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81
Structural Models of Corporate Bond Pricing: An Empirical Analysis
, 2003
"... This paper empirically tests five structural models of corporate bond pricing: those of Merton (1974), Geske (1977), Leland and Toft (1996), Longsta# and Schwartz (1995), and CollinDufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capita ..."
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Cited by 147 (5 self)
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This paper empirically tests five structural models of corporate bond pricing: those of Merton (1974), Geske (1977), Leland and Toft (1996), Longsta# and Schwartz (1995), and CollinDufresne and Goldstein (2001). We implement the models using a sample of 182 bond prices from firms with simple capital structures during the period 19861997. The conventional wisdom is that structural models do not generate spreads as high as those seen in the bond market, and true to expectations we find that the predicted spreads in our implementation of the Merton model are too low. However, most of the other structural models predict spreads that are too high on average. Nevertheless, accuracy is a problem, as the newer models tend to severely overstate the credit risk of firms with high leverage or volatility and yet su#er from a spread underprediction problem with safer bonds. The Leland and Toft model is an exception in that it overpredicts spreads on most bonds, particularly those with high coupons. More accurate structural models must avoid features that increase the credit risk on the riskier bonds while scarcely a#ecting the spreads of the safest bonds.
TimeChanged Lévy Processes and Option Pricing
, 2002
"... As is well known, the classic BlackScholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to nonnormal return innovations. Second, return ..."
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Cited by 90 (13 self)
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As is well known, the classic BlackScholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to nonnormal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. We propose that timechanged Lévy processes be used to simultaneously address these three facets of the underlying asset return process. We show that our framework encompasses almost all of the models proposed in the option pricing literature. Despite the generality of our approach, we show that it is straightforward to select and test a particular option pricing model through the use of characteristic function technology.
Derivative asset analysis in models with leveldependent and stochastic volatility
 CWI QUARTERLY
, 1996
"... In this survey we discuss models with leveldependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical BlackScholes model; they have been developed in an effort to build models that are flexible enough to cope wit ..."
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Cited by 38 (1 self)
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In this survey we discuss models with leveldependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical BlackScholes model; they have been developed in an effort to build models that are flexible enough to cope with the known deficits of the classical BlackScholes model. We start by briefly recalling the standard theory for pricing and hedging derivatives in complete frictionless markets and the classical BlackScholes model. After a review of the known empirical contradictions to the classical BlackScholes model we consider models with leveldependent volatility. Most of this survey is devoted to derivative asset analysis in stochastic volatility models. We discuss several recent developments in the theory of derivative pricing under incompleteness in the context of stochastic volatility models and review analytical and numerical approaches to the actual computation of option values.
Option Pricing by Transform Methods: Extensions, Unification, and Error Control
 Journal of Computational Finance
"... We extend and unify Fourieranalytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorith ..."
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Cited by 38 (3 self)
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We extend and unify Fourieranalytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorithms to select efficient quadrature parameters and to price with guaranteed numerical accuracy.
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.
Pricing and Hedging Spread Options
 SIAM Review
, 2003
"... Abstract. We survey theoretical and computational problems associated with the pricing and hedging of spread options. These options are ubiquitous in the financial markets, whether they be equity, fixed income, foreign exchange, commodities, or energy markets. As a matter of introduction, we present ..."
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Cited by 25 (6 self)
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Abstract. We survey theoretical and computational problems associated with the pricing and hedging of spread options. These options are ubiquitous in the financial markets, whether they be equity, fixed income, foreign exchange, commodities, or energy markets. As a matter of introduction, we present a general overview of the common features of all spread options by discussing in detail their roles as speculation devices and risk management tools. We describe the mathematical framework used to model them, and we review the numerical algorithms actually used to price and hedge them. There is already extensive literature on the pricing of spread options in the equity and fixed income markets, and our contribution is mostly to put together material scattered across a wide spectrum of recent textbooks and journal articles. On the other hand, information about the various numerical procedures that can be used to price and hedge spread options on physical commodities is more difficult to find. For this reason, we make a systematic effort to choose examples from the energy markets in order to illustrate the numerical challenges associated with these instruments. This gives us a chance to discuss an interesting application of spread options to an asset valuation problem after it is recast in the framework of real options. This approach is currently the object of intense mathematical research. In this spirit, we review the two major avenues to modeling energy price dynamics. We explain how the pricing and hedging algorithms can be implemented in the framework of models for both the spot price dynamics and the forward curve dynamics.
Pricing and Hedging Guaranteed Annuity Options via Static Option Replication
 Insurance: Mathematics and Economics
, 2003
"... In this paper we derive a market value for withprofits guaranteed annuity options (GAOs) using martingale modelling techniques. Furthermore, we show how to construct a static replicating portfolio of vanilla interest rate swaptions that replicates the withprofits GAO. Finally, we illustrate with h ..."
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Cited by 18 (3 self)
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In this paper we derive a market value for withprofits guaranteed annuity options (GAOs) using martingale modelling techniques. Furthermore, we show how to construct a static replicating portfolio of vanilla interest rate swaptions that replicates the withprofits GAO. Finally, we illustrate with historical UK interest rate data from the period 1980 to 2000 that the static replicating portfolio would have been extremely effective as a hedge against the interest rate risk involved in the GAO, that the static replicating portfolio would have been considerably cheaper than upfront reserving and also that the replicating portfolio would have provided a much better level of protection than an upfront reserve.
Can Structural Models Price Default Risk? Evidence from Bond and Credit Derivative Markets
, 2006
"... Using a set of structural models, we evaluate the price of default protection for a sample of US corporations. Credit default swaps (CDS) are commonly thought to be less influenced by nondefault factors, making them an interesting source of data for evaluating models of default risk. In contrast to ..."
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Cited by 14 (0 self)
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Using a set of structural models, we evaluate the price of default protection for a sample of US corporations. Credit default swaps (CDS) are commonly thought to be less influenced by nondefault factors, making them an interesting source of data for evaluating models of default risk. In contrast to previous evidence from corporate bond data, CDS premia are not systematically underestimated. In fact, one of our studied models has little difficulty on average in predicting their level. For robustness, we perform the same exercise for bond spreads by the same issuers on the same trading date. As expected, bond spreads are systematically underestimated, consistent with their being driven by significant nondefault components. Considering theoretical and market levels alone is insufficient to evaluate the models’ performance, as other factors might be at play in both markets. With this in mind, we relate the models’ residuals by means of linear regressions to default and nondefault proxies. We find little evidence of any default risk component in either bond or CDS residuals. However, in the residuals for bonds, we find strong evidence for nondefault components, in particular an illiquidity premium. CDS residuals reveal no such
Pricing Rate of Return Guarantees in a HeathJarrowMorton Framework
 Insurance: Mathematics and Economics
, 1999
"... Abstract. Rate of return guarantees are included in many nancial products, for example life insurance contracts or guaranteed investment contracts issued by investment banks. The holder of such a contract is guaranteed a xed periodically rate of return rather thanor in addition toa xed absolute am ..."
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Cited by 11 (2 self)
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Abstract. Rate of return guarantees are included in many nancial products, for example life insurance contracts or guaranteed investment contracts issued by investment banks. The holder of such a contract is guaranteed a xed periodically rate of return rather thanor in addition toa xed absolute amount at expiration. We consider rate of return guarantees where the underlying rate of return is either (i) the rate of return on a stock investment or (ii) the shortterm interest rate. Various types of these rate of return guarantees are priced in a general noarbitrage HeathJarrowMorton framework. We show that despite fundamental di erences in the underlying rate of return processes ((i) or (ii)), the resulting pricing formulas for the guarantees are remarkably similar. Finally,we showhowthe term structure models of Vasicek (1977) and Cox, Ingersoll, and Ross (1985) occur as special cases in our more general framework based on the model of Heath, Jarrow, and Morton (1992). Interest rate guarantees are included in several contracts guarantee the policy holder a 1.