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99
Option Pricing: A Simplified Approach
 Journal of Financial Economics
, 1979
"... This paper presents a simple discretetime model for valumg optlons. The fundamental econonuc principles of option pricing by arbitrage methods are particularly clear In this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Blac ..."
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Cited by 563 (8 self)
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This paper presents a simple discretetime model for valumg optlons. The fundamental econonuc principles of option pricing by arbitrage methods are particularly clear In this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Black&holes model, which has previously been derived only by much more difficult methods. The basic model readily lends itself to generalization in many ways. Moreover, by its very constructlon, it gives rise to a simple and efficient numerical procedure for valumg optlons for which premature exercise may be optimal. 1.
A Markov Model for the Term Structure of Credit Risk Spreads
 Review of Financial Studies
, 1997
"... This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable data ..."
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Cited by 237 (12 self)
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This article provides a Markov model for the term structure of credit risk spreads. The model is based on Jarrow and Turnbull (1995), with the bankruptcy process following a discrete state space Markov chain in credit ratings. The parameters of this process are easily estimated using observable data. This model is useful for pricing and hedging corporate debt with imbedded options, for pricing and hedging OTC derivatives with counterparty risk, for pricing and hedging (foreign) government bonds subject to default risk (e.g., municipal bonds), for pricing and hedging credit derivatives, and for risk management. This article presents a simple model for valuing risky debt that explicitly incorporates a firm's credit rating as an indicator of the likelihood of default. As such, this article presents an arbitragefree model for the term structure of credit risk spreads and their evolution through time. This model will prove useful for the pricing and hedging of corporate debt with We would like to thank John Tierney of Lehman Brothers for providing the bond index price data, and Tal Schwartz for computational assistance. We would also like to acknowledge helpful comments received from an anonymous referee. Send all correspondence to Robert A. Jarrow, Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853. The Review of Financial Studies Summer 1997 Vol. 10, No. 2, pp. 481523 1997 The Review of Financial Studies 08939454/97/$1.50 imbedded options, for the pricing and hedging of OTC derivatives with counterparty risk, for the pricing and hedging of (foreign) government bonds subject to default risk (e.g., municipal bonds), and for the pricing and hedging of credit derivatives (e.g. credit sensitive notes and spread adjusted notes). This model can also...
Post'87 Crash Fears in the S&P 500 Futures Option Market
, 1998
"... Postcrash distributions inferred from S ..."
General Properties of Option Prices
, 1996
"... When the underlying price process is a onedimensional diffusion, as well as in certain restricted stochastic volatility settings, a contingent claim's delta is always bounded by the infimum and supremum of its delta at maturity. Further, if the claim's payoff is convex (concave), then the claim's p ..."
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Cited by 62 (0 self)
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When the underlying price process is a onedimensional diffusion, as well as in certain restricted stochastic volatility settings, a contingent claim's delta is always bounded by the infimum and supremum of its delta at maturity. Further, if the claim's payoff is convex (concave), then the claim's price is a convex (concave) function of the underlying asset's value. However when volatility is less specialized, or when the underlying price follows a discontinuous or nonMarkovian process, then call prices can have properties very different from those of the BlackScholes model: a call's price can be a decreasing, concave function of the underlying price over some range; increasing with the passage of time; and decreasing in the level of interest rates. Much of the financial options literature derives precise option prices, when the underlying asset price process is completely specified. Since it is empirically difficult to ascertain what the true underlying process is, another part of t...
Credit Risk and Risk Neutral Default Probabilities: Information About Rating Migrations and Defaults,” working paper
, 1998
"... Default probabilities are important to the credit markets. Changes in default probabilities may forecast credit rating migrations to other rating levels or to default. Such rating changes can affect the firm’s cost of capital, credit spreads, bond returns, and the prices and hedge ratios of credit d ..."
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Cited by 45 (0 self)
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Default probabilities are important to the credit markets. Changes in default probabilities may forecast credit rating migrations to other rating levels or to default. Such rating changes can affect the firm’s cost of capital, credit spreads, bond returns, and the prices and hedge ratios of credit derivatives. While rating agencies such as Moodys and Standard & Poors compute historical default frequencies, option models can also be used to calculate forward looking or expected default frequencies. In this paper, we compute risk neutral probabilities or default (RNPD) using the diffusion models of Merton (1974) and Geske (1977). It is shown that the Geske model produces a term structure of RNPD’s, and the shape of this term structure may forecast impending credit events. Next, it is shown that these RNPD’s serve as bounds to estimates of actual default probabilities. Furthermore, the RNPD’s exhibit the same comparative statics as the estimates of actual default probabilities. Also, the risk neutral default probabilities may be more accurately estimated than actual default probabilities because they do not require an estimate of the firm’s drift. Given these similarities and advantages of RNPD’s, their estimates may possess significant information about credit events. To confirm this an event study of the relation between RNPD
Complete Models with Stochastic Volatility
, 1996
"... The paper proposes an original class of models for the continuous time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentiallyweighted moments of historic logprice. The instantaneous volatility is therefore driven ..."
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Cited by 42 (3 self)
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The paper proposes an original class of models for the continuous time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentiallyweighted moments of historic logprice. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preferenceindependent options prices. We find a partial differential equation for the price of a European Call Option. Smiles and skews are found in the resulting plots of implied volatility. Keywords: Option pricing, stochastic volatility, complete markets, smiles. Acknowledgement. It is a pleasure to thank the referees of an earlier draft of this paper whose perceptive comments have resulted in many improvements. 1 Research supported in part by Record Treasu...
Software Design as an Investment Activity: A Real Options Perspective
 UNIVERSITY OF VIRGINIA DEPARTMENT OF COMPUTER SCIENCE
, 1999
"... ..."
Continuoustime methods in finance: A review and an assessment
 Journal of Finance
, 2000
"... I survey and assess the development of continuoustime methods in finance during the last 30 years. The subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing, term structure theory, asset pricing, and optimal consumption and portfolio choices. ..."
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Cited by 32 (0 self)
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I survey and assess the development of continuoustime methods in finance during the last 30 years. The subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing, term structure theory, asset pricing, and optimal consumption and portfolio choices. During the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance. This latter subperiod has seen significant progress in econometric theory, computational and estimation methods to test and implement continuoustime models. Capital market frictions and bargaining issues are being increasingly incorporated in continuoustime theory. THE ROOTS OF MODERN CONTINUOUSTIME METHODS in finance can be traced back to the seminal contributions of Merton ~1969, 1971, 1973b! in the late 1960s and early 1970s. Merton ~1969! pioneered the use of continuoustime modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting.
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 22 (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.
Individual stockoption prices and credit spreads’, Working Paper
, 2006
"... This paper introduces measures of volatility and jump risk that are based on individual stock options to explain credit spreads on corporate bonds. Implied volatilities of individual options are shown to contain important information for credit spreads and improve on both implied volatilities of ind ..."
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Cited by 15 (2 self)
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This paper introduces measures of volatility and jump risk that are based on individual stock options to explain credit spreads on corporate bonds. Implied volatilities of individual options are shown to contain important information for credit spreads and improve on both implied volatilities of index options and on historical volatilities when explaining the crosssectional and timeseries variation in a panel of corporate bond spreads. Both the level of individual implied volatilities and the impliedvolatility skew matter for credit spreads. The empirical estimates are in line with the coefficients predicted by a theoretical structural firm value model. Importantly, detailed principal component analysis shows that our newly constructed determinants of credit spreads reverse the finding in the literature that structural models leave a large part of the variation in credit spreads unexplained. Furthermore, our results indicate that optionmarket liquidity has a spillover effect on the shortmaturity corporate bond market, and we show that individual option prices contain information on the likelihood of rating migrations.