This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. / For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. / For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods. / 本論文為金融衍生產品定價的兩類問題作出了研究。第一類是自由邊界問題，它可以制定一個受制於自由邊界條件的偏微分方程式(PDE)，雖然當中自由邊界條件的函數形式是已知的，但自由邊界的位置是未知的，只能通過為實際解施加連續性條件作隱式確定。這裡為兩個具體問題進行了研究，分別是固定利率按揭合約(fixed-rate mortgages)定價和方差恆彈性模型的美式期權(CEV American options)定價。第二類是多維問題，它涉及到多個相關隨機變量及他們引申出的多維PDE。這裡為一個典型例子進行了研究，稱為籃子差異期權(basket-spread options)，其基礎資產價格由相關的幾何布朗運動驅動。我們為這三個問題提出了解析近似解。 / 對於上述的自由邊界問題，我們提出了一項參數移動邊界來近似模仿未知的自由邊界，使原來的自由邊界問題轉化為移動邊界問題，從而提出一種解析近似解。控制移動邊界的參數是通過滿足近似解的一階導數連續性條件來定。得到了解析近似解令當中的衍生產品定價和避險參數能有效快速地計算出，相比於有限差分法(finite-difference method)，精度保持了但計算時間顯著降低。再透過應用一個多階段方案，將移動邊界重鑄成一項分段光滑的連續函數，能有系統地將近似解的結果逼近有限差分法的結果。 / 對於上述的多維問題，我們從Kirk(1995)的二維差異期權(spread option)近似解定價公式推廣到多維的籃子差異期權。由於最終的定價公式是封閉形式，所有避險參數也從而得到封閉式近似解。從一些模擬例子顯示出，近似解的定價和避險參數，與通過數值積分法(numerical integration)或蒙地卡羅模擬法(Monte Carlo simulation)獲得的基準值比較，只有小於百分之一的誤差。此外，透過利用一種期權價格和相關基礎變量的概率分佈關係，我們進一步推論出一項籃子差異變量的近似解分佈函數，這可應用到任何多維幾何布朗運動的線性組合變量分佈。最後，我們提出一種隱式攝動方法，把定價誤差減少高達一百倍，跟現有的近似解定價方法相比，這是其中一種最健全和準確的籃子差異期權定價方法。 / Lau, Chun Sing = 自由邊界和多維的金融衍生產品定價問題 : 解析近似解 / 劉振聲. / Thesis Ph.D. Chinese University of Hong Kong 2014. / Includes bibliographical references (leaves 174-186). / Abstracts also in Chinese. / Title from PDF title page (viewed on 12, September, 2016). / Lau, Chun Sing = Zi you bian jie he duo wei de jin rong yan sheng chan pin ding jia wen ti : jie xi jin si jie / Liu Zhensheng. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.

An important problem in mathematical finance is to develop option pricing models that are able to capture implied volatility “smile” or “skew” commonly observed in financial markets. Many existing models are based on time-homogeneous Markov processes and they often have difficulty in calibrating implied volatilities across both strikes and maturities. In this dissertation, we develop two parsimonious and analytically tractable option pricing models to evaluate VIX options and crack spread options, respectively. Our modeling approach is based on additive subordination, which is a natural generalization of classical Bochner’s subordination. Probabilistically, additive subordination corresponds to a stochastic time change with respect to an independent additive subordinator. To model the VIX dynamics, we timechange a non-affine mean-reverting 3/2 diffusion with an independent additive subordinator to capture its empirical features, such as mean reversion and jumps, as well as upward-sloping implied volatility skew in VIX options. Moreover, we develop a parsimonious and analytically tractable two-factor model for crude oil and its refined product to evaluate crack spread option, where each factor is an additive subordinate Cox-Ingersoll-Ross process. This model captures key empirical features of individual commodities, such as mean-reversion and jumps, as well as of their spread. Analytical formulas for related options prices under each model are derived via an eigenfunction expansion approach. Empirical results show that our models have great flexibility in calibrating implied volatilities across strikes and maturities of each underlying with excellent performance. Our results suggest that additive subordination is a useful technique that allows one to construct a large family of jump-diffusions and/or pure jump processes with rich time- and state-dependent local characteristics, which are suited for parsimoniously reproducing empirical features with analytical tractability. / 金融數學中的一個重要問題是建立能夠捕獲金融市場普遍觀察到的隱含波動率微笑現象的期權定價模型。許多現存的模型基於時間齊次的馬爾可夫過程且這些模型一般難以同時校準具有各種執行價格和到期時間的隱含波動率。在此博士論文中，我們建立了兩個簡潔且易於分析的期權定價模型，分別用於定價VIX期權和裂變價差期權。我們的建模方法基於additivesubordination，該方法是經典的Bochner的Subordination方法的自然延伸。從概率論上講，additive subordination定義了一個關於additive subordinator的隨機時間變換。為了對VIX的動態變化建模，我們對一個具有非仿射均值回复的3/2擴散過程進行時間變換來捕獲VIX的相關性質，如均值回复和跳躍，以及VIX期權中的向上偏的隱含波動率曲線。進一步，我們對原油和其成品油創建了一個簡潔的且易於分析的俩因子模型來定價裂變價差期權，其中每一個因子都是一個additive subordinate Cox-Ingersoll-Ross過程。這個模型可以捕獲每個油品價格的關鍵屬性，如均值回复和跳躍，以及其他之間的價差。每個模型下的相應期權價格的解析公式通過特偵函數展開的方式求解得到。實證研究表明我們的模型具有較好的靈活性，在校準每個期權品種的隱含波動率曲面方面都具有非常好的表現。我們的研究結果也表明additive subordination是一個非常有用的方法。它可以用於創建一大類具有時間和狀態相依特偵的跳躍擴散或純跳過程，這些過程可用於簡便的建模一些實證特徵且便於分析。 / Li, Jing. / Thesis Ph.D. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaves 129-142). / Abstracts also in Chinese. / Title from PDF title page (viewed on 13, September, 2016). / Detailed summary in vernacular field only.

The cyathins are a unique group of diterpenoids produced by the birds nest fungi <i>Cyathus helenae</i>, <i>C. africanus</i>, and <i>C. earlei</i>. Several of the cyathins show strong antibiotic activity. More recently, several fungal metabolites with structures closely related to those of the cyathins have been found to be potent inducers of nerve growth factor (NGF) synthesis. The structural complexity and the exciting biological activity of the cyathane family of diterpenes have prompted our efforts to develop an efficient and general synthetic approach.<p>To date, there have been seven total syntheses and six partial syntheses of cyathins. Most of these syntheses target allocyathin B2, which does not contain the common 6-7 trans ring fusion or the hydroxyl group within the seven member ring. Modifications of these routes to provide targets with these features have not been demonstrated and may be challenging. We have developed a concise asymmetric synthesis of cyathin A3, based on the enantioselective Diels-Alder reaction of quinone (106) and diene (105). Because the transformations of cyathin A3 into other cyathins are well documented, this synthesis provides a general approach to the cyathane diterpene family. In Section 2.2, the enantioselective Diels-Alder reaction of quinone 106 and diene 105 is presented. This reaction is effectively catalyzed by a carefully prepared Mikami catalyst. It was carried out on a preparative scale to give the chiral building block 108. The absolute configuration of the Diels-Alder adduct 108 was determined by NMR and X-ray analysis.<p>In Sections 2.3-5, the enantioselective total synthesis of (-)-cyathin A3 is described. This approach features the successful oxymercuration ring opening, a newly developed in situ configuration inversion, a much improved intramolecular aldol reaction and a radical cyclization. Now envisioned in our laboratory is the development of a new access to cyathin A4, which is surmised to be possible via the intermediate prepared in this synthesis.

The cyathins are a unique group of diterpenoids produced by the birds nest fungi <i>Cyathus helenae</i>, <i>C. africanus</i>, and <i>C. earlei</i>. Several of the cyathins show strong antibiotic activity. More recently, several fungal metabolites with structures closely related to those of the cyathins have been found to be potent inducers of nerve growth factor (NGF) synthesis. The structural complexity and the exciting biological activity of the cyathane family of diterpenes have prompted our efforts to develop an efficient and general synthetic approach.<p>To date, there have been seven total syntheses and six partial syntheses of cyathins. Most of these syntheses target allocyathin B2, which does not contain the common 6-7 trans ring fusion or the hydroxyl group within the seven member ring. Modifications of these routes to provide targets with these features have not been demonstrated and may be challenging. We have developed a concise asymmetric synthesis of cyathin A3, based on the enantioselective Diels-Alder reaction of quinone (106) and diene (105). Because the transformations of cyathin A3 into other cyathins are well documented, this synthesis provides a general approach to the cyathane diterpene family. In Section 2.2, the enantioselective Diels-Alder reaction of quinone 106 and diene 105 is presented. This reaction is effectively catalyzed by a carefully prepared Mikami catalyst. It was carried out on a preparative scale to give the chiral building block 108. The absolute configuration of the Diels-Alder adduct 108 was determined by NMR and X-ray analysis.<p>In Sections 2.3-5, the enantioselective total synthesis of (-)-cyathin A3 is described. This approach features the successful oxymercuration ring opening, a newly developed in situ configuration inversion, a much improved intramolecular aldol reaction and a radical cyclization. Now envisioned in our laboratory is the development of a new access to cyathin A4, which is surmised to be possible via the intermediate prepared in this synthesis.

I wish to argue the following points: 1. MT Jeremiah gives a more complex text form in its more intricate poetic structure and, therefore, represents a more ancient or earlier form of verses 10:1-18. 2. LXX Jeremiah demonstrates later interpretative and textual developments in its logical structure of verses 10:1-18, which gives emphasis to verse 11 in its structural placement of verse 9 within that of verse 5, along with the necessary deletions of verses 10:6-8 and 10. 3. Qumran, apocryphal, and pseudepigraphtical material demonstrate the cultural and scribal milieu that readily explains the alterations evident in the Septuagint text form of 10:1-18. These three primary arguments will be expressed in greater detail in chapters 2, 3, and 4. Chapter 2 concerns the Masoretic text form of 10:1-18 and explicates its text form's structure. Chapter 3 discusses the Septuagint text form of 10:1-18 and analyzes its textual developments and translation technique. Chapter 4 surveys Second Temple Period Jewish literature that contains the text of Jer 10:1-18 or references its material. I will study Jeremiah 10:1-18 with the traditional tools of textual criticism along with other biblical criticisms as well. In this thesis, I wish to argue that the texts of 4Q71 (4QJerb) and LXX Jer 10 show evidence of a secondary nature in comparison to the MT tradition as reflected in 4Q70 (4QJera). The abbreviation of the passage and the transposition of 10:9 within 10:5 reflected in 4Q71 and LXX 10 demonstrate an easier and later textual variant in comparison to the more original text form of MT Jer 10. I shall observe that 4Q71 and LXX Jer 10:1-18's alterations to MT's older text form were done for the sake of attempting to smooth out the logical flow of the pericope.

M. S.

M. S.

Esta dissertação de mestrado descreve os resultados obtidos acerca da aplicação de reações de acoplamento entre aldeídos, aminas e alquinos (A3) visando a síntese de alcalóides indolizidínicos de ocorrência natural, como a desoxicastanospermina e a swainsonina. A reação de acoplamento-A3 é uma poderosa ferramenta de construção de ligação carbono-carbono e carbono-heteroátomo, permitindo a preparação de propargilaminas que podem ser exploradas como intermediários de grande potencial sintético. A proposta está baseada na reação de acoplamento de um reagente organometálico, gerado in situ a partir de um alquino e um sal ou complexo metálico, e um eletrófilo nitrogenado, que consiste em uma imina ou sal de imínio também gerado in situ a partir de uma amina e um aldeído. Hidroxialdeídos apropriados foram preparados e empregados no acoplamento-A3 juntamente com alquinóis não-protegidos, de modo que a propargilamina resultante contivesse funcionalizações estrategicamente posicionadas visando permitir duas ciclizações via nitrogênio e a conseqüente formação de esqueletos indolizidínicos. Para este mesmo fim, diversas aminas foram testadas no acoplamento, de forma que fosse possível uma N-desproteção compatível com os demais grupos funcionais necessários à síntese dos alcalóides. Dentre estas, dibenzilamina e dialilamina levaram a bons resultados no acoplamento, utilizando um &#945;-hidroxialdeído O-protegido ou um &#948;-hidroxialdeído livre. Tal metodologia possibilitou a síntese de três propargilaminas a serem utilizadas como intermediários sintéticos na síntese de alcalóides indolizidínicos hidroxilados: 5-(dibenzilamino)-6-((2-metoxietoxi)metoxi)-8- ((tetrahidro-2H-piran-2-il)oxi)oct-3-in-1-ol, 4-(dibenzilamino)oct-2-ino-1,8-diol e 4- (dialilamino)oct-2-ino-1,8-diol; em rendimentos globais de 39% (6 etapas reacionais), 68% (2 etapas) e 57% (2 etapas), respectivamente. Entretanto, no caso específico da propargilamina derivada da dibenzilamina, não obteve-se sucesso nas tentativas de desproteção do nitrogênio e concomitante redução seletiva da ligação tripla à dupla por hidrogenação. / This Masters thesis concerns the results obtained toward the application of amine-aldehyde- akyne coupling reactions (A3) aiming at the synthesis of naturally occurring indolizidine alkaloids, such as deoxycastanospermine and swainsonine. The A3- coupling reaction is a powerful tool for the construction of carbon-carbon and carbon-heteroatom bonds, allowing the preparation of functionalized propargylamines that may be explored as synthetically useful intermediates. The proposal is centered on the coupling reaction between an organometallic reagent, generated in situ from an alkyne and a metallic salt or complex, and a nitrogenated electrofile, consisting of an imine or imminium salt that is also generated in situ from an amine and an aldehyde. Appropriate hydroxyaldehydes were prepared and used in the A3-coupling along with unprotected alkynols, so that the resulting propargylamine contained strategically placed functionalizations aiming to allow two annulations to occur via the nitrogen atom and the consequent formation of indolizidine skeletons. For the same end, several amines were tested in the coupling reaction, so that a N-deprotection compatible with the other funcional groups necessary to the synthesis of the alkaloids would be possible. Among these, dibenzylamine and diallylamine led to satisfactory results in the coupling reaction, using either a O-protected &#945;-hydroxyaldehyde or an unprotected &#948;-hydroxyaldehyde. This methodology led to the preparation of three propargylamines to be used as synthetic intermediates in the synthesis of hydroxylated indolizidine alkaloids: 5-(dibenzylamine)-6-((2- methoxyethoxy)methoxy)-8-((tetrahydro-2H-pyran-2-yl)oxy)oct-3-yn-1-ol, 4- (dibenzylamine)oct-2-yne-1,8-diol and 4-(diallylamine)oct-2-yne-1,8-diol; in overall yields of 39% (6 synthetic steps), 68% (2 steps) and 57% (2 steps), respectively. However, in the particular case of the dibenzylamine-derived propargylamine, no success was achieved in the attempts of nitrogen deprotection and concomitant selective reduction of the triple to double bond via hydrogenation.

Esta dissertação de mestrado descreve os resultados obtidos acerca da aplicação de reações de acoplamento entre aldeídos, aminas e alquinos (A3) visando a síntese de alcalóides indolizidínicos de ocorrência natural, como a desoxicastanospermina e a swainsonina. A reação de acoplamento-A3 é uma poderosa ferramenta de construção de ligação carbono-carbono e carbono-heteroátomo, permitindo a preparação de propargilaminas que podem ser exploradas como intermediários de grande potencial sintético. A proposta está baseada na reação de acoplamento de um reagente organometálico, gerado in situ a partir de um alquino e um sal ou complexo metálico, e um eletrófilo nitrogenado, que consiste em uma imina ou sal de imínio também gerado in situ a partir de uma amina e um aldeído. Hidroxialdeídos apropriados foram preparados e empregados no acoplamento-A3 juntamente com alquinóis não-protegidos, de modo que a propargilamina resultante contivesse funcionalizações estrategicamente posicionadas visando permitir duas ciclizações via nitrogênio e a conseqüente formação de esqueletos indolizidínicos. Para este mesmo fim, diversas aminas foram testadas no acoplamento, de forma que fosse possível uma N-desproteção compatível com os demais grupos funcionais necessários à síntese dos alcalóides. Dentre estas, dibenzilamina e dialilamina levaram a bons resultados no acoplamento, utilizando um &#945;-hidroxialdeído O-protegido ou um &#948;-hidroxialdeído livre. Tal metodologia possibilitou a síntese de três propargilaminas a serem utilizadas como intermediários sintéticos na síntese de alcalóides indolizidínicos hidroxilados: 5-(dibenzilamino)-6-((2-metoxietoxi)metoxi)-8- ((tetrahidro-2H-piran-2-il)oxi)oct-3-in-1-ol, 4-(dibenzilamino)oct-2-ino-1,8-diol e 4- (dialilamino)oct-2-ino-1,8-diol; em rendimentos globais de 39% (6 etapas reacionais), 68% (2 etapas) e 57% (2 etapas), respectivamente. Entretanto, no caso específico da propargilamina derivada da dibenzilamina, não obteve-se sucesso nas tentativas de desproteção do nitrogênio e concomitante redução seletiva da ligação tripla à dupla por hidrogenação. / This Masters thesis concerns the results obtained toward the application of amine-aldehyde- akyne coupling reactions (A3) aiming at the synthesis of naturally occurring indolizidine alkaloids, such as deoxycastanospermine and swainsonine. The A3- coupling reaction is a powerful tool for the construction of carbon-carbon and carbon-heteroatom bonds, allowing the preparation of functionalized propargylamines that may be explored as synthetically useful intermediates. The proposal is centered on the coupling reaction between an organometallic reagent, generated in situ from an alkyne and a metallic salt or complex, and a nitrogenated electrofile, consisting of an imine or imminium salt that is also generated in situ from an amine and an aldehyde. Appropriate hydroxyaldehydes were prepared and used in the A3-coupling along with unprotected alkynols, so that the resulting propargylamine contained strategically placed functionalizations aiming to allow two annulations to occur via the nitrogen atom and the consequent formation of indolizidine skeletons. For the same end, several amines were tested in the coupling reaction, so that a N-deprotection compatible with the other funcional groups necessary to the synthesis of the alkaloids would be possible. Among these, dibenzylamine and diallylamine led to satisfactory results in the coupling reaction, using either a O-protected &#945;-hydroxyaldehyde or an unprotected &#948;-hydroxyaldehyde. This methodology led to the preparation of three propargylamines to be used as synthetic intermediates in the synthesis of hydroxylated indolizidine alkaloids: 5-(dibenzylamine)-6-((2- methoxyethoxy)methoxy)-8-((tetrahydro-2H-pyran-2-yl)oxy)oct-3-yn-1-ol, 4- (dibenzylamine)oct-2-yne-1,8-diol and 4-(diallylamine)oct-2-yne-1,8-diol; in overall yields of 39% (6 synthetic steps), 68% (2 steps) and 57% (2 steps), respectively. However, in the particular case of the dibenzylamine-derived propargylamine, no success was achieved in the attempts of nitrogen deprotection and concomitant selective reduction of the triple to double bond via hydrogenation.

The CHRNA5/A3/B4 genomic cluster encodes for the alpha5, alpha3 and beta4 subunits of the nicotinic acetylcholine receptors (nAChRs). Human genetic studies have revealed a significant association of variants in this genomic region with nicotine dependence. However, the mechanisms through which overexpression of these three subunits may influence smoking-related behaviours is not understood. To gain insight in the possible mechanisms, we used a BAC transgenic mouse model overexpressing this cluster containing the three genes together with their transcriptional regulatory elements. We found that overexpression of the cluster: i) increases sensitivity to the pharmacological effects of nicotine; ii) modifies particular cognitive domains associated to drug addiction and hippocampal neuronal complexity and synaptic plasticity; and iii) shifts the rewarding and aversive properties of nicotine and the manifestation of nicotine-withdrawal syndrome. Our study suggests that the genomic cluster CHRNA5/A3/B4 contributes to genetic vulnerability to nicotine addiction and promotes smoking-related behaviours possibly through hippocampal plasticity changes. / El cluster genòmic CHRNA5/A3/B4 codifica per les subunitats alfa5, alfa3 i beta4 dels receptors d’acetilcolina (nAChRs). Estudis de genètica humana han revelat que variants en aquesta regió genòmica estan significativament associats a la dependencia a nicotina. Malauradament, els mecanismes pels quals la sobreexpressió d’aquestes tres subunitats influencia comportaments relacionats amb el consum de tabac no són del tot coneguts. Per tal d’entendre els possibles mecanismes, hem utilitzat un model de ratolí transgènic que sobreexpressa aquest cluster amb els tres gens i les seus elements de regulació transcripcional. Hem trobat que la sobreexpressió del cluster: i) incrementa la sensibilitat als efectes farmacològics de la nicotina; ii) modifica determinats dominis cognitius associats a l’addicció a droges i la complexitat neuronal i plasticitat sinàpica de l’hipocamp; a més a més iii) canvia les propietats de recompensa i aversió de la nicotina i la manifestació del síndrome d’abstinència. El nostre estudi suggereix que el cluster genòmic CHRNA5/A3/B4 contribueix a la vulnerabilitat genètica a l’adicció a la nicotina i promou comportaments relacionats amb el consum de tabac possiblement a través de canvis de plasticitiat a l’hipocamp.