Pricing exotic options using strong convergence properties?

In finance, the strong convergence properties of discretisations of stochastic differential equations (SDEs) are very important for the hedging and valuation of exotic options. In this paper we show how the use of the Milstein scheme can improve the convergence of the multi-level Monte Carlo method, so that the computational cost to achieve an accuracy of O(e) is reduced to O($\epsilon^{−2}$) for a Lipschitz payoff. The Milstein scheme gives first order strong convergence for all 1−dimensional systems (one Wiener process). However, for processes with two or more Wiener processes, such as correlated portfolios and stochastic volatility models, there is no exact solution for the iterated integrals of second order (Lévy area) and the Milstein scheme neglecting the Lévy area gives the same order of convergence as the Euler-Maruyama scheme. The purpose of this paper is to show that if certain conditions are satisfied, we can avoid the calculation of the Lévy area and obtain first convergence order by applying an orthogonal transformation. We demonstrate when the conditions of the 2−Dimensional problem permit this and give an exact solution for the orthogonal transformation. We present examples of pricing exotic options to demonstrate that the use of both the orthogonal Milstein scheme and the Multi-level Monte Carlo give a substantial reduction in the computation cost

Pricing exotic options using improved strong convergence

Today, better numerical approximations are required for multi-dimensional SDEs to improve on the poor performance of the standard Monte Carlo integration. With this aim in mind, the material in the thesis is divided into two main categories, stochastic calculus and mathematical finance. In the former, we introduce a new scheme or discrete time approximation based on an idea of Paul Malliavin where, for some conditions, a better strong convergence order is obtained than the standard Milstein scheme without the expensive simulation of the Lévy Area. We demonstrate when the conditions of the 2−Dimensional problem permit this and give an exact solution for the orthogonal transformation (θ Scheme or OrthogonalMilstein Scheme). Our applications are focused on continuous time diffusion models for the volatility and variance with their discrete time approximations (ARV). Two theorems that measure with confidence the order of strong and weak convergence of schemes without an exact solution or expectation of the system are formally proved and tested with numerical examples. In addition, some methods for simulating the double integrals or Lévy Area in the Milstein approximation are introduced. For mathematical finance, we review evidence of non-constant volatility and consider the implications for option pricing using stochastic volatility models. A general stochastic volatility model that represents most of the stochastic volatility models that are outlined in the literature is proposed. This was necessary in order to both study and understand the option price properties. The analytic closed-form solution for a European/Digital option for both the Square Root Model and the 3/2 Model are given. We present the Multilevel Monte Carlo path simulation method which is a powerful tool for pricing exotic options. An improved/updated version of the ML-MC algorithm using multi-schemes and a non-zero starting level is introduced. To link the contents of the thesis, we present a wide variety of pricing exotic option examples where considerable computational savings are demonstrated using the new θ Scheme and the improved Multischeme Multilevel Monte Carlo method (MSL-MC). The computational cost to achieve an an accuracy of O($\epsilon$) is reduced from O($\epsilon^{−3}$) to O($\epsilon^{−2}$) for some applications

Microphysiologic Human Tissue Constructs Reproduce Autologous Age-Specific BCG and HBV Primary Immunization in vitro

Current vaccine development disregards human immune ontogeny, relying on animal models to select vaccine candidates targeting human infants, who are at greatest risk of infection worldwide, and receive the largest number of vaccines. To help accelerate and de-risk development of early-life effective immunization, we engineered a human age-specific microphysiologic vascular-interstitial interphase, suitable for pre-clinical modeling of distinct age-targeted immunity in vitro. Our Tissue Constructs (TCs) enable autonomous extravasation of monocytes that undergo rapid self-directed differentiation into migratory Dendritic Cells (DCs) in response to adjuvants and licensed vaccines such as Bacille Calmette-Guérin (BCG) or Hepatitis B virus Vaccine (HBV). TCs contain a confluent human endothelium grown atop a tri-dimensional human extracellular matrix substrate, employ human age-specific monocytes and autologous non heat-treated plasma, and avoid the use of xenogenic materials and exogenous cytokines. Vaccine-pulsed TCs autonomously generated DCs that induced single-antigen recall responses from autologous naïve and memory CD4+ T lymphocytes, matching study participant immune-status, including BCG responses paralleling donor PPD status, BCG-induced adenosine deaminase (ADA) activity paralleling infant cohorts in vivo, and multi-dose HBV antigen-specific responses as demonstrated by lymphoproliferation and TCR sequencing. Overall, our microphysiologic culture method reproduced age- and antigen-specific recall responses to BCG and HBV immunization, closely resembling those observed after a birth immunization of human cohorts in vivo, offering for the first time a new approach to early pre-clinical selection of effective age-targeted vaccine candidates

Ringed sideroblasts in βâ thalassemia

Symptomatic βâ thalassemia is one of the globally most common inherited disorders. The initial clinical presentation is variable. Although common hematological analyses are typically sufficient to diagnose the disease, sometimes the diagnosis can be more challenging. We describe a series of patients with βâ thalassemia whose diagnosis was delayed, required bone marrow examination in one affected member of each family, and revealed ringed sideroblasts, highlighting the association of this morphological finding with these disorders. Thus, in the absence of characteristic congenital sideroblastic mutations or causes of acquired sideroblastic anemia, the presence of ringed sideroblasts should raise the suspicion of βâ thalassemia.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136352/1/pbc26324.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136352/2/pbc26324_am.pd

Microphysiologic Human Tissue Constructs Reproduce Autologous Age-Specific BCG and HBV Primary Immunization <i>in vitro</i>

Current vaccine development disregards human immune ontogeny, relying on animal models to select vaccine candidates targeting human infants, who are at greatest risk of infection worldwide, and receive the largest number of vaccines. To help accelerate and de-risk development of early-life effective immunization, we engineered a human age-specific microphysiologic vascular-interstitial interphase, suitable for pre-clinical modeling of distinct age-targeted immunity in vitro. Our Tissue Constructs (TCs) enable autonomous extravasation of monocytes that undergo rapid self-directed differentiation into migratory Dendritic Cells (DCs) in response to adjuvants and licensed vaccines such as Bacille Calmette-Guérin (BCG) or Hepatitis B virus Vaccine (HBV). TCs contain a confluent human endothelium grown atop a tri-dimensional human extracellular matrix substrate, employ human age-specific monocytes and autologous non heat-treated plasma, and avoid the use of xenogenic materials and exogenous cytokines. Vaccine-pulsed TCs autonomously generated DCs that induced single-antigen recall responses from autologous naïve and memory CD4+ T lymphocytes, matching study participant immune-status, including BCG responses paralleling donor PPD status, BCG-induced adenosine deaminase (ADA) activity paralleling infant cohorts in vivo, and multi-dose HBV antigen-specific responses as demonstrated by lymphoproliferation and TCR sequencing. Overall, our microphysiologic culture method reproduced age- and antigen-specific recall responses to BCG and HBV immunization, closely resembling those observed after a birth immunization of human cohorts in vivo, offering for the first time a new approach to early pre-clinical selection of effective age-targeted vaccine candidates.</p

Mutations in PYCR2, Encoding Pyrroline-5-Carboxylate Reductase 2, Cause Microcephaly and Hypomyelination

Despite recent advances in understanding the genetic bases of microcephaly, a large number of cases of microcephaly remain unexplained, suggesting that many microcephaly syndromes and associated genes have yet to be identified. Here, we report mutations in PYCR2, which encodes an enzyme in the proline biosynthesis pathway, as the cause of a unique syndrome characterized by postnatal microcephaly, hypomyelination, and reduced cerebral white-matter volume. Linkage mapping and whole-exome sequencing identified homozygous mutations (c.355C>T [p.Arg119Cys] and c.751C>T [p.Arg251Cys]) in PYCR2 in the affected individuals of two consanguineous families. A lymphoblastoid cell line from one affected individual showed a strong reduction in the amount of PYCR2. When mutant cDNAs were transfected into HEK293FT cells, both variant proteins retained normal mitochondrial localization but had lower amounts than the wild-type protein, suggesting that the variant proteins were less stable. A PYCR2-deficient HEK293FT cell line generated by genome editing with the clustered regularly interspaced short palindromic repeat (CRISPR)-Cas9 system showed that PYCR2 loss of function led to decreased mitochondrial membrane potential and increased susceptibility to apoptosis under oxidative stress. Morpholino-based knockdown of a zebrafish PYCR2 ortholog, pycr1b, recapitulated the human microcephaly phenotype, which was rescued by wild-type human PYCR2 mRNA, but not by mutant mRNAs, further supporting the pathogenicity of the identified variants. Hypomyelination and the absence of lax, wrinkly skin distinguishes this condition from that caused by previously reported mutations in the gene encoding PYCR2’s isozyme, PYCR1, suggesting a unique and indispensable role for PYCR2 in the human CNS during development

Dominant-negative mutations in human IL6ST underlie hyper-IgE syndrome

Autosomal dominant hyper-IgE syndrome (AD-HIES) is typically caused by dominant-negative (DN) STAT3 mutations. Patients suffer from cold staphylococcal lesions and mucocutaneous candidiasis, severe allergy, and skeletal abnormalities. We report 12 patients from 8 unrelated kindreds with AD-HIES due to DN IL6ST mutations. We identified seven different truncating mutations, one of which was recurrent. The mutant alleles encode GP130 receptors bearing the transmembrane domain but lacking both the recycling motif and all four STAT3-recruiting tyrosine residues. Upon overexpression, the mutant proteins accumulate at the cell surface and are loss of function and DN for cellular responses to IL-6, IL-11, LIF, and OSM. Moreover, the patients’ heterozygous leukocytes and fibroblasts respond poorly to IL-6 and IL-11. Consistently, patients with STAT3 and IL6ST mutations display infectious and allergic manifestations of IL-6R deficiency, and some of the skeletal abnormalities of IL-11R deficiency. DN STAT3 and IL6ST mutations thus appear to underlie clinical phenocopies through impairment of the IL-6 and IL-11 response pathways