Approximate solution to a hybrid model with stochastic volatility: a singular-perturbation strategy

We study a hybrid model of Schobel-Zhu-Hull-White-type from a singular-perturbation-analysis perspective. The merit of the paper is twofold: On one hand, we find boundary conditions for the deterministic non-linear degenerate parabolic partial differential equation for the evolution of the stock price. On the other hand, we combine two-scales regular- and singular-perturbation techniques to find an approximate solution to the pricing PDE. The aim is to produce an expression that can be evaluated numerically very fast

Cheapest-to-Deliver Collateral: A Common Factor Approach

The collateral choice option gives the collateral posting party the opportunity to switch between different collateral currencies which is well-known to impact the asset price. Quantification of the option's value is of practical importance but remains challenging under the assumption of stochastic rates, as it is determined by an intractable distribution which requires involved approximations. Indeed, many practitioners still rely on deterministic spreads between the rates for valuation. We develop a scalable and stable stochastic model of the collateral spreads under the assumption of conditional independence. This allows for a common factor approximation which admits analytical results from which further estimators are obtained. We show that in modelling the spreads between collateral rates, a second order model yields accurate results for the value of the collateral choice option. The model remains precise for a wide range of model parameters and is numerically efficient even for a large number of collateral currencies.Comment: 23 pages, 4 figures, 4 table

Persistent left superior vena cava with an absent right superior vena cava in a 72-year-old male with multivessel coronary artery disease

Congenital anomalies of systemic veins are usually asymptomatic and foundincidentally during ultrasonography, computed tomography (CT) or magneticresonance examinations performed for other clinical indications. Persistent leftsuperior vena cava (PLSVC) with absent right superior vena cava (RSVC) is thecongenital aberration in the thoracic venous system which occurs in only 0.09%to 0.13% of patients who have congenital heart defects. In this paper, we presentthe extremely rare case of a 72-year-old male with PLSVC associated withan absence of RSVC, referred for coronary CT angiography. Multidetector CTangiography is a powerful tool for the detection of venous anomalies, which isessential before invasive procedures such as the implantation of pacemakers

Prevalence of congenital coronary artery anomalies and variants in 726 consecutive patients based on 64-slice coronary computed tomography angiography

  Background: Coronary computed tomography angiography (CCTA) is helpful in making a precise noninvasive evaluation of coronary anatomy, allowing concomitant evaluation of other cardiac structures. The aim of this study was to determine the prevalence of coronary artery variations detected by 64-slice mutidetector CT. Materials and methods: The results of ECG-gated CCTA in 726 consecutive patients (mean age 58 years) were analysed retrospectively. The main indicationsfor CCTA were a typical chest pain, angina pectoris, screening for coronary artery disease and determination of the patency of bypass grafts or stents. Acquisitionwas performed with a 64-detector CT scanner with retrospective ECG gating. Imaging results were assessed by experienced cardiovascular radiologist. Results: The overall incidence of coronary artery anomalies was 1.1% (8 out of 726 participants). The most common anomaly was an anomalous origin of the circumflex artery from the right coronary sinus with a retroaortic course (4 patients,0.6%), followed by origin of right coronary artery from the left coronary sinus (2 patients, 0.3%). One patient with abnormal origin of the left main artery from the right coronary sinus (0.1%) and 1 patient with a circumflex artery origin from the proximal segment of the right coronary artery (0.1%) were observed, both with retroartic course. Conclusions: CCTA is a noninvasive imaging technique useful for the precise evaluation of variations of the coronary arteries. This study shows similar results to other reports on this subject.

Approximate solution to a hybrid model with stochastic volatility: a singular-perturbation strategy

We study a hybrid model of Sch¨obel-Zhu-Hull-White-type from a singular-perturbationanalysis perspective. The merit of the paper is twofold: On one hand, we find boundary conditions for the deterministic non-linear degenerate parabolic partial differential equation for the evolution of the stock price. On the other hand, we combine two-scales regular- and singular-perturbation techniques to find an approximate solution to the pricing PDE. The aim is to produce an expression that can be evaluated numerically very fast

Sensitivities and Hedging of the Collateral Choice Option

The collateral choice option allows a collateral-posting party the opportunity to change the type of security in which the collateral is deposited. Due to non-zero collateral basis spreads, this optionality significantly impacts asset valuation. Because of the complexity of valuing the option, many practitioners resort to deterministic assumptions on the collateral rates. In this article, we focus on a valuation model of the collateral choice option based on stochastic dynamics. Intrinsic differences in the resulting collateral choice option valuation and its implications for collateral management are presented. We obtain sensitivities of the collateral choice option price under both the deterministic and the stochastic model, and we show that the stochastic model attributes risks to all involved collateral currencies. Besides an inability to capture volatility effects, the deterministic model exhibits a digital structure in which only the cheapest-to-deliver currency influences the valuation at a given time. We further consider hedging an asset with the collateral choice option by a portfolio of domestic and foreign zero-coupon bonds that do not carry the collateral choice option. We propose static hedging strategies based on the crossing times of the deterministic model and based on variance-minimization under the stochastic model. We show how the weights of this model can be explicitly determined with the semi-analytical common factor approach and we show in numerical experiments that this strategy offers good hedging performance under minimized variance

Efficient Wrong-Way Risk Modelling for Funding Valuation Adjustments

Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modelling. Yet, it can be challenging to compute WWR efficiently. We propose to split the relevant exposure profile into two parts: an independent part and a WWR-driven part. For the first part, already available exposures can be used where correlations between the funding spread and market risks are ignored. We express the second part of the exposure profile in terms of the stochastic drivers and approximate these by a common Gaussian stochastic factor. The proposed approximation is generic, is an add-on to the existing xVA calculations and provides an efficient and robust way to include WWR in FVA modelling. Furthermore, the approximation provides some intuition on WWR. Case studies are presented for an interest rate swap and a representative multi-currency portfolio of swaps. They illustrate that the approximation method is applicable in a practical setting due to its generic nature. We analyze the approximation error and illustrate how the approximation can be used to compute WWR sensitivities, which are needed for risk management

The intrahepatic signalling niche of hedgehog is defined by primary cilia positive cells during chronic liver injury

Background & Aims: In vertebrates, canonical Hedgehog (Hh) pathway activation requires Smoothened (SMO) translocation to the primary cilium (Pc), followed by a GLI-mediated transcriptional response. In addition, a similar gene regulation occurs in response to growth factors/cytokines, although independently of SMO signalling. The Hh pathway plays a critical role in liver fibrosis/regeneration; however, the mechanism of activation in chronic liver injury is poorly understood. This study aimed to characterise Hh pathway activation upon thioacetamide (TAA)- induced chronic liver injury in vivo by defining Hh-responsive cells, namely cells harbouring Pc and Pc-localised SMO. Methods: C57BL/6 mice (wild-type or Ptc1+/_) were TAA-treated. Liver injury and Hh ligand/pathway mRNA and protein expression were assessed in vivo. SMO/GLI manipulation and SMO dependent/ independent activation of GLI-mediated transcriptional response in Pc-positive (Pc+) cells were studied in vitro. Results: In vivo, Hh activation was progressively induced following TAA. At the epithelial-mesenchymal interface, injured hepatocytes produced Hh ligands. Progenitors, myofibroblasts, leukocytes and hepatocytes were GLI2+. Pc+ cells increased following TAA, but only EpCAM+/GLI2+ progenitors were Pc+/SMO+. In vitro, SMO knockdown/hGli3-R overexpression reduced proliferation/viability in Pc+ progenitors, whilst increased proliferation occurred with hGli1 overexpression. HGF induced GLI transcriptional activity independently of Pc/SMO. Ptc1+/_ mice exhibited increased progenitor, myofibroblast and fibrosis responses. Conclusions: In chronic liver injury, Pc+ progenitors receive Hh ligand signals and process it through Pc/SMO-dependent activation of GLI-mediated transcriptional response. Pc/SMO-independent GLI activation likely occurs in Pc_/GLI2+ cells. Increased fibrosis in Hh gain-of-function mice likely occurs by primary progenitor expansion/proliferation and secondary fibrotic myofibroblast expansion, in close contact with progenitors