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147
A closedform solution for options with stochastic volatility with applications to bond and currency options
 Review of Financial Studies
, 1993
"... I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond option ..."
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Cited by 1512 (6 self)
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I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strikeprice biases in the BlackScholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems. Many plaudits have been aptly used to describe Black and Scholes ’ (1973) contribution to option pricing theory. Despite subsequent development of option theory, the original BlackScholes formula for a European call option remains the most successful and widely used application. This formula is particularly useful because it relates the distribution of spot returns I thank Hans Knoch for computational assistance. I am grateful for the suggestions of Hyeng Keun (the referee) and for comments by participants
The pricing of options on assets with stochastic volatilities
 JOURNAL OF FINANCE
, 1987
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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 365 (34 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...
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 303 (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 ____________________________________________...
Stock Return Characteristics, Skew Laws,
 and the Differential Pricing of Individual Equity Options,” Review of Financial Studies,
, 2003
"... 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 138 (10 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 article explains the presence and evolution of riskneutral skewness over time and in the cross section of individual stocks. Skewness continues to occupy a prominent role in equity markets. In the traditional asset pricing literature, stocks with negative coskewness command a higher equilibrium risk compensation [see
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 136 (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...
Economics language and assumptions: How theories can become selffulfilling
 Academy of Management Review
, 2005
"... Accepted for publication in the Academy of Management Review. The authors gratefully ..."
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Cited by 104 (3 self)
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Accepted for publication in the Academy of Management Review. The authors gratefully
Constructing a market, performing theory: the historical sociology of a financial derivatives exchange
 American Journal of Sociology
, 2003
"... This analysis of the history of the Chicago Board Options Exchange explores the performativity of economics, a theme in economic sociology recently developed by Callon. Economics was crucial to the creation of financial derivatives exchanges: it helped remedy the drastic loss of legitimacy suffered ..."
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Cited by 89 (3 self)
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This analysis of the history of the Chicago Board Options Exchange explores the performativity of economics, a theme in economic sociology recently developed by Callon. Economics was crucial to the creation of financial derivatives exchanges: it helped remedy the drastic loss of legitimacy suffered by derivatives in the first half of the 20th century. Option pricing theory—a “crown jewel ” of neoclassical economics—succeeded empirically not because it discovered preexisting price patterns but because markets changed in ways that made its assumptions more accurate and because the theory was used in arbitrage. The performativity of economics, however, has limits, and an emphasis on it needs to be combined with classic themes in economic sociology, such as Granovetterian embedding and the way in which exchanges can be cultures and moral communities in which collective action problems can be solved.