The αVG model for multivariate asset pricing: calibration and extension

Luciano and Semeraro proposed a class of multivariate asset pricing models where the asset log-returns are modeled by a multivariate Brownian motion time-changed by a multivariate subordinator which consists of the weighted sum of a common and an idiosyncratic subordinator. In the original setting, Luciano and Semeraro imposed some constraints on the subordinator parameters such that the multivariate subordinator is of the same subordinator sub-class as its components, leading to asset log-returns of a particular Lévy type. This restriction leads to marginal characteristic functions which are independent on the common subordinator setting. In this paper, we propose to extend the original model by relaxing the constraints on the subordinator parameters, leading to marginal characteristic functions which become a function of the whole parameter set. Under this generalized version, the volatility of the log-returns depends on both the common and idiosyncratic subordinator settings, and not only on the idiosyncratic one, which makes the generalized model more in line with the empirical evidence of the presence of both an idiosyncratic and a common component in the business clock. For the numerical study, we compare the calibration fit of both univariate option surfaces and market implied correlations for a period extending from the 2nd of June 2008 until the 30th of October 2009 under the two model settings and assess the calibration risk arising from different calibration procedures by pricing traditional multivariate exotic options. In particular we show that the decoupling calibration procedure fails to accurately replicate the market dependence structure under the original model for highly correlated asset returns and we propose an alternative methodology which rests on a joint calibration of the univariate and the dependence structure and which leads to an accurate fit of the market reality under both the generalized and original models.     

Comparing alternative Lévy base correlation models for pricing and hedging CDO tranches

In this paper we investigate alternative Lévy base correlation models that arise from the Gamma, Inverse Gaussian and CMY distribution classes. We compare these models with the basic (exponential) Lévy base correlation model and the classical Gaussian base correlation model. For all investigated models, the Lévy base correlation curve is significantly flatter than the corresponding Gaussian curve, which indicates better correspondence of the Lévy models with reality. Furthermore, we present the results of pricing bespoke tranchlets and comparing deltas of both standard and custom-made tranches under all the considered models. We focus on deltas with respect to the CDS index and individual CDSs, and the hedge ratio for hedging the equity tranche with the junior mezzanine.     

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for the existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.     

Wavelet Galerkin pricing of American options on Lévy driven assets

The price of an American-style contract on assets driven by a class of Markov processes containing, in particular, Lévy processes of pure jump type with infinite jump activity is expressed as the solution of a parabolic variational integro-differential inequality (PIDI). A Galerkin discretization in logarithmic price using a wavelet basis is presented. Log-linear complexity in each time-step is achieved by wavelet compression of the moment matrix of the price process’ jump measure and by wavelet preconditioning of the large matrix LCPs at each time-step. Efficiency is demonstrated by numerical experiments for pricing American put contracts on various jump-diffusion and pure jump models. Failure of the smooth pasting principle is observed for American put contracts for certain finite variation pure jump price processes.     

Option pricing under stochastic volatility and tempered stable Lévy jumps

The purpose of this paper is to introduce a stochastic volatility model for option pricing that exhibits Lévy jump behavior. For this model, we derive the general formula for a European call option. A well known particular case of this class of models is the Bates model, for which the jumps are modeled by a compound Poisson process with normally distributed jumps. Alternatively, we turn our attention to infinite activity jumps produced by a tempered stable process. Then we empirically compare the estimated log-return probability density and the option prices produced from this model to both the Bates model and the Black–Scholes model. We find that the tempered stable jumps describe more precisely market prices than compound Poisson jumps assumed in the Bates model.     

Fast and accurate pricing of barrier options under Lévy processes

We suggest two new fast and accurate methods, the fast Wiener–Hopf (FWH) method and the iterative Wiener–Hopf (IWH) method, for pricing barrier options for a wide class of Lévy processes. Both methods use the Wiener–Hopf factorization and the fast Fourier transform algorithm. We demonstrate the accuracy and fast convergence of both methods using Monte Carlo simulations and an accurate finite difference scheme, compare our results with those obtained by the Cont–Voltchkova method, and explain the differences in prices near the barrier. The first author is supported, in part, by grant RFBR 09-01-00781.     

Option pricing and hedging under a stochastic volatility Lévy process model

In this paper, we discuss a stochastic volatility model with a Lévy driving process and then apply the model to option pricing and hedging. The stochastic volatility in our model is defined by the continuous Markov chain. The risk-neutral measure is obtained by applying the Esscher transform. The option price using this model is computed by the Fourier transform method. We obtain the closed-form solution for the hedge ratio by applying locally risk-minimizing hedging.     

COS method for option pricing under a regime-switching model with time-changed Lévy processes

We extend the regime-switching model to the rich class of time-changed Lévy processes and use the Fourier cosine expansion (COS) method to price several options under the resulting models. The extension of the COS method to price under the regime-switching model is not straightforward because it requires the evaluation of the characteristic function which is based on a matrix exponentiation which is not an easy task. For a two-state economy, we give an analytical expression for computing this matrix exponential, and for more than two states, we use the Carathéodory–Fejér approximation to find the option prices efficiently. In the new framework developed here, it is possible to allow switches not only in the model parameters as is commonly done in literature, but we can also completely switch among various popular financial models under different regimes without any additional computational cost. Calibration of the different regime-switching models with real market data shows that the best models are the regime-switching time-changed Lévy models. As expected by the error analysis, the COS method converges exponentially and thus outperforms all other numerical methods that have been proposed so far.     

Stein’s method and zero bias transformation for CDO tranche pricing

We propose an original approximation method, which is based on Stein’s method and the zero bias transformation, to calculate CDO tranches in a general factor framework. We establish first-order correction terms for the Gaussian and the Poisson approximations respectively and we estimate the approximation errors. The application to the CDO pricing consists of combining the two approximations. This work is partially supported by Fondation de risque.     

Applications of Gram–Charlier expansion and bond moments for pricing of interest rates and credit risk

The purpose of this paper is to demonstrate the powerful and flexible applicability of the Gram–Charlier expansion to pricing of a wide variety of interest rate related products involving interest rate risk and credit risk. In this paper, we develop easily implemented approximations of the prices of several derivatives; swaptions, CMS, CMS options, and vulnerable options. Associated with the default risk, a survival contingent forward measure is constructed.     

Effect of perceived risk on nuclear power plant operators’ safety behavior and errors

Safety behavior and human errors are major concerns for nuclear power plant operators. The present study investigated how nuclear power plant operators’ perceived risk influences the quality of their own work performance in terms of safety behavior and errors. In total, 349 operators from two nuclear power plants in China participated in the present study. We found that perceived risk had a negative linear relationship with safety behavior and a quadratic relationship with errors. Leader support played a moderating role in the relationships between perceived risk, safety behavior, and errors. These results supported the job demands–resources model and provided further evidence for the relationship between perceived risk and outcomes related to safety behavior and errors. Our findings suggest that an effective way to address the issue of high perceived risk is to provide a supportive environment.     

CLA’s,PLA’s and a new method for pricing general passport options

This paper is primarily concerned with pricing a general passport option (GPO) within the standard Black–Scholes framework. We show that in all possible cases of the allowed trading strategy, the price can be decomposed into simple portfolios of standard European calls and puts and a contract we call a ‘PLA’ or a put on the log-asset price. For completeness, we also introduce the call on the log-asset price (or CLA) and explore their properties and applications. The decomposition of the GPO into its constituent parts is achieved with the help of the Method of Images to convert certain barrier option payoffs into equivalent European payoffs. This technique considerably simplifies the calculation and adds significant transparency to what is otherwise regarded as very complex problem. Curiously, a spin-off of the method to price the GPO suggests an alternative and simpler way to price lookback options.     

Coherent and convex monetary risk measures for unbounded càdlàg processes

Assume that the random future evolution of values is modelled in continuous time. Then, a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. In this paper we study coherent and convex monetary risk measures on the space of all càdlàg processes that are adapted to a given filtration. We show that if such risk measures are required to be real-valued, then they can only depend on a stochastic process in a way that is uninteresting for many applications. Therefore, we allow them to take values in ( −∞, ∞]. The economic interpretation of a value of ∞ is that the corresponding financial position is so risky that no additional amount of money can make it acceptable. The main result of the paper gives different characterizations of coherent or convex monetary risk measures on the space of all bounded adapted càdlàg processes that can be extended to coherent or convex monetary risk measures on the space of all adapted càdlàg processes. As examples we discuss a new approach to measure the risk of an insurance company and a coherent risk measure for unbounded càdlàg processes induced by a so called m-stable set.Due to errors during the typesetting process, this article was published incorrectly in Finance Stoch 9(3):369–387 (2005). The address of the first author was printed incorrectly, and in the whole paper the angular brackets were misprinted as [ ]. The complete corrected article is given here. The online version of the original paper can be found at: http://dx.doi.org/10.1007/s00780-004-0150-7     

The impact of directors’ and officers’ insurance on audit pricing: Evidence from UK companies

This paper examines the impact of directors’ and officers’ (D&O) insurance on audit pricing in a large sample of UK companies. The existence of D&O insurance is expected to exert a dual impact on auditors’ pricing decisions. The presence of an additional source of funds to satisfy stakeholder claims in the event of audit client failure suggests that audit fees in insured companies should be lower. Alternatively, recent research has identified a positive link between the presence of D&O insurance and a number of characteristics traditionally associated with more expensive audits. The main objective of this study is to ascertain which of these influences pre-dominates. Analysing a sample of 753 UK listed companies in the early 1990s, when companies were obliged to disclose the presence of D&O insurance, this study shows that D&O insurance is associated with higher audit fees. It also confirms that insured companies are larger, more complex and present a greater audit risk (using a range of measures) than uninsured companies. Further analysis suggests that the impact of D&O insurance on audit fees may be influenced by company size, auditor size, and the extent of non-executive presence on the company's board.     

Distribution of occupation times for constant elasticity of variance diffusion and the pricing of α-quantile options

The main results of this paper are the derivation of the distribution functions of occupation times under the constant elasticity of variance process. The distribution functions can then be used to price α-quantile options. We also derive the fixed-floating symmetry relation for α-quantile options when the underlying asset price process follows a geometric Brownian motion.     

Variation and share-weighted variation swaps on time-changed Lévy processes

For a family of functions G, we define the G-variation, which generalizes power variation; G-variation swaps, which pay the G-variation of the returns on an underlying share price F; and share-weighted G-variation swaps, which pay the integral of F with respect to G-variation. For instance, the case G(x)=x ² reduces these notions to, respectively, quadratic variation, variance swaps, and gamma swaps. We prove that a multiple of a log contract prices a G-variation swap, and a multiple of an FlogF contract prices a share-weighted G-variation swap, under arbitrary exponential Lévy dynamics, stochastically time-changed by an arbitrary continuous clock having arbitrary correlation with the Lévy driver, under integrability conditions. We solve for the multipliers, which depend only on the Lévy process, not on the clock. In the case of quadratic G and continuity of the underlying paths, each valuation multiplier is 2, recovering the standard no-jump variance and gamma-swap pricing results. In the presence of jump risk, however, we show that the valuation multiplier differs from 2, in a way that relates (positively or negatively, depending on the specified G) to the Lévy measure’s skewness. In three directions this work extends Carr–Lee–Wu, which priced only variance swaps. First, we generalize from quadratic variation to G-variation; second, we solve for not only unweighted but also share-weighted payoffs; and third, we apply these tools to analyze and minimize the risk in a family of hedging strategies for G-variation.     

Generalized stochastic target problems for pricing and partial hedging under loss constraints��application in optimal book liquidation

We consider a singular version with state constraints of the stochastic target problems studied in Soner and Touzi (SIAM J. Control Optim. 41:404?C424, 2002; J. Eur. Math. Soc. 4:201?C236, 2002) and more recently Bouchard et al. (SIAM J. Control Optim. 48:3123?C3150, 2009), among others. This provides a general framework for the pricing of contingent claims under risk constraints. Our extended version perfectly fits the market models with proportional transaction costs and the order book liquidation issues. Our main result is a direct PDE characterization of the associated pricing function. As an example application, we discuss the valuation of VWAP-guaranteed-type book liquidation contracts, for a general class of risk functions.     

A high-low-based omnibus test for symmetry, the Lévy property, and other hypotheses on intraday returns

We consider different models for intraday log-returns: Lévy models, symmetric models, and Lévy processes subjected to independent continuous time-changes. For these models, we show bivariate interchangeability of intraday up- and downside volatility ratios which are built using daily high-low prices. Using conditional inference permutation tests on bivariate interchangeability, we develop an omnibus test for the above-mentioned models. Empirically, we find strong evidence against intraday returns belonging to these model classes, as we reject bivariate interchangeability of the volatility ratios for half of the components of the DJIA, two thirds of the S&P 500 shares and almost all stocks of the German DAX.