In the setting of ‘‘affine’ ’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks ’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.

. The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less then one. 1. Introduction A basic problem of mathematical finance is the problem of an economic agent, who invests in a financial market so as to maximize the expected utility of his terminal wealth. In the framework of a continuous-time model the problem was studied for the first time by R. Merton in two seminal papers [27] and [28] (see also [29] as well as [32] for a treatment of the discrete time case). Using the methods of stochastic optimal control Merton derived a non-linear partial differential equation (Bellman equation) for the value function of the optimization problem. He al...

This paper estimates recent default risk premia for U.S. corporate debt, based on a close relationship between default probabilities, as estimated by Moody's KMV EDFs, and default swap (CDS) market rates. The default-swap data, obtained through CIBC from 22 banks and specialty dealers, allow us to establish a strong link between actual and risk-neutral default probabilities for the 69 firms in the three sectors that we analyze: broadcasting and entertainment, healthcare, and oil and gas. We find dramatic variation over time in risk premia, from peaks in the thrid quarter of 2002, dropping by roughly 50% to late 2003.

We construct a model for pricing sovereign debt that accounts for the risks of both default and restructuring, and allows for compensation for illiquidity. Using a new and relatively efficient method, we estimate the model using Russian dollar-denominated bonds. We consider the determinants of the Russian yield spread, the yield differential across different Russian bonds, and the implications for market integration, relative liquidity, relative expected recovery rates, and implied expectations of different default scenarios. THIS PAPER DEVELOPS A MODEL of the termstructure of credit spreads on sovereign bonds that accommodates: (i) Default or repudiation: The sovereign announces that it will stop making payments on its debt; (ii) Restructuring or renegotiation: The sovereign and the lenders ‘‘agree’ ’ to reduce (or postpone) the remaining payments; and (iii) A‘‘regime switch,’’such as a change of government or the default of another sovereign bond that changes the perceived risk of future defaults.We build on the framework of Duffie and Singleton (1999), showing that

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-Scholes 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 risk-neutral 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 Black-Scholes 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...

As is well known, the classic Black-Scholes 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 non-normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. We propose that time-changed 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.

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This paper develops an arbitrage-free time-series model of yields in continuous time that incorporates central bank policy. Policy-related events, such as FOMC meetings and releases of macroeconomic news the Fed cares about, are modeled as jumps. The model introduces a class of linear-quadratic jump-diffusions as state variables, which allows for a wide variety of jump types but still leads to tractable solutions for bond prices. I estimate a version of this model with U.S. interest rates, the Federal Reserve’s target rate, and key macroeconomic aggregates. The estimated model improves bond pricing, especially at short maturities. The “snake-shape ” of the volatility curve is linked to monetary policy inertia. A new monetary policy shock series is obtained by assuming that the Fed reacts to information available right before the FOMC meeting. According to the estimated policy rule, the Fed is mainly reacting to information contained in the yield-curve. Surprises in analyst forecasts turn out to be merely temporary components of macro variables, so that the “hump-shaped” yield response to these surprises is not consistent with a Taylor-type policy rule.

In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of derivative asset analysis. Both classes of models are generalisations of the classical Black-Scholes 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 Black-Scholes model. After a review of the known empirical contradictions to the classical Black-Scholes model we consider models with level-dependent 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.

This paper solves a long-standing open problem in mathematical finance: to find a solution to the problem of maximizing utility from terminal wealth of an agent with a random endowment process, in the general, semimartingale model for incomplete markets, and to characterize it via the associated dual problem. We show that this is indeed possible if the dual problem and its domain are carefully defined. More