Pricing derivatives with stochastic volatility

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter 6) and time dependent volatility in futures option (Chapter 7). In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach was investigated in the context of various benchmark models for equities and com- modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and the Schwartz (1997) two-factor model. It is shown that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by-product delivers super-hedging strategies which can be easily implemented. In Chapter 5, two types of three-factor models were studied to give the value of com- modities futures contracts, which allow volatility to be stochastic. Both these two models have closed-form solutions for futures contracts price. However, it is shown that Model 2 is better than Model 1 theoretically and also performs very well empiri- cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages; hence, it is also a good choice to price the value of commodity futures contracts. Fur- thermore, if these two models are used at the same time, a more accurate price for commodity futures contracts can be obtained in most situations. In Chapter 6, the applicability of the asymptotic approach developed in Fouque et al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997) multi-factor model, featuring both stochastic convenience yield and stochastic volatility. It is shown that the zero-order term in the expansion coincides with the Schwartz (1997) two-factor term, with averaged volatility, and an explicit expression for the first-order correction term is provided. With empirical data from the natural gas futures market, it is also demonstrated that a significantly better calibration can be achieved by using the correction term as compared to the standard Schwartz (1997) two-factor expression, at virtually no extra effort. In Chapter 7, a new pricing formula is derived for futures options in the Schwartz (1997) two-factor model with time dependent spot volatility. The pricing formula can also be used to find the result of the time dependent spot volatility with futures options prices in the market. Furthermore, the limitations of the method that is used to find the time dependent spot volatility will be explained, and it is also shown how to make sure of its accuracy.

Determination of the cytotoxic capacity of organotin compounds derivatives from salicylidene benzoylhidrazone

The successful application of metal complexes in the treatment of many diseases, including cancer, is a rapidly expanding area in biomedical chemistry and research. Organotin compounds studies show the versatility and the attractive features of these molecules. In the same manner, has been reported the development of new compounds derivative from bezoylhidrazones, which possess the azomethine fragment (-N = CH-), key pillar for designing new drugs with biological activity. Based on the above, we are interested in to synthesize four tin compounds derivatives from benzoylhidrazones, and the evaluation of their cytotoxic capacity. Conclusions and contribution: In this research work, we reported four new tin compounds derivatives from bezoylhidrazones, which were characterized by spectroscopic and spectrometric techniques and X-ray diffraction In the same manner, cytotoxic ability of each compound was studied and reported and compared with metaled base drugs like cisplatin and carboplatin. Also, in some cases it was possible to use their luminescent ability to study their intracellular behavior.

Evaluation of anti-inflammatory activity of derivatives from aerial parts of Baccharis uncinella

Context: Species of Baccharis exhibit antibiotic, antiseptic, and wound-healing properties, and have been used in the traditional medicine of South America for the treatment of inflammation, headaches, diabetes, and hepatobiliary disorders.Objective: To investigate the anti-inflammatory activity of organic phases from EtOH extract of the aerial parts of Baccharis uncinella DC (Asteraceae).Materials and methods: The crude EtOH extract from the aerial parts of B. uncinella was subjected to partition procedures and the corresponding CH(2)Cl(2) and EtOAc phases were subjected to several chromatographic separation procedures. Thus, these phases and their purified compounds were assayed for evaluation of anti-inflammatory activity.Results: The CH(2)Cl(2) phase from EtOH extract from B. uncinella contained two triterpenoids (oleanolic and ursolic acids) and one flavonoid (pectolinaringenin), whereas the respective EtOAc phase showed to be composed mainly by two phenylpropanoid derivatives (caffeic and ferulic acids). The CH(2)Cl(2) and EtOAc phases as well as their isolated compounds exhibited anti-inflammatory effects against inflammatory reactions induced by phospholipase A2 (from Crotalus durissus terrificus venom) and by carrageenan.Discussion and conclusion: The results suggested that the components obtained from partition phases of EtOH extract of B. uncinella could represent lead molecules for the development of anti-inflammatory agents. Additionally, the results confirmed the use of Baccharis genus in the traditional medicine of South America for the treatment of inflammation and other heath disorders. To date, the present work describes for the first time the anti-inflammatory effects of compounds isolated from B. uncinella.

Charged pullulan derivatives for the development of nanocarriers by polyelectrolyte complexation

Pullulan, a neutral polysaccharide, was chemically modified in order to obtain two charged derivatives: reaction with SO3(.)DMF complex afforded a sulfate derivative (SP), while reaction with glycidyltrimethylammonium chloride gave a quaternary ammonium salt (AP). The presence of the charged groups was confirmed by FTIR. Assessment of the positions where the reaction took place was based on (1)H- and (13)C NMR (COSY, HSQC-TOCSY, HSQC-DEPT, and HMBC) experiments. Estimation of the degree of substitution (DS) was made from elemental analysis data, and further confirmed by NMR peak areas in the case of AP. These new derivatives showed the capability to condense with each other, forming nanoparticles with the ability to associate a model protein (BSA) and displaying adequate size for drug delivery applications, therefore making them good candidates for the production of pullulan-based nanocarriers by polyelectrolyte complexation.

Reduction of 1,2-dicarbonyl compounds and of their N-phenylimine derivatives by sodium cyanide under aprotic conditions

Some aromatic 1,2-dicarbonyl compounds, i.e. 9,10-phenanthrenequinone, acenaphthenequinone and benzil, and their corresponding N-phenyl monoimines, have been reduced, using dry acetonitrile as the solvent, in the presence of sodium cyanide as a reducing agent. Comparative potentiostatic preparative-scale electrolysis is described.

Synthesis and antibacterial profile of novel azomethine derivatives of β-phenylacrolein moiety

Purpose: To develop some novel molecules effective against antibiotic-resistant bacterial infections. Methods: A series of azomethines (SB-1 to SB-6) were synthesized from β-phenyl acrolein moiety. The structures of the synthesized compounds were confirmed on the basis of their UV ultra-violet (UV) spectroscopy (λmax: 200 - 400 nm), Fourier transform infra-red (FTIR, vibrational frequency: 500-4000 cm-1), 1H nuclear magnetic resonance (NMR, chemical shift: 0 - 10 ppm), 13C NMR (chemical shift: 0 - 200 ppm), mass spectrometry (m/z values: 0 - 500) and carbon hydrogen nitrogen (CHN) elemental analysis. The new compounds were screened for antibacterial activity by test-tube dilution and disc diffusion methods using gentamicin as reference standard. Results: The structures of azomethine were in full agreement with their spectral data. Among all the synthesized compounds, compounds SB-5 and SB-6 exhibited the highest minimum inhibitory concentration (MIC) of 62.5 μg/mL. At MIC of 250 μg/mL, all compounds SB-1 to SB-6 displayed significant antibacterial activity, compared to gentamycin (p < 0.05). SB-5 and SB-6 were active against S. aureus, P. aeruginosa and K. pneumoniae; SB-3 was active against B. subtilis and S. aureus. SB-4 was active against P. aeruginosa and S. aureus while SB-1 and SB-2 were active against S. aureus. Conclusion: The synthesized compounds possess antibacterial activities compared to those of gentamycin.

Corrigendum to “The envelope theorem for multiobjective convex programming via contingent derivatives” [J. Math. Anal. Appl. 372 (1) (2010) 197–207]

The aim of this note is to formulate an envelope theorem for vector convex programs. This version corrects an earlier work, “The envelope theorem for multiobjective convex programming via contingent derivatives” by Jiménez Guerra et al. (2010) [3]. We first propose a necessary and sufficient condition allowing to restate the main result proved in the alluded paper. Second, we introduce a new Lagrange multiplier in order to obtain an envelope theorem avoiding the aforementioned error.

Design, synthesis and antiproliferative activity of hydroxyacetamide derivatives against HeLa cervical carcinoma cell and breast cancer cell line

Purpose: To design and develop a new series of histone deacetylase inhibitors (FP1 - FP12) and evaluate their inhibitory activity against hydroxyacetamide (HDAC) enzyme mixture-derived HeLa cervical carcinoma cell and MCF-7. Methods: The designed molecules (FP1 - FP12) were docked using AUTODOCK 1.4.6. FP3 and FP8 showed higher interaction comparable to the prototypical HDACI. The designed series of 2-[[(3- Phenyl/substituted Phenyl-[4-{(4-(substituted phenyl)ethylidine-2-Phenyl-1,3-Imidazol-5-One}](-4H- 1,2,4-triazol-5-yl)sulfanyl]-N-hydroxyacetamide derivatives (FP1-FP12) was synthesized by merging 2- [(4-amino-3-phenyl-4H- 1, 2, 4-triazol-5-yl) sulfanyl]-N-hydroxyacetamide and 2-{[4-amino-3-(2- hydroxyphenyl)-4H-1,2, 4-triazol-5-yl]sulfanyl}-N hydroxyacetamide derivatives with aromatic substituted oxazolone. The biological activity of the synthesized molecule (FP1-FP12) was evaluated against HDAC enzyme mixture-derived HeLa cervical carcinoma cell and breast cancer cell line (MCF-7). Results: HDAC inhibitory activity of FP10 showed higher IC50 (half-maximal concentration inhibitory activity) of 0.09 μM, whereas standard SAHA molecule showed IC50 of 0.057 μM. On the other hand, FP9 exhibited higher GI50 (50 % of maximal concentration that inhibited cell proliferation) of 22.8 μM against MCF-7 cell line, compared with the standard, adriamycin, with GI50 of (-) 50.2 μM. Conclusion: Synthesis, spectral characterization, and evaluation of HDAC inhibition activity and in vitro anticancer evaluation of novel hydroxyacetamide derivatives against MCF-7 cell line have been achieved. The findings indicate the emergence of potentialanticancer compounds.

S-Alkylated/aralkylated 2-(1H-indol-3-yl-methyl)-1,3,4- oxadiazole-5-thiol derivatives. 1. Synthesis and characterization

Purpose: To synthesize and characterize S-alkylated/aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4- oxadiazole-5-thiol derivatives. Methods: 2-(1H-indol-3-yl)acetic acid (1) was reacted with absolute ethanol and catalytic amount of sulfuric acid to form ethyl 2-(1H-indol-3-yl)acetate (2) which was transformed to 2-(1H-indol-3- yl)acetohydrazide (3) by refluxing with hydrazine hydrate in methanol. Ring closure reaction of 3 with carbon disulfide and ethanolic potassium hydroxide yielded 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5- thiol (4) which was finally treated with alkyl/aralkyl halides (5a-u) in DMF and NaH to yield Salkylated/ aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiols (6a-u). Structural elucidation was done by IR, 1H-NMR and EI-MS techniques Results: 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiol (4) was synthesized as the parent molecule and was characterized by IR and the spectrum showed peaks resonating at (cm-1) 2925 (Ar-H), 2250 (S-H ), 1593 (C=N ) and 1527 (Ar C=C ); 1H-NMR spectrum showed signals at δ 11.00 (s, 1H, NH-1ʹ), 7.49 ( br.d, J = 7.6 Hz, 1H, H-4\'), 7.37 (br.d, J = 8.0 Hz, 1H, H-7\'), 7.34 (br.s, 1H, H-2\'), 7.09 (t, J = 7.6 Hz, 1H, H-5\'), 7.00 (t, J = 7.6 Hz, 1H, H-6\') and 4.20 (s, 2H, CH2-10ʹ). EI-MS presented different fragments peaks at m/z 233 (C11H9N3OS)˙+ [M+2]+, 231 (C11H9N3OS)˙+ [M]+, 158 (C10H8NO)+, 156 (C10H8N2)˙+, 130 (C9H8N)+. The derivatives (6a-6u) were prepared and characterized accordingly. Conclusion: S-alkylated/aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiols (6a-u) were successfully synthesized.

S-Alkylated/aralkylated 2-(1H-indol-3-yl-methyl)-1,3,4- oxadiazole-5-thiol derivatives. 2. Anti-bacterial, enzymeinhibitory and hemolytic activities

Purpose: To evaluate the antibacterial, enzyme-inhibitory and hemolytic activities of Salkylated/ aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiol derivatives. Methods: Antibacterial activities of the compounds were evaluated using broth dilution method in 96 well plates. Enzyme inhibitory activities assays were investigated against α-glucosidase, butyrylcholinesterase (BchE) and lipoxygenase (LOX) using acarbose, eserine and baicalien as reference standards, respectively. A mixture of enzyme, test compound and the substrate was incubated and variation in absorbance noted before and after incubation. In tests for hemolytic activities, the compounds were incubated with red blood cells and variations in absorbance were used as indices their hemolytic activities. Results: The compounds were potent antibacterial agents. Five of them exhibited very good antibacterial potential similar to ciprofloxacin, and had minimum inhibitory concentrations (MIC) of at least 9.00 ± 4.12 μM against S. aureus, E.coli, and B. subtilis. One of the compounds had strong enzyme inhibitory potential against α-glucosidase, with IC50 of 17.11 ± 0.02 μg/mL which was better than that of standard acarbose (IC50 38.25 ± 0.12 μg/mL). Another compound had 1.5 % hemolytic activity. Conclusion: S-Alkylated/aralkylated 2-(1H-indol-3-ylmethyl)-1,3,4-oxadiazole-5-thiol deviratives with valuable antibacterial, anti-enzymatic and hemolytic activities have been successfully synthesized. These compounds may be useful in the development of pharmaceutical products.

Study of ammonia borane and its derivatives: Influence of nanoconfinements and pressures

Recently, ammonia borane has increasingly attracted researchers’ attention because of its merging applications, such as organic synthesis, boron nitride compounds synthesis, and hydrogen storage. This dissertation presents the results from several studies related to ammonia borane. ^ The pressure-induced tetragonal to orthorhombic phase transition in ammonia borane was studied in a diamond anvil cell using in situ Raman spectroscopy. We found a positive Clapeyron-slope for this phase transformation in the experiment, which implies that the phase transition from tetragonal to orthorhombic is exothermic. The result of this study indicates that the rehydrogenation of the high pressure orthorhombic phase is expected to be easier than that of the ambient pressure tetragonal phase due to its lower enthalpy. ^ The high pressure behavior of ammonia borane after thermal decomposition was studied by in situ Raman spectroscopy at high pressures up to 10 GPa. The sample of ammonia borane was first decomposed at ∼140 degree Celcius and ∼0.7 GPa and then compessed step wise in an isolated sample chamber of a diamond anvil cell for Raman spectroscopy measurement. We did not observe the characteristic shift of Raman mode under high pressure due to dihydrogen bonding, indicating that the dihydrogen bonding disappears in the decomposed ammonia borane. Although no chemical rehydrogenation was detected in this study, the decomposed ammonia borane could store extra hydrogen by physical absorption. ^ The effect of nanoconfinement on ammonia borane at high pressures and different temperatures was studied. Ammonia borane was mixed with a type of mesoporous silica, SBA-15, and restricted within a small space of nanometer scale. The nano-scale ammonia borane was decomposed at ∼125 degree Celcius in a diamond anvil cell and rehydrogenated after applying high pressures up to ∼13 GPa at room temperature. The successful rehydrogenation of decomposed nano-scale ammonia borane gives guidance to further investigations on hydrogen storage. ^ In addition, the high pressure behavior of lithium amidoborane, one derivative of ammonia borane, was studied at different temperatures. Lithium amidoborane (LAB) was decomposed and recompressed in a diamond anvil cell. After applying high pressures on the decomposed lithium amidoborane, its recovery peaks were discovered by Raman spectroscopy. This result suggests that the decomposition of LAB is reversible at high pressures.^

Selective Sonogashira Couplings in 1,2,4,5-tetrazine derivatives

1,2,4,5-Tetrazines are six-membered heterocyclic compounds in which the four nitrogen atoms are displayed in a symmetric fashion. Their reactivity is quite different from other heterocyclic aromatic systems due to its unique electron-withdrawing character, comparable to tetra-nitrobenzene. 1 In particular, 1,2,4,5- tetrazines are known to take part in [4+2] inverse-Diels–Alder cycloaddition processes which efficiently lead to the construction of substituted pyridazine systems that are important in drug development and biomarker applications. 2 However, the electronic character of 1,2,4,5-tetrazines hampered the development of 3- ethynyl- and 3,6-diethynyl-1,2,4,5-tetrazine derivatives for molecular electronic applications, proved by the scarcity of examples found in the literature. 3 Herein, we describe the synthesis and characterization of two novel ethynyl-based 1,2,4,5-tetrazine derivatives. Synthesis of 3,6-(4-bromophenyl)-1,2,4,5-tetrazine precursor (1) was achieved in good yield by Pinner’s method, starting from 4-bromobenzonitrile. Despite its low solubility in common organic solvents, this precursor was found to react smoothly under typical Sonogashira coupling conditions to selectively afford the 3-ethynyl (2) and 3,6-diethynyl (3) protected derivatives (Figure 1). Reaction conditions were evaluated in order to provide the best yields and to promote selectivity of the mono- or disubstituted ethynyl derivatives. Finally, deprotection was achieved affording, in the case of compound 3, an unprecedented 3,6- diethynyl-1,2,4,5-tetrazine compound. Time-Dependent Density Functional Theory (TDDFT) calculations for both deprotected ethynyl derivatives were used to simulate electronic spectra. A deep knowledge of the relevant electronic transitions involved and quantitatively satisfactory results of the calculated electronic excitations in comparison with experimental data were obtained.

New cholinesterase inhibitors for Alzheimer's disease: Structure Activity Studies (SARs) and molecular docking of isoquinolone and azepanone derivatives

A library of isoquinolinone and azepanone derivatives were screened for both acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE) activity. The strategy adopted included (a) in vitro biological assays, against eel AChE (EeAChE) and equine serum BuChE (EqBuChE) in order to determine the compounds IC50 and their dose-response activity, consolidated by (b) molecular docking studies to evaluate the docking poses and interatomic interactions in the case of the hit compounds, validated by STD-NMR studies. Compound (1f) was identified as one of these hits with an IC50 of 89.5 mu M for EeAChE and 153.8 mu M for EqBuChE, (2a) was identified as a second hit with an IC50 of 108.4 mu M (EeAChE) and 277.8 mu M (EqBuChE). In order to gain insights into the binding mode and principle active site interactions of these molecules, (R)-(1f) along with 3 other analogues (also as the R-enantiomer) were docked into both RhAChE and hBuChE models. Galantamine was used as the benchmark. The docking study was validated by performing an STD-NMR study of (1f) with EeAChE using galantamine as the benchmark.

Derivatives of cardanol through the ene reaction with diethyl azodicarboxylate.

2016

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.