Towards a General Theory of Good Deal Bounds

We consider an incomplete market in the form of a multidimensional Markovian factor model, driven by a general marked point process (representing discrete jump events) as well as by a standard multidimensional Wiener process. Within this framework we study arbitrage free good deal pricing bounds for derivative assets along the lines of Cochrane and Saa-Requejo, extending the CSR results to the point process case. As a concrete application we present numerical results for the classic Merton jump-diffusion model. As a by product of the general theory we also extend the Hansen-Jagannathan bounds for the Sharpe Ratio to the point process setting.Incomplete markets; good deal bounds; financial derivatives; arbitrage pricing

On the Term Structure of Futures and Forward Prices

We investigate the term structure of forward and futures prices for models where the price processes are allowed to be driven by a general marked point process as well as by a multidimensional Wiener process. Within an infinite dimensional HJM-type model for futures and forwards we study the properties of futures and forward convenience yield rates. For finite dimensional factor models, we develop a theory of affine term structures, which is shown to include almost all previously known models. We also derive two general pricing formulas for futures options. Finally we present an easily applicable sufficient condition for the possibility of fitting a finite dimensional futures price model to an arbitrary initial futures price curve, by introducing a time dependent function in the drift term.term structure; futures price; forward price; options; jump-diffusion model; affine term structure

Parameter Estimation and Reverse Martingales

Within the framework of transitive sufficient processes we investigate identifiability properties of unknown parameters. In particular we consider unbiased parameter estimators, which are shown to be closely connected to time reversal and to reverse martingales. One of the main results is that, within our framework, every unbiased estimator process is a reverse martingale, thus automatically giving us strong consistency results. We also study structural properties of unbiased estimators, and it is shown that the existence of an unbiased parameter estimator is equivalent to the existence of a solution to an inverse boundary value problem. We give explicit representation formulas for the estimators in terms of Feynman-Kac type representations using complex valued diffusions, and we also give Cramér-Rao bounds for the estimation error.Parameter estimation; time reversal; martingale theory

On the Timing Option in a Futures Contract

The timing option embedded in a futures contract allows the short position to decide when to deliver the underlying asset during the last month of the contract period. In this paper we derive, within a very general incomplete market framework, an explicit model independent formula for the futures price process in the presence of a timing option. We also provide a characterization of the optimal delivery strategy, and we analyze some concrete examples.Futures contract; timing option; optimal stopping

A Note on the Pricing of Real Estate Index Linked Swaps

In this paper we discuss the pricing of commercial real estate index linked swaps (CREILS). This particular pricing problem has been studied by Buttimer et al. (1997) in a previous paper. We show that their results are only approximately correct and that the true theoretical price of the swap is in fact equal to zero. This result is shown to hold regardless of the specific model chosen for the index process, the dividend process, and the interest rate term structure. We provide an intuitive economic argument as well as a full mathematical proof of our result. In particular we show that the nonzero result in the previous paper is due to two specific numerical approximations introduced in that paper, and we discuss these approximation errors from a theoretical as well as from a numerical point of view.Real estate; index linked swaps; arbitrage

Diversified Portfolios in Continuous Time

We study a financial market containing an infinite number of assets, where each asset price is driven by an idiosyncratic random source as well as by a systematic noise term. Introducing 2 asymptotic assets" which correspond to certain infinitely well diversified portfolios we study absence of (asymptotic) arbiytrage, and in this context we obtain continuous time extensions of atemporal APT results. We also study completeness and derivative pricing, showing that the possibility of forming infinitely well diversified portfolios has the property of completing the market. It also turns out that models where the all risk is of diffusion type are qualitatively quite different from models where one risk is of diffusion type and the other is of Poisson type. We also present a simple martingale based theory for absence of asymptotic arbitrage.Large economies; diversifiable risk; APT; asymptotic arbitrage; completeness; martingales

Finite dimensional Markovian realizations for stochastic volatility forward rate models

We consider forward rate rate models of HJM type, as well as more general infinite dimensional SDEs, where the volatility/diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework we use the previously developed Hilbert space realization theory in order provide general necessary and sufficent conditions for the existence of a finite dimensional Markovian realizations for the stochastic volatility models. We illustrate the theory by analyzing a number of concrete examples.HJM models; stochastic volatility; factor models; forward rates; state space models; Markovian realizations; infinite dimensional SDEs

On the Geometry of Interest Rate Models

In this paper, which is a substantial extension of the earlier essay Björk (2001), we give an overview of some recent work on the geometric properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. 1. When is a given forward rate model consistent with a given family of forward rate curves? 2. When can the inherently infinite dimensional forward rate process be realized by means of a Markovian finite dimensional state space model. We consider interest rate models of Heath-Jarrow-Morton type, where the forward rates are driven by a multidimensional Wiener process, and where he volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Within this framework we give necessary and sufficient conditions for consistency, as well as for the existence of a finite dimensional realization, in terms of the forward rate volatilities. We also study stochastic volatility HJM models, and we provide a systematic method for the construction of concrete realizations.Forward rate curves; interest rate models; factor models; state space models; Markovian realizations;

Towards a General Theory of Bond Markets.

The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are used to define the evolution of the value of a portfolio of bonds corresponding to a trading strategy which is a measure- valued predictable process. The existence of an equivalent martingale measure is discussed and HJM-type conditions are derived for a jump-diffusion model. The question of market completeness is considered as a problem of the range of a certain integral operator. We introduce a concept of approximate market completeness and show that a market is approximately complete if an equivalent martingale measure is unique.Bond market; term structure of interest rates; stochastic integral; Banach space-valued integrators; measure-valued portfolio; jump-diffusion model; martingale measure; arbitrage; market completeness

Tasquinimod (ABR-215050), a quinoline-3-carboxamide anti-angiogenic agent, modulates the expression of thrombospondin-1 in human prostate tumors

<p>Abstract</p> <p>Background</p> <p>The orally active quinoline-3-carboxamide tasquinimod [ABR-215050; CAS number 254964-60-8), which currently is in a phase II-clinical trial in patients against metastatic prostate cancer, exhibits anti-tumor activity via inhibition of tumor angiogenesis in human and rodent tumors. To further explore the mode of action of tasquinimod, <it>in vitro </it>and <it>in vivo </it>experiments with gene microarray analysis were performed using LNCaP prostate tumor cells. The array data were validated by real-time semiquantitative reversed transcriptase polymerase chain reaction (sqRT-PCR) and protein expression techniques.</p> <p>Results</p> <p>One of the most significant differentially expressed genes both <it>in vitro </it>and <it>in vivo </it>after exposure to tasquinimod, was thrombospondin-1 (TSP1). The up-regulation of TSP1 mRNA in LNCaP tumor cells both <it>in vitro </it>and <it>in vivo </it>correlated with an increased expression and extra cellular secretion of TSP1 protein. When nude mice bearing CWR-22RH human prostate tumors were treated with oral tasquinimod, there was a profound growth inhibition, associated with an up-regulation of TSP1 and a down- regulation of HIF-1 alpha protein, androgen receptor protein (AR) and glucose transporter-1 protein within the tumor tissue. Changes in TSP1 expression were paralleled by an anti-angiogenic response, as documented by decreased or unchanged tumor tissue levels of VEGF (a HIF-1 alpha down stream target) in the tumors from tasquinimod treated mice.</p> <p>Conclusions</p> <p>We conclude that tasquinimod-induced up-regulation of TSP1 is part of a mechanism involving down-regulation of HIF1α and VEGF, which in turn leads to reduced angiogenesis via inhibition of the "angiogenic switch", that could explain tasquinimods therapeutic potential.</p