Johnson's Formula Research Articles

Peripartum Prediction of Fetal Weight in Gravidas With Obesity.

Estimated fetal weight (EFW) is an important metric at delivery as neonates with abnormal birthweight and their mothers are at higher risk of birth complications. Data regarding optimal EFW assessment in gravidas with obesity is inconsistent, and with the increasing incidence of obesity, clarification of this question is crucial. We aimed to compare accuracy of ultrasound (US)-derived EFW and clinical assessments of EFW in predicting neonatal birthweight among gravidas with obesity. This prospective cohort study enrolled gravidas with obesity and a singleton pregnancy admitted for delivery at term. EFW was determined using either US biometry or clinical assessment (Leopold's maneuvers, Johnson's formula, and Insler's formula) at time of admission. Our primary outcome was accurate EFW, defined as EFW within 500 g of birthweight. Secondary outcomes included ability to predict small-for-gestational age (SGA) and large-for-gestational age (LGA) birthweights. These outcomes were compared between all EFW methods. A total of 250 gravidas with a median body mass index of 36.4 kg/m2 were enrolled. Admission US outperformed Leopold's maneuvers in obtaining accurate EFW (81.6% versus 74.5%, P = .03). When comparing all methods, Johnson's and Insler's formulae performed the worst, accurately predicting EFW in only 27.4% and 14.3% of cases, respectively. Likewise, US-derived EFW outperformed Leopold's maneuvers and fundal height in the prediction of SGA and LGA neonates. US is more accurate than clinical assessment of EFW in gravidas with obesity both for estimation of actual birthweight and prediction of abnormal birthweight. Universal late third-trimester or peripartum US for EFW should be considered in gravidas with obesity.

The Insler and Johnson formulas for determining estimated fetal weight to baby's birth weight

Fetal weight has a very important meaning for planning midwifery care. Deviations found can be corrected immediately both during pregnancy and childbirth so that treatment is carried out on time. Clinical decisions made include the choice of type of delivery. This is expected to improve pregnancy outcomes for the welfare of the mother and fetus. The purpose of this study was to determine the difference in estimated fetal weight using the Insler Formula and the Johnson Formula compared to the baby's birth weight. This study used a cross sectional design. Sample taken by consecutive sampling. The criteria selected were third trimester pregnant women > 37-42 weeks pregnant, carrying out pregnancy checks until giving birth at the Garuda and Ibrahim Aji Public Health Centers in Bandung City from July to November 2022. Estimated fetal weight was measured during antenatal checks using the Insler and Johnson formulas. The estimated fetal weight is compared with the actual weight of the newborn. Based on the results of a study that compared the estimated fetal weight with the baby's birth weight, it was found that there was no significant difference between the use of the Insler and Johnson formulas to measure the estimated fetal weight and birth weight p value > 0.05. The Johnson and Insler formula can be applied by student midwives or midwife practitioners when conducting antenatal care in the third trimester (gestational age > 37-42 weeks). This formula is a simple detection method, using simple tools, easy to obtain and can be used anytime and anywhere, namely a measuring tape. In addition, the measurement guidelines and calculation formulas are simple and easy to apply.

A new approach to the operator formalism for Gromov-Witten invariants of the cap and tube

Based on Johnson's operator formula for the equivariant Gromov-Witten theory of P1-orbifolds, we give a new approach to the operator formalism by Okounkov and Pandharipande regarding the C⁎-equivariant Gromov-Witten theory of P1 relative to one or two points. We also extend their operator formalism in the non-equivariant specialization to the case where we allow negative contact orders.

Accuracy of Johnson's Formula for Estimating Fetal Weight Compared to Actual Birth Weight: A Study of 600 Cases in Rangpur Medical College

Introduction: The estimation of fetal weight during pregnancy has a significant impact on the survival of newborns and some immediate and late sequelae of the life of newborns. Estimation of fetal weight also plays a paramount role in determining time, mode, and place of delivery. There are many methods to estimate fetal weight like the palpation method, fundal height measurement, and radio frequency volume reduction. Johnson's method is one of the clinical methods that require no expense and is easier to estimate the precise birth weight and fetal weight. This study aimed to analyze the accuracy of the Johnsons formula for estimating fetal weight compared to actual birth weight. Methods: This cross-sectional prospective study took place in the Gynecology and Obstetrics Department of Rangpur Medical College Hospital, Rangpur, between May 2015 to October 2015, six (06) months after approval. The sample size was 600 as per inclusion criteria. Data were collected through face-to-face interviews with the women by using a pre- design questionnaire after proper counseling and informed written consent. The purposive sampling method was used in the study. Data processing was consisting of registration schedule, editing, computerization, preparation of dummy table, analyzing & matching of data. Statistical analysis was carried out by using the Statistical Package for Social Sciences version 16.0 for Windows. The mean values were calculated for continuous variables. The quantitative observations were indicated by frequencies and percentages. Paired t-test was used for continuous variables. Pearson's correlation coefficients were used to test the relationship between the groups. P values <0.05 was considered statistically significant. Result: The mean age was found 24.5±5.1 years with a range from 18 to 38 years. The mean symphysio fundal height was found 32.4±2.0 cm with a range from 28 to 36 cm. The mean estimated fetal weight was found 3205.2±287.9 grams with a range from 2635 to 3875 grams. The mean actual birth weight after delivery was found 3019.0±359.0 grams with a range from 2200 to 3800 grams. The difference was statistically significant (p<0.05) between the two groups. A positive significant correlation (r=0.929; p=0.001) was found between actual birth weight and estimated fetal weight by Johnson's formula. A positive significant correlation (r=0.517; p=0.001) was found between actual birth weight and symphysio fundal height. A positive significant correlation (r=0.129; p=0.002) was also found between the actual birth weight neonate and the BMI of the mother. Conclusion: Antenatal and intranatal fetal weight can be estimated with reasonable accuracy, clinically using Johnson's formula. Ultrasound is not available in remote areas where Johnson's formula is easy and simple to calculate and can be included in the training program of medical and paramedical staff and birth attendants.

Comparison of Actual Birth Weight with the Ultrasonographic and Clinical Estimation of Fetal Birth Weight: A Prospective Study

Introduction: Determination of fetal weight is important for the management during labour and delivery. It helps in determining the mode of delivery and aids in diagnosing low birth weight, macrosomia, and intrauterine growth restriction fetus. Ultrasound may not be available in under-resourced settings. Therefore, it is important to study the accuracy of clinical estimation of fetal weight with the sonographic and actual birth weight.
 Methods: One hundred and fifty women fulfilling the inclusion criteria were enrolled for the study. Clinical estimation of fetal weight was done by using the Johnson formula. Then the women were subjected to ultrasound. Sonographic estimation of fetal weight was done by the Hadlock method. The two estimated fetal weights were then compared with the actual birth weight. Data were analyzed using SPSS (VERSION 16).
 Results: Actual birth weight has a strong correlation with the ultrasonographic birth weight (p=0.01). However, the clinical birth weight estimation was less correlating to the actual birth weight (p=0.638)
 Conclusion: The ultrasound method is better in determining the actual birth weight as compared to the clinical method. Hence, ultrasound has to be recommended whenever available.

Accuracy of Johnson-Toshack, Niswander and Risanto formulas to predict the estimated fetal weight based on symphysis-fundal height measurement

Estimated fetal weight has a very important for planning whether the vaginal delivery is possible or not. There are various methods to determine the estimated fetal weight, ranging from conventional such using symphysis-fundal height and abdominal circumference measurements to more modern method such as using ultrasound examination. The estimated fetal weight can be calculated using several formulas such as the Johnson-Toshack, Niswander and Risanto formulas. The aim of this study was to compare the estimated fetal weight using the Johnson-Toshack, Niswander and Risanto formulas using simple symphysis-fundal height measurements. In this retrospective cross-sectional study, we assessed the medical records of 44 patients at Arifin Achmad Hospital of Indonesia from November 2020 to August 2021. The performance of the formulas was assessed using independent t-test. Our data suggested there was no significant difference between estimated fetal weight using Johnson formula (p=1.000), Risanto formula (p=1.000) and Niswander formulas compared to actual fetal birth weight (p=0.156). In conclusion, Johnson-Toshack, Niswander and Risanto formula could be used by medical personnel to calculate the estimated fetal weight in order to plan the delivery methods. This is crucial in particular in areas with limited resources such as ultrasound to calculate fetal weight in Indonesia.

Reliability of a clinical method in estimating foetal weight and predicting route of delivery in term parturient monitored at a voluntary agency hospital in Southwest Nigeria.

BackgroundThe antepartum estimation of foetal weight is a major determinant of the route of delivery and this has become vital in modern day obstetrics. The limitations to the use of obstetric ultrasonography, considered as the gold standard in estimating foetal weight, make clinical estimation methods attractive alternatives, especially in resource- constrained settings where many un-booked women may report for delivery.AimTo determine the reliability of intrapartum clinical foetal weight estimation in predicting the actual birth weight (ABW) and route of delivery among term parturient.SettingThe study was conducted at the Sacred Heart Hospital, Lantoro, a voluntary mission agency hospital in Southwest Nigeria.MethodsThis cross-sectional study was conducted among 291 term parturient recruited by systematic random sampling between June and September 2017. The clinical estimation of foetal weight was carried out using Johnson’s formula.ResultsThe accuracy of Johnson’s formula to predict the ABW was 59.5%; while for the mode of delivery, it was 130 (75.1%) for spontaneous vaginal delivery (SVD) and 43 (24.9%) for caesarean section (CS). The sensitivity of the accuracy of Johnson’s formula to predict the mode of delivery was 75.1%, with a specificity of 35.6%, a positive predictive value (PPV) of 63.1%, and a negative predictive value (NPV) of 49.4%.ConclusionThe intrapartum clinical foetal weight estimation at term determined by Johnson’s formula was reliably predictive of ABW and SVD, but it was unreliable in predicting the need for a CS.

ESTIMATION OF FETAL WEIGHT BY CLINICAL METHODS AND ULTRASOUND AND CORRELATING ITS ACCURACY WITH ACTUAL BIRTH WEIGHT IN TERM PREGNANCIES AT ANMMCH, GAYA, BIHAR

Objective:This study was to estimate the fetal weight in term pregnancy by clinical methods and ultrasound and to compare the results with actual birth weight (ABW). Material and Methods:This study was conducted at Department of Obstetrics and Gynaecology, Anugrah Narayan Magadh Medical College and Hospital, Gaya, Bihar from December 2019 to May 2020. It was a prospective study covering 200 pregnant women at term gestation. Results: Estimated birth weight by abdominal girth × symphysis fundal height (AG × SFH) formula was closest to the ABW (P = 0.060), as compared to the estimated birth weight by Johnson's formula (P = 0.000) and Hadlock's formula (P = 0.000). Therefore, of the three formulae studied, AG × SFH formula had better predictive value as compared to Johnson's and Hadlock's formulae. The accuracy of AG × SFH (Insler's formula) for estimating the fetal weight at term was found to be comparable to Hadlock's formula (P= 0.104). Conclusion: Clinical estimation of birth weight denitely has a role in the management of labor and delivery. AG × SFH is a simple, easy, costeffective, and universally applicable method to predict fetal birth weight which can be used even by paramedics like midwives and also in centers where ultrasound is not available.

Clinical and Ultrasound Estimation of Fetal Weight at Term and Its accuracy with Birth Weight

Background: Accurate estimation of fetal weight is of paramount importance in the management of labor and delivery. Objective: To evaluate fetal weight by clinical and ultrasound methods and its correlation to actual birth weight. Patients and Methods: This comparative cross sectional study was conducted at maternity hospital Zagazig University Hospitals and Zagazig General Hospital, in the period from September 2018 to March 2019. 84 women with singleton pregnancy, full term, no medical disorders with pregnancy were selected from Antenatal Clinics and Maternity Wards. They were prepared for elective caesarean section within 24 hours. Full history was taken then general and abdominal examination was done, followed by obstetric palpation (Leopold's manoeuver) to evaluate fundal level, fundal and umbilical grip and first pelvic grip by the right hand to grasp the presenting part (head). Local examination was done to evaluate cervical dilatation if present, degree of descent of the fetal head into pelvis and the fetal station. Results: The Hadlocks formula is more accurate than Johnson’s formula. The sensitivity of ultrasound was 82.0% higher than clinical (76.7%). Conclusions: Antenatal fetal weight can be estimated with reasonable accuracy, by ultrasounography using Hadlocks formula and clinically using Johnson's formula.

Clinical and Ultrasound Estimation of Fetal Weight at Term and Its accuracy with Birth Weight

Background: Accurate estimation of fetal weight is of paramount importance in the management of labor and delivery. Objective: To evaluate fetal weight by clinical and ultrasound methods and its correlation to actual birth weight. Patients and Methods: This comparative cross sectional study was conducted at maternity hospital Zagazig University Hospitals and Zagazig General Hospital, in the period from September 2018 to March 2019. 84 women with singleton pregnancy, full term, no medical disorders with pregnancy were selected from Antenatal Clinics and Maternity Wards. They were prepared for elective caesarean section within 24 hours. Full history was taken then general and abdominal examination was done, followed by obstetric palpation (Leopold's manoeuver) to evaluate fundal level, fundal and umbilical grip and first pelvic grip by the right hand to grasp the presenting part (head). Local examination was done to evaluate cervical dilatation if present, degree of descent of the fetal head into pelvis and the fetal station. Results: The Hadlocks formula is more accurate than Johnson’s formula. The sensitivity of ultrasound was 82.0% higher than clinical (76.7%). Conclusions: Antenatal fetal weight can be estimated with reasonable accuracy, by ultrasounography using Hadlocks formula and clinically using Johnson's formula.

Error Analysis for Determination of Accuracy of Johnson’s Formula, Dare’s Formula and Mother's Opinion for the Estimation of Birth Weight: Results of an Iranian Cross‐Sectional Study

Abstract Accurate fetal weight estimation is important for the management of birth. According to the existing literature, none of the clinical techniques is superior to any other. This study aimed to compare error analysis for the determination of the accuracy of Johnson’s formula, Dare’s formula and mother's opinion for the estimation of birth weight. A cross-sectional study involving 147 full-term, cephalic, singleton pregnancies, was performed. The mother’s opinion was recorded and Johnson’s and Dare’s formulas were used to calculate the fetal weight. Accuracy was determined by percentage error, absolute percentage error, and proportion of estimates within 10% of actual birth-weight. Statistical analysis was done using the RM ANOVA, Friedman and Cochran. P < 0.05 was considered significant. The birth weight was correctly estimated in 34.7%, 58.5%, 66% of the cases using the mother’s estimate, Dare’s and Johnson’s formulas. Respectively the proportion of the mother's estimate and Dare’s formula was significantly lower than that of Johnson’s formula for all birth weights. No significant difference was observed in all the measures of accuracy for the low birth-weight range. The mean error of Johnson's formula in both normal weight and macrosomic groups was less than those obtained by the Dare's formula and mother's opinion. The Johnson’s formula is more accurate in actual birth weight estimation than the Dare ’s one and mother's opinion. In the normal weight range, Johnson’s formula is more accurate of the two, while in the macrosomic group, Dare’s formula appears to be more accurate.

Design criterion for fatigue strengthening of riveted beams in a 120-year-old railway metallic bridge using pre-stressed CFRP plates

This study presents a design criterion developed for fatigue strengthening of a 120-year-old metallic railway bridge in Switzerland and presents a pre-stressed un-bonded reinforcement (PUR) system developed to apply the strengthening. The PUR system uses carbon fiber reinforced polymer (CFRP) plates; however, unlike conventional pre-stressed CFRP reinforcement methods, preparation of the existing metallic bridge surface is not required. This decreases the time required for on-site strengthening procedures. The principle of the constant life diagram (CLD) and two fatigue failure criteria (Johnson and Goodman) are described. Analytical formulations are developed based on the CLD method to determine the minimum CFRP pre-stress level required to prevent fatigue crack initiation. The PUR system uses an applied pre-stress force to reduce the mean stress level (and stress ratio) to shift an existing fatigue-susceptible metallic detail from the ‘at risk’ finite life regime to the ‘safe’ infinite life regime. The applied CLD method is particularly valuable when the stress history of the detail is not known and it is difficult to assess the remaining fatigue life. Moreover, it is shown that the currently adopted approach in many structural codes which emphasizes stress range as the dominant parameter influencing fatigue life are non-conservative for tension–tension stress patterns (i.e., stress ratios of 0<R<1). Analyses show that the modified Johnson formula accurately reflects the combined effect of stress range, mean stress level, and material properties, and offers a relatively easy design procedure. Details of a retrofit field application on members of a riveted wrought iron railway bridge are given. A wireless sensor network (WSN) system is used for long-term monitoring of the on-site CFRP stress levels and temperature of the retrofitted details. WSN measurements indicate that increases in ambient temperature result in increased CFRP pre-stress levels.

Effective conductivity of composite with imperfect contact between elliptic fibers and matrix: Maxwell’s homogenization scheme

In the present paper, we use Maxwell homogenization scheme to calculate effective transverse conductivity of a fibrous composite with imperfect contact between the matrix and the parallel elliptic fibers. The developed theory extends the Hasselman–Johnson formula to the composites with elliptic fibers. The complete solution of the conductivity problem for single elliptic inclusion with imperfect interface provides the mathematical background of the method. In the Maxwell homogenization scheme, the effective inclusion is an ellipse with aspect ratio governed by the orientation distribution of elliptic fibers. The formula for effective conductivity is derived by equating the induced dipole moment of effective inclusion to the total dipole moment of individual inhomogeneities. In addition to the usual shape of inclusions, their volume content and phase conductivities, our model accounts also for the interface conductivity and orientation distribution of fibers. The obtained solution has been verified by comparison with the available in literature analytical solutions and numerical data for the particular cases. The reported numerical data validate the equivalent inhomogeneity shape choice. The interface conductivity and fiber orientation statistics are shown to be of primary importance for the effective conductivity of composite.

The first elements of the quotient of a numerical semigroup by a positive integer

Given three pairwise coprime positive integers $a_1,a_2,a_3 \in \mathbb{Z}^+$ we show the existence of a relation between the sets of the first elements of the three quotients $\frac{\langle a_i,a_j \rangle}{a_k}$ that can be made for every $\{i.j,k\}=\{1,2,3\}$. Then we use this result to give an improved version of Johnson's semi-explicit formula for the Frobenius number $g(a_1,a_2,a_3)$ without restriction on the choice of $a_1,a_2,a_3$ and to give an explicit formula for a particular class of numerical semigroups.

Estimación clínica y ultrasonográfica del peso fetal en embarazos a términos

AimTo compare the correlations between estimated fetal weight (EFW) based on clinical and ultrasonographic findings with birthweight in patients in labor managed in the Obstetrics Emergency Unit of the Pedro García Clara Hospital in Ciudad Ojeda. MethodsWe carried out a comparative, correlational and applied study with a non-experimental, contemporary, cross-sectional, field design that included a sample of 100 pregnant women in the active phase of labor. EFW was determined by Johnson's formula and the Hadlock III equation. To determine the diagnostic value of the two methods, the results were then correlated with birthweight. ResultsEFW was 3,421.4±519.05g with Johnson's formula and 3,407.95±495.94g with ultrasound, while birthweight was 3,284.10±504.59g. A directly proportional and significant correlation was found between these estimates and birthweight (P<.001). Both methods showed low absolute and percentage errors; 58% of clinical estimates and 69% of ultrasound estimates had a margin of error within 10% of the birthweight. Overall accuracy was 88% for Johnson's formula and 92% for ultrasound. However, the sensitivity and specificity of these methods was very low for low birthweight. The clinical method had higher sensitivity for cases of macrosomy. ConclusionBoth the clinical method and ultrasound are accurate and precise for estimating fetal weight as both correspond proportionally to birthweight.

Symphysio Fundal Height (SFH) Measurement as a Predictor of Birth Weight

Fetal weight is a very important factor to make a decision about labor and delivery. Assuming that in large fetuses, dystocia and other complications like cerebral edema, neurological damage, hypoxia and asphyxia may result during or after the delivery. On the other hand, one of the causes of high perinatal mortality in our country is high rate of low birth weight. Rural people may not have access to ultrasonography which is one of the methods to predict birth weight. For these people alternative easy method is necessary. So we can assess fetal birth weight by measuring symphysio-fundal height. Total 100 consecutive pregnant women of gestational age more than 32 weeks admitted for delivery in the Obstetric and Gynaecology department of Faridpur General Hospital were the subject of this study. After selection of cases, a thorough clinical history was taken and elaborate physical examination was done. Common criteria for collection of data were followed in every case. The fetal weight estimated by Johnson's formula was recorded in the predesigned data sheet and then was compared with birth weight following delivery of the fetus. Collected data were compiled and relevant statistical calculations were done using computer based software. Statistical tests (Correlation) were done between actual birth weight (taken as dependant variable) and fetal weight (found by Johnson's Formula), symphysio fundal height (SFH), pre-delivery weight and height of the patients (taken as independent variables) and the tests revealed that actual birth weight was significantly correlated with fetal weight (found by Johnson's Formula), SFH, pre-delivery weight and height of the patients. Among these fetal weight and SFH had shown highest correlation. Regression analysis showed that SFH, maternal height and maternal weight explained respectively 59%, .011% and .009% of observed variation of birth weight. DOI: http://dx.doi.org/10.3329/fmcj.v7i2.13498 Faridpur Med. Coll. J. 2012;7(2): 54-58

Analysis of Mechanical Failure of Polymer Microneedles by Axial Force.

A polymeric microneedle has been developed for drug delivery applications. The ultimate goal of the polymeric microneedle is insertion into the specified region without failure for effective transdermal drug delivery. Mechanical failure of various geometries of microneedles by axial load was modeled using the Euler formula and the Johnson formula to predict the failure force of tapered-column microneedles. These formulas were compared with measured data to identify the mechanical behavior of microneedles by determining the critical factors including the actual length and end-fixed factor. The comparison of the two formulas with the data showed good agreement at the end-fixity (K) of 0.7. This value means that a microneedle column has one fixed end and one pinned end, and that part of the microneedle was overloaded by axial load. When the aspect ratio of length to equivalent diameter is 12:1 at 3 GPa of Young's modulus, there is a transition from the Euler region to the Johnson region by the decreased length and increased base diameter of the microneedle. A polymer having less than 3 GPa of stiffness would follow the Euler formula. A 12:1 aspect ratio of length to equivalent diameter of the microneedle was the mechanical indicator determining the failure mode between elastic buckling and inelastic buckling at less than 3 GPa of Young's modulus of polymer. Microneedles with below a 12:1 aspect ratio of length-to-equivalent diameter and more than 3 GPa of Young's were recommended for reducing sudden failure by buckling and for successfully inserting the microneedle into the skin.

Examples of the Hurwitz transform

Espinosa and Moll [2], [3] studied “the Hurwitz transform” meaning an integral over [0, 1] of a Fourier series multiplied by the Hurwitz zeta function ζ ( z , u ) , and obtained numerous results for those which arise from the Hurwitz formula. Ito's recent result [4] turns out to be one of the special cases of Espinosa and Moll's theorem. However, they did not give rigorous treatment of the relevant improper integrals. In this note we shall appeal to a deeper result of Mikolas [9] concerning the integral of the product of two Hurwitz zeta functions and derive all important results of Espinosa and Moll. More importantly, we shall record the hidden and often overlooked fact that some novel-looking results are often the result of “duplicate use of the functional equation”, which ends up with a disguised form of the original, as in the case of Johnson's formula [5]. Typically, Example 9.1 ((1.12) below) is the result of a triplicate use because it depends not only on our Theorem 1, which is the result of a duplicate use, but also on (1.3), the functional equation itself.

PRICING AND HEDGING OF A GENERAL KIND OF MULTIASSET OPTION (

Our aims is to propose an evaluation and a replicating strategy for a general kind of multiasset option in an international multicurrencies no-arbitrage world with Gaussian interest rates. Johnson's formula for the option on the maximum of several assets is derived as a particular case of ours, and two examples of application, namely the MAP strategy and the option on the arithmetic mean of several assets, are presented.

Richardson extrapolation techniques for the pricing of American‐style options

AbstractIn this article, the authors reexamine the American‐style option pricing formula of R. Geske and H.E. Johnson (1984), and extend the analysis by deriving a modified formula that can overcome the possibility of nonuniform convergence (which is likely to occur for nonstandard American options whose exercise boundary is discontinuous) encountered in the original Geske–Johnson methodology. Furthermore, they propose a numerical method, the Repeated‐Richardson extrapolation, which allows the estimation of the interval of true option values and the determination of the number of options needed for an approximation to achieve a given desired accuracy. Using simulation results, our modified Geske–Johnson formula is shown to be more accurate than the original Geske–Johnson formula for pricing American options, especially for nonstandard American options. This study also illustrates that the Repeated‐Richardson extrapolation approach can estimate the interval of true American option values extremely well. Finally, the authors investigate the possibility of combining the binomial Black–Scholes method proposed by M. Broadie and J.B. Detemple (1996) with the Repeated‐Richardson extrapolation technique. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:791–817, 2007