| 1. |
- Arnarson, Teitur, et al.
(författare)
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On the size of the non-coincidence set of parabolic obstacle problems with applications to American option pricing
- 2007
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Ingår i: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 0025-5521 .- 1903-1807. ; 101:1, s. 148-160
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Tidskriftsartikel (refereegranskat)abstract
- The following paper is devoted to the study of the positivity set U = {L phi > 0} arising in parabolic obstacle problems. It is shown that U is contained in the non-coincidence set with a positive distance between the boundaries uniformly in the spatial variable if the boundary of U satisfies an interior C-1 -Dini condition in the space variable and a Lipschitz condition in the time variable. We apply our results to American option pricing and we thus show that the positivity set is strictly contained in the continuation region, which means that the option should not be exercised in U or on the boundary of U.
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| 2. |
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| 3. |
- Dyverfeldt, Petter, et al.
(författare)
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Extending 4D Flow Visualization to the Human Right Ventricle
- 2009
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Ingår i: Proceedings of International Society for Magnetic Resonance in Medicine: 17th Scientific Meeting 2009. - : International Society for Magnetic Resonance in Medicine. ; , s. 3860-3860
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Konferensbidrag (refereegranskat)abstract
- The right ventricle has an important role in cardiovascular disease. However, because of the complex geometry and the sensitivity to the respiratory cycle, imaging of the right ventricle is challenging. We investigated whether 3D cine phase-contrast MRI can provide data with sufficient accuracy for visualizations of the 4D blood flow in the right ventricle. Whole-heart 4D flow measurements with optimized imaging parameters and post-processing tools were made in healthy volunteers. Pathlines emitted from the right atrium could be traced through the right ventricle to the pulmonary artery without leaving the blood pool and thereby met our criteria for sufficient accuracy.
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| 4. |
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| 5. |
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| 6. |
- Eriksson, Jonatan
(författare)
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Monotonicity in the volatility of single-barrier option prices
- 2006
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Ingår i: International Journal of Theoretical and Applied Finance. - 0219-0249. ; 9:6, s. 987-996
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Tidskriftsartikel (refereegranskat)abstract
- We generalize earlier results on barrier options for puts and calls and log-normal stock processes to general local volatility models and convex contracts. We show that Γ ≥ 0, that Δ has a unique sign and that the option price is increasing with the volatility for convex contracts in the following cases: If the risk-free rate of return dominates the dividend rate, then it holds for up-and-out options if the contract function is zero at the barrier and for down-and-in options in general. If the risk-free rate of return is dominated by the dividend rate, then it holds for down-and-out options if the contract function is zero at the barrier and for up-and-in options in general. We apply our results to show that a hedger who misspecifies the volatility using a time-and-level dependent volatility will super-replicate any claim satisfying the above conditions if the misspecified volatility dominates the true (possibly stochastic) volatility almost surely.
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| 7. |
- Eriksson, Jonatan, 1975-
(författare)
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On the pricing equations of some path-dependent options
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis consists of four papers and a summary. The common topic of the included papers are the pricing equations of path-dependent options. Various properties of barrier options and American options are studied, such as convexity of option prices, the size of the continuation region in American option pricing and pricing formulas for turbo warrants. In Paper I we study the effect of model misspecification on barrier option pricing. It turns out that, as in the case of ordinary European and American options, this is closely related to convexity properties of the option prices. We show that barrier option prices are convex under certain conditions on the contract function and on the relation between the risk-free rate of return and the dividend rate. In Paper II a new condition is given to ensure that the early exercise feature in American option pricing has a positive value. We give necessary and sufficient conditions for the American option price to coincide with the corresponding European option price in at least one diffusion model. In Paper III we study parabolic obstacle problems related to American option pricing and in particular the size of the non-coincidence set. The main result is that if the boundary of the set of points where the obstacle is a strict subsolution to the differential equation is C1-Dini in space and Lipschitz in time, there is a positive distance, which is uniform in space, between the boundary of this set and the boundary of the non-coincidence set. In Paper IV we derive explicit pricing formulas for turbo warrants under the classical Black-Scholes assumptions.
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| 8. |
- Persson, Jonas, et al.
(författare)
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Pricing turbo warrants
- 2006
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We numerically price the financial contracts named turbo warrant that were released early in 2005. They have been studied mathematically in [Eriksson05] where explicit pricing formulas for the Geometric Brownian motion were derived. For more general underlying stochastic processes we have no analytical formulas and numerical methods are necessary. In this work two different methods are compared, stochastic pricing using a Monte Carlo method and a deterministic PDE approach using finite differences. The methods are evaluated in terms of numerical efficiency, computation time and accuracy. In the numerical experiments the geometric Brownian motion has been used as underlying stochastic process. Our results show that for low accuracy the methods are almost equal in efficiency but for higher accuracy the finite difference method is much more efficient.
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| 9. |
- Takeuchi, Fumihiko, et al.
(författare)
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A genome-wide association study confirms VKORC1, CYP2C9, and CYP4F2 as principal genetic determinants of warfarin dose
- 2009
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Ingår i: PLoS genetics. - : Public Library of Science (PLoS). - 1553-7390 .- 1553-7404. ; 5:3
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Tidskriftsartikel (refereegranskat)abstract
- We report the first genome-wide association study (GWAS) whose sample size (1,053 Swedish subjects) is sufficiently powered to detect genome-wide significance (p<1.5×10−7) for polymorphisms that modestly alter therapeutic warfarin dose. The anticoagulant drug warfarin is widely prescribed for reducing the risk of stroke, thrombosis, pulmonary embolism, and coronary malfunction. However, Caucasians vary widely (20-fold) in the dose needed for therapeutic anticoagulation, and hence prescribed doses may be too low (risking serious illness) or too high (risking severe bleeding). Prior work established that ~30% of the dose variance is explained by single nucleotide polymorphisms (SNPs) in the warfarin drug target VKORC1 and another ~12% by two non-synonymous SNPs (*2, *3) in the cytochrome P450 warfarin-metabolizing gene CYP2C9. We initially tested each of 325,997 GWAS SNPs for association with warfarin dose by univariate regression and found the strongest statistical signals (p<10−78) at SNPs clustering near VKORC1 and the second lowest p-values (p<10−31) emanating from CYP2C9. No other SNPs approached genome-wide significance. To enhance detection of weaker effects, we conducted multiple regression adjusting for known influences on warfarin dose (VKORC1, CYP2C9, age, gender) and identified a single SNP (rs2108622) with genome-wide significance (p = 8.3×10−10) that alters protein coding of the CYP4F2 gene. We confirmed this result in 588 additional Swedish patients (p<0.0029) and, during our investigation, a second group provided independent confirmation from a scan of warfarin-metabolizing genes. We also thoroughly investigated copy number variations, haplotypes, and imputed SNPs, but found no additional highly significant warfarin associations. We present power analysis of our GWAS that is generalizable to other studies, and conclude we had 80% power to detect genome-wide significance for common causative variants or markers explaining at least 1.5% of dose variance. These GWAS results provide further impetus for conducting large-scale trials assessing patient benefit from genotype-based forecasting of warfarin dose.Author SummaryRecently, geneticists have begun assaying hundreds of thousands of genetic markers covering the entire human genome to systematically search for and identify genes that cause disease. We have extended this “genome-wide association study” (GWAS) method by assaying ~326,000 markers in 1,053 Swedish patients in order to identify genes that alter response to the anticoagulant drug warfarin. Warfarin is widely prescribed to reduce blood clotting in order to protect high-risk patients from stroke, thrombosis, and heart attack. But patients vary widely (20-fold) in the warfarin dose needed for proper blood thinning, which means that initial doses in some patients are too high (risking severe bleeding) or too low (risking serious illness). Our GWAS detected two genes (VKORC1, CYP2C9) already known to cause ~40% of the variability in warfarin dose and discovered a new gene (CYP4F2) contributing 1%–2% of the variability. Since our GWAS searched the entire genome, additional genes having a major influence on warfarin dose might not exist or be found in the near-term. Hence, clinical trials assessing patient benefit from individualized dose forecasting based on a patient's genetic makeup at VKORC1, CYP2C9 and possibly CYP4F2 could provide state-of-the-art clinical benchmarks for warfarin use during the foreseeable future.
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| 10. |
- Wadelius, Mia, et al.
(författare)
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The largest prospective warfarin-treated cohort supports genetic forecasting
- 2009
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Ingår i: Blood. - : American Society of Hematology. - 0006-4971 .- 1528-0020. ; 113:4, s. 784-792
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Tidskriftsartikel (refereegranskat)abstract
- Genetic variants of cytochrome P450 2C9 (CYP2C9) and vitamin K epoxide reductase (VKORC1) are known to influence warfarin dose, but the effect of other genes has not been fully elucidated. We genotyped 183 polymorphisms in 29 candidate genes in 1496 Swedish patients starting warfarin treatment, and tested for association with response. CYP2C9*2 and *3 explained 12% (P = 6.63 x 10(-34)) of the variation in warfarin dose, while a single VKORC1 SNP explained 30% (P = 9.82 x 10(-100)). No SNP outside the CYP2C gene cluster and VKORC1 regions was significantly associated with dose after correction for multiple testing. During initiation of therapy, homozygosity for CYP2C9 and VKORC1 variant alleles increased the risk of over-anticoagulation, hazard ratios 21.84 (95% CI 9.46; 50.42) and 4.56 (95% CI 2.85; 7.30), respectively. One of 8 patients with CYP2C9*3/*3 (12.5%) experienced severe bleeding during the first month compared with 0.27% of other patients (P = .066). A multiple regression model using the predictors CYP2C9, VKORC1, age, sex, and druginteractions explained 59% of the variance in warfarin dose, and 53% in an independent sample of 181 Swedish individuals. In conclusion, CYP2C9 and VKORC1 significantly influenced warfarin dose and predicted individuals predisposed to unstable anticoagulation. Our results strongly support that initiation of warfarin guided by pharmacogenetics would improve clinical outcome.
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