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26
Implied Volatility Functions: Empirical Tests
, 1995
"... Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black/Scholes constant volatility assumption is violat ..."
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Cited by 294 (4 self)
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Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black/Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset's return is a deterministic function of the asset price and time. Since the volatility function in their model has an arbitrary specification, the deterministic volatility (DV) option valuation model has the potential of fitting the observed crosssection of option prices exactly. Using a sample of S&P 500 index options during the period June 1988 and December 1993, we attempt to evaluate the economic significance of the implied volatility function by examining the predictive and hedging performance of the DV option valuation model. Discussion draft: September 8, 1995 ____________________________________________...
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 140 (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...
Of Smiles and Smirks: A TermStructure Perspective
 JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS
, 1998
"... An extensive empirical literature in finance has documented not only the presence of anamolies in the BlackScholes model, but also the "termstructures" of these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical ..."
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Cited by 137 (5 self)
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An extensive empirical literature in finance has documented not only the presence of anamolies in the BlackScholes model, but also the "termstructures" of these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts in the literature at addressing these anamolies have largely focussed on two extensions of the BlackScholes model: introducing jumps into the return process, and allowing volatility to be stochastic. This paper employs commonlyused versions of these two classes of models to examine the extent to which the models are theoretically capable of resolving the observed anamolies. We find that each model exhibits some "termstructure" patterns that are fundamentally inconsistent with those observed in the data. As a consequence, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models fare better than jumps in this regard.
Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates
, 2000
"... This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate t ..."
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Cited by 11 (0 self)
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This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S&P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premium of stochastic volatility to gauge each model’s performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or “leverage effect ” does help to explain the skewness of the volatility “smile”, allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino & Turnbull (1990), our empirical findings strongly suggest the existence of a nonzero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the
Pricing foreign currency and crosscurrency options under garch
 Journal of Derivatives Fall
, 1999
"... Canada and the University of Toronto Connaught Fund. Both authors wish to thank an anonymous referee and the Editor for useful suggestions and comments. Pricing Foreign Currency and CrossCurrency Options Under GARCH The main objective of this paper is to propose an alternative valuation framework f ..."
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Cited by 7 (2 self)
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Canada and the University of Toronto Connaught Fund. Both authors wish to thank an anonymous referee and the Editor for useful suggestions and comments. Pricing Foreign Currency and CrossCurrency Options Under GARCH The main objective of this paper is to propose an alternative valuation framework for pricing foreign currency and crosscurrency options, which is capable of accommodating existing empirical regularities. The paper generalizes the GARCH option pricing methodology of Duan (1995) to a twocountry setting. Specifically, we assume a bivariate nonlinear GARCH system for the exchange rate and the foreign asset price, and generalize the local riskneutral valuation principle for pricing derivatives. We define an equilibrium price measure in the twocountry economy and derive the locally riskneutralized GARCH processes for the exchange rate and the foreign asset price. Foreign currency options and crosscurrency options are then valued using Monte Carlo simulations. Our setup accommodates rich empirical regularities such as stochastic volatility, fat tailed distributions and leverage effect extensively documented for financial data series. Numerical results show that our proposed model exhibits properties that are consistent with the documented empirical regularities for foreign currency options and quanto options. 1.
Pricing stock options under stochastic volatility and stochastic interest rates with efficient method . . .
, 1998
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An Option Pricing Formula for the GARCH diffusion Model
, 2003
"... We derive analytically the first four conditional moments of the integrated variance implied by the GARCH diffusion process. An analytical closed form approximation for European options under the GARCH diffusion model is obtained from these moments. Using Monte Carlo simulations we show that this ap ..."
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Cited by 6 (1 self)
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We derive analytically the first four conditional moments of the integrated variance implied by the GARCH diffusion process. An analytical closed form approximation for European options under the GARCH diffusion model is obtained from these moments. Using Monte Carlo simulations we show that this approximation is accurate for a large set of reasonable parameters. The closedform option pricing solution allows to study easily implied volatility surfaces induced by the GARCH diffusion model.
Accounting for biases in BlackScholes
, 1998
"... Prices of currency options commonly di er from the BlackScholes formula along two dimensions: implied volatilities vary by strike price (volatility smiles) and maturity (implied volatility of atthemoney options increases, on average, with maturity). We account for both using GramCharlier expansi ..."
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Cited by 4 (1 self)
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Prices of currency options commonly di er from the BlackScholes formula along two dimensions: implied volatilities vary by strike price (volatility smiles) and maturity (implied volatility of atthemoney options increases, on average, with maturity). We account for both using GramCharlier expansions to approximate the conditional distribution of the logarithm of the price of the underlying security. In this setting, volatility is approximately a quadratic function of moneyness, a result we use to infer skewness and kurtosis from volatility smiles. Evidence suggests that both kurtosis in currency prices and biases in BlackScholes option prices decline with maturity. JEL Classi cation Codes: G12, G13, F31, C14. Keywords: currency options � skewness and kurtosis � GramCharlier expansions� implied volatility. We welcome comments, including references to related papers we inadvertently overlooked.
Asymptotic Analysis of Stochastic Volatility Models” Wilmott Associates
, 2002
"... In this paper, we consider the pricing of options when the underlying asset value S and its volatility σ are described by the stochastic differential equations, dS/S = r dt+ σ dX (1) dσ = Adt +B dY (2) ..."
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Cited by 3 (1 self)
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In this paper, we consider the pricing of options when the underlying asset value S and its volatility σ are described by the stochastic differential equations, dS/S = r dt+ σ dX (1) dσ = Adt +B dY (2)