeseries returns and option prices on three currency pairs that form a triangular relation. Estimation shows ..."
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Cited by 30 (4 self)
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We develop models of stochastic discount factors in international economies that produce stochastic risk premiums and stochastic skewness in currency options. We estimate the models using timeseries returns and option prices on three currency pairs that form a triangular relation. Estimation shows that the average risk premium in Japan is larger than that in the US or the UK, the global risk premium is more persistent and volatile than the countryspecific risk premiums, and investors respond differently to different shocks. We also identify highfrequency jumps in each economy, but find that only downside jumps are priced. Finally, our analysis shows that the risk premiums are economically compatible with movements in stock and bond market fundamentals.
A GARCH Option Pricing Model with Filtered Historical Simulation
 Review of Financial Studies
, 2008
"... We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model’s flexibility to fit market option prices. An extensive ..."
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Cited by 29 (3 self)
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We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model’s flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 Index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black–Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.