José Manuel Corcuera

• University of Barcelona

We study the equilibrium in the model proposed by Kyle (Econometrica 53(6):1315–1335, 1985) and extended to the continuous-time setting by Back (Rev Financ Stud 5(3):387–409, 1992). The novelty of this paper is that we consider a framework where the price pressure can be random. We also allow for a random release time of the fundamental value of th...

The continuous-time version of Kyle [(1985) Continuous auctions and insider trading, Econometrica 53 (6), 1315-1335.] developed by Back [(1992) Insider trading in continuous time, The Review of Financial Studies 5 (3), 387-409.] is studied here. In Back's model, there is asymmetric information in the market in the sense that there is an insider hav...

We study the equilibrium in the model proposed by Kyle in 1985 and extended to the continuous time setting by Back in 1992. The novelty of this paper is that we consider a framework where the price pressure can be random. We also allow for a random release time of the fundamental value of the asset. This framework includes all the particular Kyle m...

In 1988 Dybvig introduced the payoff distribution pricing model (PDPM) as an alternative to the capital asset pricing model (CAPM). Under this new paradigm agents preferences depend on the probability distribution of the payoff and for the same distribution agents prefer the payoff that requires less investment. In this context he gave the notion o...

In 1988 Dybvig introduced the payo distribution pricing model (PDPM) as an alternative to the capital asset pricing model (CAPM). Under this new paradigm agents preferences depend on the probability distribution of the payo and for the same distribution agents prefer the payo that requires less investment. In this context he gave the notion of ecie...

In this paper we analyze an extension of the Jeanblanc and Valchev [12] model by considering a short-term uncertainty model with two noises. It is a combination of the ideas of Duffie and Lando [9] and Jeanblanc and Valchev [12]: share quotations of the firm are available at the financial market, and these can be seen as noisy information about the...

In this paper we analyze an extension of the Jeanblanc and Valchev (2005) model by considering a short-term uncertainty model with two noises. It is a combination of the ideas of Duffie and Lando (2001) and Jeanblanc and Valchev (2005): share quotations of the firm are available at the financial market, and these can be seen as noisy information ab...

Contingent Convertible Bonds, or CoCos, are contingent capital instruments which are converted into shares, or may suer a principal write-down, if certain trigger event occurs. In this paper we discuss some approaches to the problem of pricing CoCos when its conversion and the other relevant credit events are triggered by the issuer's share price....

In this paper we obtain some formulas for pricing contingent convertibles subject to what we call extension risk, i.e., the possibility that bond issuer does not buy back the bond at pre specified call dates and then new coupons rate are established until bond maturity. We follow a structural approach and we address the finite and infinite maturity...

In a unified framework we study equilibrium in the presence of an insider having information on the signal of the firm value, which is naturally connected to the fundamental price of the firm related asset. The fundamental value itself is announced at a future random (stopping) time. We consider the two cases in which this release time of informati...

In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral of the weight process with respect to the Brownian motion w...

In this paper we try to review the research done so far about ambit processes, and their applications. The notion of ambit process was introduced by Barndoff-Nielsen and Schmiegel in 2007. Since then, many papers have been written studying their properties and applying them to model in different natural or economic phenomena. As it is shown in the...

We look at the problem of pricing contingent convertible bonds (CoCos) where the underlying risky asset dynamics are given by a smile conform model, more precisely, an exponential Lévy process incorporating jumps and heavy tails. A core mathematical quantity, needed in closed form in order to produce an exact analytical expression for the price of...

Contingent Convertibles (CoCos) are contingent capital instruments which convert into shares, or have a principal write down, if a trigger event takes place. CoCos exhibit the undesirable so-called death-spiral effect: by actively hedging the equity risk, investors can (unintentionally) force the conversion by making the share price deteriorate and...

In this article, we study a bond market where short rates evolve as r t =∫ -∞ t g(t-s)σ s W(ds) where g:(0,∞)→ℝ is deterministic, σ≥0 is also deterministic, and W is the stochastic Wiener measure. Processes of this type are also called Brownian semistationary processes and they are particular cases of ambit processes. These processes are, in genera...

This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in [Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolski...

As a consequence of the seminal work of D. Nualart and G. Peccati [Ann. Probab. 33, No. 1, 177–193 (2005; Zbl 1097.60007)], we have new central limit theorems for functionals of Gaussian processes that have allowed us to elucidate the asymptotic behavior of the multipower variation of certain ambit processes, see Ole E. Barndorff-Nielsen, the autho...

In this paper we review some old and new results about the enlargement of filtrations problem, as well as their applications to credit risk and insider trading problems. The enlargement of filtrations problem consists in the study of conditions under which a semimartingale remains a semimartingale when the filtration is enlarged, and, in such a cas...

In this paper we study the asymptotic behaviour of power and multipower variations of processes $Y$:\[Y_t=\int_{-\in fty}^tg(t-s)\sigma_sW(\mathrm{d}s)+Z_t,\] where $g:(0,\infty)\rightarrow\mathbb{R}$ is deterministic, $\sigma >0$ is a random process, $W$ is the stochastic Wiener measure and $Z$ is a stochastic process in the nature of a drift term...

In this paper the authors introduce the new concept of implied liquidity based on the recent developed two-way price theory (conic finance). Implied liquidity isolates and quantifies liquidity risk in financial markets. It is shown on real market option data on the major US indices how liquidity dried up in the troubled year end of 2008. These inve...

We look at the problem of pricing CoCo bonds where the underlying risky asset dynamics are given by a smile conform model, more precisely an exponential Lévy process incorporating jumps and heavy tails. A core mathematical quantity that is needed in closed form in order to produce an exact analytical expression for the price of a CoCo is the law of...

In this paper we analyze the completeness problem in a bond market where the short rate is driven by a non-homogeneous Lé process. Even though it is known that under certain conditions we have a kind of uniqueness of the risk neutral measure, little is known about how to hedge in this market. We elucidate that perfect replication formulas are not,...

The derivative of the log-likelihood function, known as score function, plays a central role in parametric statistical inference. It can be used to study the asymptotic behavior of likelihood and pseudo-likelihood estimators. For instance, one can deduce the local asymptotic normality property which leads to various asymptotic properties of these e...

The continuous-time version of Kyle's [6] model, known as the Back's [2] model, of asset pricing with asymmetric information, is studied. A larger class of price processes and a larger classes of noise traders' processes are studied. The price process, as in Kyle's [6] model, is allowed to depend on the path of the market order. The process of the...

In general, geometric additive models are incomplete and the perfect replication of derivatives, in the usual sense, is not possible. In this paper we complete the market by introducing the so-called power-jump assets. Using a static hedging formula, in order to relate call options and power-jump assets, we show that this market can also be complet...

In this paper the authors introduce the new concept of implied liquidity on the basis of the recent developed two-way price theory (conic finance). Implied liquidity isolates and quantifies in a fundamental way liquidity risk in financial markets. It is shown on real market option data on the major US indices how liquidity dried up in the troubled...

In this article we consider the asymptotic behavior of the power variation of processes of the form , where Sα is an α-stable process with index of stability 0αu from discrete observations.

We present some new asymptotic results for functionals of higher order differences of Brownian semi-stationary processes. In an earlier work we have derived a similar asymptotic theory for first order differences. However, the central limit theorems were valid only for certain values of the smoothness parameter of a Brownian semistationary process,...

In this paper we consider the asymptotic behavior of functionals of processes of the form ∫ 0t u s dB s H , where B H is a fractional Brownian motion with Hurst parameter H, and u is a process with finite q-variation, q<1/(1−H). We establish the stable convergence of the corresponding fluctuations.

We develop the asymptotic theory for the realised power variation of the processes X=ϕ•G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path of the process ϕ we prove the convergence in probability for...

This paper introduces the concept of implied Lévy volatility, hereby extending the intuitive Black-Scholes implied volatility into a more general context. More precisely, Lévy implied time and space volatility are introduced and a study of the shape of implied Lévy volatilities is made. Model performance is studied by analyzing delta-hedging strate...

Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing limit laws, due to Nualart, Peccati, and others.

In this paper the author considers an autoregressive process where the parameters of the process are unknown and try to obtain pivots for predicting future observations. If we do a probabilistic prediction with the estimated model, where the parameters are estimated by a sample of size n, we introduce an error of order n-1 in the coverage probabil...

Convergence in probability and central limit laws of bipower variation for Gaussian processes with stationary increments and for integrals with respect to such processes are derived. The main tools of the proofs are some recent powerful techniques of Wiener/Itô/Malliavin calculus for establishing limit laws, due to Nualart, Peccati and others.

We consider market models where the stock price process is driven by a non-homogeneous Lévy process. In general, these market models are incomplete but can be completed by introducing in the market an infinite set of new assets, the power-jump assets. We use the martingale method in order to obtain the optimal portfolios in these markets.

We show some results about the asymptotic behavior of the power variation and how they can be used for statistical purposes in the context of some integral long-memory processes. These processes are obtained as integrals with respect to a fractional Brownian motion with Hurst parameter H> 1/2.

In this paper we consider the asymptotic behavior of the realized power variation of processes of the form R t 0 us − dS α s , where S α is an α-stable pro-cess with index of stability 0 < α < 2 and u is a process of finite q-variation with q < α max(0,α−1) , which may be correlated to S α . We establish sta-ble convergence of the corresponding flu...

We consider the asymptotic behaviour of the realized power variation of processes of the form [math] , where [math] is a fractional Brownian motion with Hurst parameter [math] , and [math] is a process with finite [math] -variation, [math] . We establish the stable convergence of the corresponding fluctuations. These results provide new statistical...

In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric Levy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However, the model c...

The problem of prediction is considered in a multidimensional setting. Extending an idea presented by Barndorff-Nielsen and Cox, a predictive density for a multivariate random variable of interest is proposed. This density has the form of an estimative density plus a correction term. It gives simultaneous prediction regions with coverage error of s...

Except for the geometric Brownian model and the geometric Poissonian model, the general geometric Lévy market models are incomplete models and there are many equivalent martingale measures. In this paper we suggest to enlarge the market by a series of very special assets (power-jump assets) related to the suitably compensated power-jump processes o...

In this paper we consider a market driven by a Wiener process where there is an insider and a regular trader. The insider has privileged information which has been deformed by an independent noise vanishing as the revelation time approaches. At this time, the information of every trader is the same. We obtain the semimartingale decomposition of the...

Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem. Originally published in 2000,...

In the case of prior knowledge about the unknown parameter, the Bayesian predictive density coincides with the Bayes estimator for the true density in the sense of the Kullback-Leibler divergence, but this is no longer true if we consider another loss function. In this paper we present a generalized Bayes rule to obtain Bayes density estimators wit...

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a mul...

In the case of prior knowledge about the unknown parameter, the Bayesian predictive density coincides with the Bayes estimator for the true density in the sense of the Kullback-Leibler divergence, but this is no longer true if we consider another loss function. In this paper we present a generalized Bayes rule to obtain Bayes density estimators wit...

In this paper we characterize the local structure of monotone and regular divergences, which include f-divergences as a particular case, by giving their Taylor expansion up to fourth order. We extend a previous result obtained by Cencov, using the invariant properties of Amari's a-connections.

The parametric statistical models with suitable regularity conditions have a natural Riemannian manifold structure, given by the information metric. Since the parameters are merely labels for the probability measures, an inferential statement should be formulated through intrinsic objects, invariant under reparametrizations. In this context the est...

Abstract In this paper we consider the asymptotic behavior of the realized power variation of processes of the form , 2, and u is a process with finite q-variation, q < 1/(1 H). We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory eect,and the Hurst pa...

In the present note the problem of prediction is considered in a multidimensional set-ting. Extending an idea presented in Barndorff-Nielsen and Cox (1996), a predictive density for the future multivariate random variable is proposed. This density has the form of an estimative density plus a correction term which is easily calculated. It gives simu...