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15
The Variance Gamma Process and Option Pricing.
 European Finance Review
, 1998
"... : A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional par ..."
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Cited by 196 (26 self)
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: A three parameter stochastic process, termed the variance gamma process, that generalizes Brownian motion is developed as a model for the dynamics of log stock prices. The process is obtained by evaluating Brownian motion with drift at a random time given by a gamma process. The two additional parameters are the drift of the Brownian motion and the volatility of the time change. These additional parameters provide control over the skewness and kurtosis of the return distribution. Closed forms are obtained for the return density and the prices of European options. The statistical and risk neutral densities are estimated for data on the S&P500 Index and the prices of options on this Index. It is observed that the statistical density is symmetric with some kurtosis, while the risk neutral density is negatively skewed with a larger kurtosis. The additional parameters also correct for pricing biases of the Black Scholes model that is a parametric special case of the option pricing model d...
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 79 (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...
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.
An adaptive evolutionary approach to option pricing via genetic programming
 Proceedings of the 6th International Conference on Computational Finance
, 1998
"... Please do not quote without permission * Chidambaran is visiting at NYU, on leave from Tulane. Lee holds joint appointments at Tulane and HKUST. Trigueros is at Tulane. We are grateful for the comments from participants at seminars at Tulane ..."
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Cited by 12 (0 self)
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Please do not quote without permission * Chidambaran is visiting at NYU, on leave from Tulane. Lee holds joint appointments at Tulane and HKUST. Trigueros is at Tulane. We are grateful for the comments from participants at seminars at Tulane
When are Options Overpriced? The BlackScholes Model and Alternative Characterisations of the Pricing Kernel”, working paper
, 1999
"... An important determinant of option prices is the elasticity ofthe pricing kernel used to price all claims in the economy. In this paper, we rst show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is ..."
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Cited by 10 (1 self)
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An important determinant of option prices is the elasticity ofthe pricing kernel used to price all claims in the economy. In this paper, we rst show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the stochastic process followed by the underlying asset. Given that the underlying information process follows a geometric Brownian motion, we demonstrate that constant elasticity of the pricing kernel is equivalent to a Brownian motion for the forward price of the underlying asset, so that the BlackScholes formula correctly prices options on the asset. In contrast, declining elasticity implies that the forward price process is no longer a Brownian motion: it has higher volatility and exhibits autocorrelation. In this case, the BlackScholes formula underprices all options. 2 1
Pricing Excessofloss Reinsurance Contracts Against Catastrophic Loss
, 1998
"... : This paper develops a pricing methodology and pricing estimates for the proposed Federal excessof loss (XOL) catastrophe reinsurance contracts. The contracts, proposed by the Clinton Administration, would provide peroccurrence excessofloss reinsurance coverage to private insurers and reinsure ..."
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Cited by 9 (1 self)
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: This paper develops a pricing methodology and pricing estimates for the proposed Federal excessof loss (XOL) catastrophe reinsurance contracts. The contracts, proposed by the Clinton Administration, would provide peroccurrence excessofloss reinsurance coverage to private insurers and reinsurers, where both the coverage layer and the fixed payout of the contract are based on insurance industry losses, not company losses. In financial terms, the Federal government would be selling earthquake and hurricane catastrophe call options to the insurance industry to cover catastrophic losses in a loss layer above that currently available in the private reinsurance market. The contracts would be sold annually at auction, with a reservation price designed to avoid a government subsidy and ensure that the program would be self supporting in expected value. If a loss were to occur that resulted in payouts in excess of the premiums collected under the policies, the Federal government would use...
Option Valuation with Conditional Heteroskedasticity and NonNormality
, 2009
"... We provide results for the valuation of European style contingent claims for a large class of specifications of the underlying asset returns. Our valuation results obtain in a discrete time, infinite statespace setup using the noarbitrage principle and an equivalent martingale measure. Our approac ..."
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Cited by 8 (5 self)
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We provide results for the valuation of European style contingent claims for a large class of specifications of the underlying asset returns. Our valuation results obtain in a discrete time, infinite statespace setup using the noarbitrage principle and an equivalent martingale measure. Our approach allows for general forms of heteroskedasticity in returns, and valuation results for homoskedastic processes can be obtained as a special case. It also allows for conditional nonnormal return innovations, which is critically important because heteroskedasticity alone does not suffice to capture the option smirk. We analyze a class of equivalent martingale measures for which the resulting riskneutral return dynamics are from the same family of distributions as the physical return dynamics. In this case, our framework nests the valuation results obtained by Duan (1995) and Heston and Nandi (2000) by allowing for a timevarying price of risk and nonnormal innovations. We provide extensions of these results to more general equivalent martingale measures and to discrete time stochastic volatility models, and we analyze the relation between our results and those obtained for continuous time models.
Pricing ExcessofLoss Reinsurance Contracts against Catastrophic Loss
, 1998
"... This paper develops a pricing methodology and pricing estimates for the proposed Federal excessof loss (XOL) catastrophe reinsurance contracts. The contracts, proposed by the Clinton Administration, would provide peroccurrence excessofloss reinsurance coverage to private insurers and reinsurers, ..."
Abstract
 Add to MetaCart
This paper develops a pricing methodology and pricing estimates for the proposed Federal excessof loss (XOL) catastrophe reinsurance contracts. The contracts, proposed by the Clinton Administration, would provide peroccurrence excessofloss reinsurance coverage to private insurers and reinsurers, where both the coverage layer and the fixed payout of the contract are based on insurance industry losses, not company losses. In financial terms, the Federal government would be selling earthquake and hurricane catastrophe call options to the insurance industry to cover catastrophic losses in a loss layer above that currently available in the private reinsurance market. The contracts would be sold annually at auction, with a reservation price designed to avoid a government subsidy and ensure that the program would be self supporting in expected value. If a loss were to occur that resulted in payouts in excess of the premiums collected under the policies, the Federal government would use it...