On the goodness of fit of Kirk's formula for spread option prices

In this paper we investigate the goodness of fit of the Kirk's approximation formula for spread option prices in the correlated lognormal framework. Towards this end, we use the Malliavin calculus techniques to find an expression for the short-time implied volatility skew of options with random strikes. In particular, we obtain that this skew is very pronounced in the case of spread options with extremely high correlations, which cannot be reproduced by a constant volatility approximation as in the Kirk's formula. This fact agrees with the empirical evidence. Numerical examples are given.

Estimation du débit de filtration glomérulaire par la formule DFG = K x T/Pcr [Estimation of glomerular filtration rate by the formula GFR = K x T/Pc].

BACKGROUND: Creatinine clearance is the most common method used to assess glomerular filtration rate (GFR). In children, GFR can also be estimated without urine collection, using the formula GFR (mL/min x 1.73 m2) = K x height [cm]/Pcr [mumol/L]), where Pcr represents the plasma creatinine concentration. K is usually calculated using creatinine clearance (Ccr) as an index of GFR. The aim of the present study was to evaluate the reliability of the formula, using the standard UV/P inulin clearance to calculate K. METHODS: Clearance data obtained in 200 patients (1 month to 23 years) during the years 1988-1994 were used to calculate the factor K as a function of age. Forty-four additional patients were studied prospectively in conditions of either hydropenia or water diuresis in order to evaluate the possible variation of K as a function of urine flow rate. RESULTS: When GFR was estimated by the standard inulin clearance, the calculated values of K was 39 (infants less than 6 months), 44 (1-2 years) and 47 (2-12 years). The correlation between the values of GFR, as estimated by the formula, and the values measured by the standard clearance of inulin was highly significant; the scatter of individual values was however substantial. When K was calculated using Ccr, the formula overestimated Cin at all urine flow rates. When calculated from Ccr, K varied as a function of urine flow rate (K = 50 at urine flow rates of 3.5 and K = 64 at urine flow rates of 8.5 mL/min x 1.73 m2). When calculated from Cin, in the same conditions, K remained constant with a value of 50. CONCLUSIONS: The formula GFR = K x H/Pcr can be used to estimate GFR. The scatter of values precludes however the use of the formula to estimate GFR in pathophysiological studies. The formula should only be used when K is calculated from Cin, and the plasma creatinine concentration is measured in well defined conditions of hydration.

Modeling the forensic two-trace problem with Bayesian networks

The forensic two-trace problem is a perplexing inference problem introduced by Evett (J Forensic Sci Soc 27:375-381, 1987). Different possible ways of wording the competing pair of propositions (i.e., one proposition advanced by the prosecution and one proposition advanced by the defence) led to different quantifications of the value of the evidence (Meester and Sjerps in Biometrics 59:727-732, 2003). Here, we re-examine this scenario with the aim of clarifying the interrelationships that exist between the different solutions, and in this way, produce a global vision of the problem. We propose to investigate the different expressions for evaluating the value of the evidence by using a graphical approach, i.e. Bayesian networks, to model the rationale behind each of the proposed solutions and the assumptions made on the unknown parameters in this problem.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.

Comment on "Geochemistry, petrogenesis and tectonic setting of the Samothraki mafic suite, NE Greece: Trace-element, isotopic and zircon age constraints'' by N. Koglin, D. Kostopoulos & T. Reischmann [Tectonophysics 473, 53-68 (doi:10.1016/j.tecto.2008.10.028)]

The work by Koglin et al. (Koglin, N., Kostopoulos, D., Reichmann, T., 2009. Geochemistry, petrogenesis and tectonic setting of the Samothraki mafic Suite, NE Greece: Trace-element, isotopic and zircon age constraints. Tectonophysics 473, 53-68. doi: 10.1016/j.tecto.2008.10.028), where the authors have proposed to nullify the scenario presented by Bonev and Stampfli (Bonev, N., Stampfli, G., 2008. Petrology, geochemistry and geodynamic implications of Jurassic island arc magmatism as revealed by mafic volcanic rocks in the Mesozoic low-grade sequence, eastern Rhodope, Bulgaria. Lithos 100, 210-233) is here Put under discussion. The arguments for this proposal are reviewed in the light of available stratigraphic and radiometric age constraints, geochemical signature and tectonics of highly relevant Jurassic ophiolitic suites occurring immediately north of the Samothraki mafic suite. Our conclusion is that the weak arguments and the lack of knowledge on the relevant constraints from the regional geologic information make inconsistent the Proposal and the model of these authors. (C) 2009 Elsevier B.V. All rights reserved.

A decomposition formula for option prices in the Heston model and applications to option pricing approximation

By means of classical Itô's calculus we decompose option prices asthe sum of the classical Black-Scholes formula with volatility parameterequal to the root-mean-square future average volatility plus a term dueby correlation and a term due to the volatility of the volatility. Thisdecomposition allows us to develop first and second-order approximationformulas for option prices and implied volatilities in the Heston volatilityframework, as well as to study their accuracy. Numerical examples aregiven.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

Stable isotope and trace element stratigraphy across the Permian-Triassic transition: A redefinition of the boundary in the Velebit Mountain, Croatia

Stable isotopes of carbonates (delta(13)C(carb), delta(18)O(carb)), organic matter (delta(13)C(org), delta(15)N(org)) and major, trace and rare earth element (REE) compositions of marine carbonate rocks of Late Permian to Early Triassic age were used to establish the position of the Permian-Triassic boundary (PTB) at two continuous sections in the Velebit Mountain, Croatia. The chosen sections - Rizvanusa and Brezimenjaca - are composed of two lithostratigraphic units, the Upper Permian Transitional Dolomite and the overlying Sandy Dolomite. The contact between these units, characterized by the erosional features and sudden occurrence of ooids and siliciclastic grains, was previously considered as the chronostratigraphic PTB. The Sandy Dolomite is characterized by high content of non-carbonate material (up to similar to 30 wt.% insoluble residue), originated from erosion of the uplifted hinterland. A relatively rich assemblage of Permian fossils (including Geinitzina, Globivalvulina, Hemigordius, bioclasts of gastropods, ostracods and brachiopods) was found for the first time in Sandy Dolomite, 5 m above the lithologic boundary in the Rizvanusa section. A rather abrupt negative delta(13)C(carb) excursion in both sections appears in rocks showing no recognizable facies change within the Sandy Dolomite, -2 parts per thousand at Rizvanusa and -1.2 parts per thousand at Brezimenjaca, 11 m and 0.2 m above the lithologic contact, respectively. This level within the lower part of the Sandy Dolomite is proposed as the chemostratigraphic PTB. In the Rizvanusa section, the delta(13)C(org) values decline gradually from similar to-25 parts per thousand in the Upper Permian to similar to-29 parts per thousand in the Lower Triassic. The first negative delta(13)C(org) excursion occurs above the lithologic contact, within the uppermost Permian deposits, and appears to be related to the input of terrigenous material. The release of isotopically light microbial soil-biomass into the shallow-marine water may explain this sudden decrease of delta(13)C(org) values below the PTB. This would support the hypothesis that in the western Tethyan realm the land extinction, triggering a sudden drop of woody vegetation and related land erosion, preceded the marine extinction. The relatively low delta(15)N(org) values at the Permian-Triassic (P-Tr) transition level, close to approximate to 0 parts per thousand, and a secondary negative delta(13)C(org) excursion of -0.5 parts per thousand point to significant terrestrial input and primary contribution of cyanobacteria. The profiles of the concentrations of redox-sensitive elements (Ce, Mn, Fe, V), biogenic or biogenic-scavenged elements (P, Ba, Zn, V), Ce/Ce* values, and normalized trace elements, including Ba/Al, Ba/Fe, Ti/Al, Al/(Al + Fe + Mn) and Mn/Ti show clear excursions at the Transitional Dolomite-Sandy Dolomite lithologic boundary and the chemostratigraphic P-Tr boundary. The stratigraphic variations indicate a major regression phase marking the lithologic boundary, transgressive phases in the latest Permian and a gradual change into shallow/stagnant anoxic marine environment towards the P-Tr boundary level and during the earliest Triassic. (C) 2010 Elsevier B.V. All rights reserved.

Comparison of the glomerular filtration rate in children by the new revised Schwartz formula and a new generalized formula.

The most widely used formula for estimating glomerular filtration rate (eGFR) in children is the Schwartz formula. It was revised in 2009 using iohexol clearances with measured GFR (mGFR) ranging between 15 and 75 ml/min × 1.73 m(2). Here we assessed the accuracy of the Schwartz formula using the inulin clearance (iGFR) method to evaluate its accuracy for children with less renal impairment comparing 551 iGFRs of 392 children with their Schwartz eGFRs. Serum creatinine was measured using the compensated Jaffe method. In order to find the best relationship between iGFR and eGFR, a linear quadratic regression model was fitted and a more accurate formula was derived. This quadratic formula was: 0.68 × (Height (cm)/serum creatinine (mg/dl))-0.0008 × (height (cm)/serum creatinine (mg/dl))(2)+0.48 × age (years)-(21.53 in males or 25.68 in females). This formula was validated using a split-half cross-validation technique and also externally validated with a new cohort of 127 children. Results show that the Schwartz formula is accurate until a height (Ht)/serum creatinine value of 251, corresponding to an iGFR of 103 ml/min × 1.73 m(2), but significantly unreliable for higher values. For an accuracy of 20 percent, the quadratic formula was significantly better than the Schwartz formula for all patients and for patients with a Ht/serum creatinine of 251 or greater. Thus, the new quadratic formula could replace the revised Schwartz formula, which is accurate for children with moderate renal failure but not for those with less renal impairment or hyperfiltration.

New combined serum creatinine and cystatin C quadratic formula for GFR assessment in children.

BACKGROUND AND OBJECTIVES: The estimated GFR (eGFR) is important in clinical practice. To find the best formula for eGFR, this study assessed the best model of correlation between sinistrin clearance (iGFR) and the solely or combined cystatin C (CysC)- and serum creatinine (SCreat)-derived models. It also evaluated the accuracy of the combined Schwartz formula across all GFR levels. DESIGN, SETTING, PARTICIPANTS, & MEASUREMENTS: Two hundred thirty-eight iGFRs performed between January 2012 and April 2013 for 238 children were analyzed. Regression techniques were used to fit the different equations used for eGFR (i.e., logarithmic, inverse, linear, and quadratic). The performance of each model was evaluated using the Cohen κ correlation coefficient and the percentage reaching 30% accuracy was calculated. RESULTS: The best model of correlation between iGFRs and CysC is linear; however, it presents a low κ coefficient (0.24) and is far below the Kidney Disease Outcomes Quality Initiative targets to be validated, with only 84% of eGFRs reaching accuracy of 30%. SCreat and iGFRs showed the best correlation in a fitted quadratic model with a κ coefficient of 0.53 and 93% accuracy. Adding CysC significantly (P<0.001) increased the κ coefficient to 0.56 and the quadratic model accuracy to 97%. Therefore, a combined SCreat and CysC quadratic formula was derived and internally validated using the cross-validation technique. This quadratic formula significantly outperformed the combined Schwartz formula, which was biased for an iGFR≥91 ml/min per 1.73 m(2). CONCLUSIONS: This study allowed deriving a new combined SCreat and CysC quadratic formula that could replace the combined Schwartz formula, which is accurate only for children with moderate chronic kidney disease.

Evaluating solutions to process, view and listen mathematical formula within an accessible context

Proves de conversió de fòrmules matemàtiques des d'editors de text ofimàtics i des de Làtex. Visionat en HTML i MathML. El millor resultat s'aconsegueix amb MSWord+MathType i IE+MathPlayer.

Effect of a whey-predominant starter formula containing LCPUFAs and oligosaccharides (FOS/GOS) on gastrointestinal comfort in infants.

Development of new infant formulas aims to replicate the benefits of breast milk. One benefit of breast milk over infant formulas is greater gastrointestinal comfort. We compared indicators of gastrointestinal comfort in infants fed a whey-predominant formula containing long-chain polyunsaturated fatty acids, galacto-oligo-saccharides and fructo-oligosaccharides, and infants fed a control casein-predominant formula without additional ingredients. The single-centre, prospective, double-blind, controlled trial randomly assigned healthy, full-term infants (n=144) to receive exclusively either experimental or control formula from 30 days to 4 months of age. A group of exclusively breast-fed infants served as reference (n=80). At 1, 2, 3, and 4 months, infants' growth parameters were measured and their health assessed. Parents recorded frequency and physical characteristics of infants' stool, frequency of regurgitation, vomiting, crying and colic. At 2-months, gastric emptying (ultrasound) and intestinal transit time (H2 breath test) were measured, and stool samples collected for bacterial analysis. Compared to the control (n=69), fewer of the experimental group (n=67) had hard stools (0.7 vs 7.5%, p<0.001) and more had soft stools (90.8 vs 82.3%, p<0.05). Also compared to the control, the experimental group's stool microbiota composition (mean % bifidobacteria: 78.1 (experimental, n=17), 63.7 (control, n=16), 74.3 (breast-fed, n=20), gastric transit times (59.6 (experimental, n=53), 61.4 (control, n=62), 55.9 (breast-fed, n=67) minutes) and intestinal transit times (data not shown) were closer to that of the breast-fed group. Growth parameter values were similar for all groups. The data suggest that, in infants, the prebiotic-containing whey-based formula provides superior gastrointestinal comfort than a control formula.