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.

Assessment of volumetric bone mineral density of the femoral neck in postmenopausal women with and without vertebral fractures using quantitative multi-slice CT.

OBJECTIVE: To demonstrate the validity and reliability of volumetric quantitative computed tomography (vQCT) with multi-slice computed tomography (MSCT) and dual energy X-ray absorptiometry (DXA) for hip bone mineral density (BMD) measurements, and to compare the differences between the two techniques in discriminating postmenopausal women with osteoporosis-related vertebral fractures from those without. METHODS: Ninety subjects were enrolled and divided into three groups based on the BMD values of the lumbar spine and/or the femoral neck by DXA. Groups 1 and 2 consisted of postmenopausal women with BMD changes <-2SD, with and without radiographically confirmed vertebral fracture (n=11 and 33, respectively). Group 3 comprised normal controls with BMD changes > or =-1SD (n=46). Post-MSCT (GE, LightSpeed16) scan reconstructed images of the abdominal-pelvic region, 1.25 mm thick per slice, were processed by OsteoCAD software to calculate the following parameters: volumetric BMD values of trabecular bone (TRAB), cortical bone (CORT), and integral bone (INTGL) of the left femoral neck, femoral neck axis length (NAL), and minimum cross-section area (mCSA). DXA BMD measurements of the lumbar spine (AP-SPINE) and the left femoral neck (NECK) also were performed for each subject. RESULTS: The values of all seven parameters were significantly lower in subjects of Groups 1 and 2 than in normal postmenopausal women (P<0.05, respectively). Comparing Groups 1 and 2, 3D-TRAB and 3D-INTGL were significantly lower in postmenopausal women with vertebral fracture(s) [(109.8+/-9.61) and (243.3+/-33.0) mg/cm3, respectively] than in those without [(148.9+/-7.47) and (285.4+/-17.8) mg/cm(3), respectively] (P<0.05, respectively), but no significant differences were evident in AP-SPINE or NECK BMD. CONCLUSION: the femoral neck-derived volumetric BMD parameters using vQCT appeared better than the DXA-derived ones in discriminating osteoporotic postmenopausal women with vertebral fractures from those without. vQCT might be useful to evaluate the effect of osteoporotic vertebral fracture status on changes in bone mass in the femoral neck.

Occipitoaxial spinal interarticular stabilization with vertebral artery preservation for atlantal lateral mass failure.

The treatment of craniocervical instability caused by diverse conditions remains challenging. Different techniques have been described to stabilize the craniocervical junction. The authors present 2 cases in which tumoral destruction of the C-1 lateral mass caused craniocervical instability. A one-stage occipitoaxial spinal interarticular stabilization (OASIS) technique with titanium cages and posterior occipitocervical instrumentation was used to reconstruct the C-1 lateral mass and stabilize the craniocervical junction. The ipsilateral vertebral artery was preserved. The OASIS technique offers single-stage tumor resection, C-1 lateral mass reconstruction, and stabilization with a loadsharing construct. It could be an option in the treatment of select cases of C-1 lateral mass failure.

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.

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.

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.

The effect of treatment with calcitonin on vertebral fracture rate in osteoporosis.

The efficacy of treatments for osteoporosis does not become evident when evaluated by fracture incidence (FI). Vertebral FI decreased in all controlled studies on calcitonin, but not significantly. Small sample sizes and short periods of treatment may have masked a possible therapeutic benefit, but longer, controlled studies with sodium fluoride or etidronate in larger groups of patients also failed to show a decrease in FI. The present analysis of nine published, therapeutic studies which indicate the FI per year and the initial prevalence of vertebral fractures, examines the question of whether the initial prevalence of fractures has an effect on the subsequent incidence of new fractures and whether the therapeutic effects have to be evaluated as a function of the initial prevalence of fractures. Bearing in mind the differences in roentgenological evaluation and in the size and quality of the various studies, the analysis revealed (1) that in the control groups there was a higher FI in patients with more than three vertebral fractures at baseline (estimated odds ratio (OR) = 49, p = 0.011); (2) that a similar trend, although not statistically significant, was observed in treated patients; (3) that the groups of control patients treated for more than 1 year showed in general an increase in FI beyond the first year and that the reverse was true in treated patients. In conclusion, failure to allow for the initial prevalence of vertebral fractures at the individual level in therapeutic trials of calcitonin to treat osteoporosis and prevent new fractures might have contributed to the absence of a demonstrable benefit of the treatment in those studies.

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).

Vertebral microarchitecture and fragility fracture in men: a TBS study.

INTRODUCTION: Although osteoporosis is considered a disease of women, 25% of the individuals with osteoporosis are men. BMD measurement by DXA is the gold standard used to diagnose osteoporosis and assess fracture risk. Nevertheless, BMD does not take into account alterations of microarchitecture. TBS is an index of bone microarchitecture extracted from the spine DXA. Previous studies have reported the ability of the spine TBS to predict osteoporotic fractures in women. This is the first case-controlled study in men to evaluate the potential diagnostic value of TBS as a complement to bone mineral density (BMD), by comparing men with and without fractures. METHODS: To be eligible for this study, subjects had to be non-Hispanic US white men aged 40 and older. Furthermore, subjects were excluded if they have or have had previously any treatment or illness that may influence bone metabolism. Fractured subjects were included if the presence of at least one fracture was confirmed. Cases were matched for age (±3 years) and BMD (±0.04 g/cm(2)) with three controls. BMD and TBS were first retrospectively evaluated at AP spine (L1-L4) with a Prodigy densitometer (GE-Lunar, Madison, USA) and TBS iNsight® (Med-Imaps, France) in Lausanne University Hospital blinded from clinical outcome. Inter-group comparisons were undertaken using Student's t-tests or Wilcoxon signed rank tests. Odds ratios were calculated per one standard deviation decrease as well as areas under the receiver operating curve (AUC). RESULTS: After applying inclusion/exclusion criteria, a group of 180 male subjects was obtained. This group consists of 45 fractured subjects (age=63.3±12.6 years, BMI=27.1±4.2 kg/m(2)) and 135 control subjects (age=62.9±11.9 years, BMI=26.7±3.9 kg/m(2)) matched for age (p=0.86) and BMD (p=0.20). A weak correlation was obtained between TBS and BMD and between TBS and BMI (r=0.27 and r=-0.28, respectively, p<0.01). Subjects with fracture have a significant lower TBS compared to control subjects (p=0.013), whereas no differences were obtained for BMI, height and weight (p>0.10). TBS OR per standard deviation is 1.55 [1.09-2.20] for all fracture type. When considering vertebral fracture only TBS OR reached 2.07 [1.14-3.74]. CONCLUSION: This study showed the potential use of TBS in men. TBS revealed a significant difference between fractured and age- and spine BMD-matched nonfractured subjects. These results are consistent with those previously reported on for men of other nationalities.

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.

Usefulness of bone densitometry in postmenopausal women with clinically diagnosed vertebral fractures.

Objective: To analyse whether bone mineral density (BMD) assessment is required in postmenopausal women presenting with low trauma vertebral fracture. Methods: Women with vertebral fracture diagnosed over a 10 year period were recruited from our database. The following were excluded: (a) patients with high energy trauma; (b) patients with malignancies; (c) patients with a metabolic bone disease other than osteoporosis. All postmenopausal women were included in whom BMD had been evaluated at both the lumbar spine and femoral neck by dual energy x ray absorptiometry during the six months after the diagnosis. Patients with a potential cause of osteoporosis other than age and menopause were not considered. A total of 215 patients were identified. Results: The mean (SD) age of the patients was 65.9 (6.9) years. BMD at the lumbar spine was 0.725 (0.128) g/cm2 and the T score was ¿2.94 (1.22); BMD at the femoral neck was 0.598 (0.095) g/cm2 and the T score was ¿2.22 (0.89). The BMD of the patients was significantly lower than that of the general population at both the lumbar spine and femoral neck. When the lowest value of the two analysed zones was considered, six patients (3%) showed a normal BMD, 51 (23.5%) osteopenia, and 158 (73.5%) osteoporosis. The prevalence of osteoporosis at the femoral neck increased with age; it was 25% in patients under 60, 35% in patients aged 60¿70, and 60% in patients over 70. Conclusion: These results indicate that bone densitometry is not required in postmenopausal women with clinically diagnosed vertebral fractures if it is performed only to confirm the existence of a low BMD.