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126
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
Option pricing when underlying stock returns are discontinuous
 Journal of Financial Economics
, 1976
"... The validity of the classic BlackScholes option pricing formula dcpcnds on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying ..."
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Cited by 1001 (3 self)
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The validity of the classic BlackScholes option pricing formula dcpcnds on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying stock return dynamics can be described by a stochastic process with a continuous sample path. In this paper, an option pricing formula is derived for the moregeneral cast when the underlying stock returns are gcncrated by a mixture of both continuous and jump processes. The derived formula has most of the attractive features of the original Black&holes formula in that it does not dcpcnd on investor prcfcrenccs or knowledge of the expcctsd return on the underlying stock. Morcovcr, the same analysis applied to the options can bc extcndcd to the pricingofcorporatc liabilities. 1. Intruduction In their classic paper on the theory of option pricing, Black and Scholcs (1973) prcscnt a mode of an:llysis that has rcvolutionizcd the theory of corporate liability pricing. In part, their approach was a breakthrough because it leads to pricing formulas using. for the most part, only obscrvablc variables. In particular,
An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantees: An Application of Modern Option Pricing Theory
 Journal of Banking and Finance
, 1977
"... It is not uncommon in the arrangement of a loan to include as part of the financial package a guarantee of the loan by a third party. Examples are guarantees by a parent company of loans made to its subsidiaries or government guarantees of loans made to private corporations. Also included would be g ..."
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Cited by 444 (6 self)
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It is not uncommon in the arrangement of a loan to include as part of the financial package a guarantee of the loan by a third party. Examples are guarantees by a parent company of loans made to its subsidiaries or government guarantees of loans made to private corporations. Also included would be guarantees of bank deposits by the Federal Deposit Insurance Corporation. As with other forms of insurance, the issuing of a guarantee imposes a liability or cost on the guarantor. In this paper, a formula is derived to evaluate this cost. The method used is to demonstrate an isomorphic correspondence between loan guarantees and common stock put options, and then to use the well developed theory of option pricing to derive the formula. 1.
Nonparametric Estimation of StatePrice Densities Implicit In Financial Asset Prices
 JOURNAL OF FINANCE
, 1997
"... Implicit in the prices of traded financial assets are ArrowDebreu prices or, with continuous states, the stateprice density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and derive its asymptotic sampling theory. This estimator provides an arbitragefree metho ..."
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Cited by 339 (6 self)
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Implicit in the prices of traded financial assets are ArrowDebreu prices or, with continuous states, the stateprice density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and derive its asymptotic sampling theory. This estimator provides an arbitragefree method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an assetpricing perspective, e.g., negative skewness and excess kurtosis for asset returns, volatility "smiles" for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.
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.
The Russian option: Reduced regret
 Ann. Appl. Probab
, 1993
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 72 (3 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
The probability density function of interest rates implied in the price of options
, 1998
"... The purpose of the “Temi di discussione ” series is to promote the circulation of working papers prepared within the Bank of Italy or presented in Bank seminars by outside economists with the aim of stimulating comments and suggestions. The views expressed in the articles are those of the authors an ..."
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Cited by 49 (6 self)
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The purpose of the “Temi di discussione ” series is to promote the circulation of working papers prepared within the Bank of Italy or presented in Bank seminars by outside economists with the aim of stimulating comments and suggestions. The views expressed in the articles are those of the authors and do not involve the responsibility of the Bank.
Risk vs. ProfitPotential; A Model for Corporate Strategy
 J. Econ. Dynam. Control
, 1996
"... A firm whose net earnings are uncertain, and that is subject to the risk of bankruptcy, must choose between paying dividends and retaining earnings in a liquid reserve. Also, different operating strategies imply different combinations of expected return and variance. We model the firm's cash re ..."
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Cited by 47 (1 self)
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A firm whose net earnings are uncertain, and that is subject to the risk of bankruptcy, must choose between paying dividends and retaining earnings in a liquid reserve. Also, different operating strategies imply different combinations of expected return and variance. We model the firm's cash reserve as the difference between the cumulative net earnings and the cumulative dividends. The first is a diffusion (additive), whose drift/volatility pair is chosen dynamically from a finite set, A. The second is an arbitrary nondecreasing process, chosen by the firm. The firm's strategy must be nonclairvoyant. The firm is bankrupt at the first time, T , at which the cash reserve falls to zero (T may be infinite), and the firm's objective is to maximize the expected total discounted dividends from 0 to T , given an initial reserve, x; denote this maximum by V (x). We calculate V explicitly, as a function of the set A and the discount rate. The optimal policy has the form: (1) pay no dividends if ...
Discretely Adjusted Option Hedges
 Journal of Financial Economics
, 1980
"... This paper analyses the distribution of returns on a hedged portfolio, consisting of a European call option and its associated stock, when the portfolio is rebalanced at discrete time intervals. Under the assumpttons of the BlackScholes model this distributron is particularly skew. In tests of the ..."
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Cited by 45 (1 self)
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This paper analyses the distribution of returns on a hedged portfolio, consisting of a European call option and its associated stock, when the portfolio is rebalanced at discrete time intervals. Under the assumpttons of the BlackScholes model this distributron is particularly skew. In tests of the average return on a hedged portfolio this skewness leads to biased tstatrstics. The paper explores the nature and extent of this bias and suggests procedures for overcoming it. Other aspects of discrete hedging are also discussed. 1.