Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary

This paper presents a new numerical method for pricing American call options when the volatility of the price of the underlying stock is stochastic. By exploiting a log-linear relationship of the optimal exercise boundary with respect to volatility changes, we derive an integral representation of an American call price and the early exercise premium which holds under stochastic volatility. This representation is used to develop a numerical method for pricing the American options based on an approximation of the optimal exercise boundary by Chebyshev polynomials. Numerical results show that our numerical approach can quickly and accurately price American call options both under stochastic and/or constant volatility.American call option, Stochastic volatility, Early exercise boundary, Chebyshev polynomials

Efficient method for aeroelastic tailoring of composite wing to minimize gust response

Aeroelastic tailoring of laminated composite structure demands relatively high computational time especially for dynamic problem. This paper presents an efficient method for aeroelastic dynamic response analysis with significantly reduced computational time. In this method, a relationship is established between the maximum aeroelastic response and quasi-steady deflection of a wing subject to a dynamic loading. Based on this relationship, the time consuming dynamic response can be approximated by a quasi-steady deflection analysis in a large proportion of the optimization process. This method has been applied to the aeroelastic tailoring of a composite wing of a tailless aircraft for minimum gust response. The results have shown that 20%–36% gust response reduction has been achieved for this case. The computational time of the optimization process has been reduced by 90% at the cost of accuracy reduction of 2~4% comparing with the traditional dynamic response analysis

Towards Multiplexed Electrogenerated Chemiluminescent Detection

The main objective of this dissertation is to understand and study the principle of electrogenerated chemiluminescence (ECL) and its applications to detect biomolecules simultaneously. Four aspects of ECL were studied. In order to carry out multiplexed ECL detection, both classical and several novel ECL systems have been investigated. In the first aspect, significant effect of chloride ions on the ECL behavior of the tris(2,2′-bipyridyl) ruthenium(II) (Ru(bpy)3 2+)/tri-n-propylamine (TPrA) system at Au electrode was investigated. At low concentrations (e.g., [Cl-] \u3c 5 mM), the ECL was enhanced; at relatively high concentrations, however, the ECL intensity decreased with the increase of the [Cl-]. At [Cl-] = 90 mM, ~ 50% and 100% ECL inhibition was observed for the first and the second ECL wave, respectively. The electrogenerated chloroaurate anions (AuCl2 - and AuCl4 -) which were verified using an electrochemical quartz-crystal microbalance (EQCM) method were found to be responsible for the ECL inhibition. This study suggests that care must be taken when Au working electrode is used for ECL studies in chloride-containing buffer solutions (widely used in DNA probes) and/or with the commonly used chloride-containing reference electrodes since in these cases the ECL behavior may significantly disagree with that obtained using other electrodes and reaction media. In the second aspect, the electrochemical behavior of a trinuclear ruthenium(II)- containing complex, [((phen)2Ru(dpp))2RhCl2]5+ (where phen = 1,10-phenanthroline, dpp = 2,3-bis-2-pyridylpyrazine), was studied in acetonitrile (MeCN) and aqueous solutions. In MeCN containing 0.10 M tetra-n-butylammonium perchlorate (TBAP), the complex displayed a reversible, overlapping RuII/III redox process with E1/2 = +1.21 V vs Ag/Ag+ (10 mM), an irreversible reduction of RhIII/I at -0.73 V vs Ag/Ag+, and two quasireversible dpp/dpp- couples with E1/2 = -1.11 V and -1.36 V vs Ag/Ag+ at a Pt electrode with a scan rate of 50 mV s-1. In 0.20 M Tris buffer solution (pH 7.4), an irreversible, overlapping RuII/III oxidation at +1.48 V vs Ag/AgCl (3 M KCl), and an irreversible reduction of RhIII/II at -0.78 V vs Ag/AgCl were observed at a glassy carbon electrode with a scan rate of 50 mV/s. Investigations on the ECL of the complex revealed that 2-(dibutylamino) ethanol (DBAE) was superior to TPrA as an ECL coreactant within their entire concentration range of 10-100 mM in MeCN, and in aqueous media, as low as 1.0 nM of the complex could be detected using TPrA coreactant ECL. A maximum ECL emission of 640 nm, which is about 55 nm blue-shifted with respect to its fluorescence peak, was observed in MeCN with DBAE as a coreactant. Interactions of the complex with calf thymus DNA (ctDNA) were conducted with a flow-cell based QCM, and a binding constant of 2.5×105 M-1 was calculated on the basis of the Langmuir isotherm equation. In the third aspect, ECL behavior of core/shell semiconductor CdSe/ZnS nanocrystals coated with a carboxyl polymer layer (quantum dot, Qdot, or QDs) was studied in aqueous solutions using TPrA and DBAE as ECL coreactant. Upon the anodic potential scanning, strong ECL emissions were observed at glassy carbon (GC) electrode within the potential range of ~0.75 to 1.5 V vs Ag/AgCl (3.0 M KCl) when DBAE was used as the coreactant. The ECL behavior of the Qdot was found to be strongly dependent on the types and concentrations of ECL coreactants as well as the nature of the working electrode. The ECL emission measured with the Qdot/DBAE/GC electrode system has a peak value of ~625 nm, which matched well with its fluorescence. The Qdot as a label for ECL-based C-reactive protein (CRP) immunoassays was realized by covalent binding of avidin on its surface, which allowed biotinalyted antibodies to be attached and interacted with antigens and the antibodies linked to micro-sized magnetic beads. The newly formed sandwich type aggregates were separated magnetically from the solution matrix, followed by the ECL generation in the presence of the coreactant DBAE. ECL experiments were carried out with a potential scan from 0 to 1.5 V vs Ag/AgCl at partially transparent Au/CD electrodes, and the integrated ECL intensity was found to be linearly proportional to the CRP concentration over the range of 1.0-10.0 μg/mL. In the fourth aspect, the ECL behavior of Ru(bpy)3 2+, 9,10-diphenylanthracene DPA), and rubrene (RUB) with DBAE or TPrA as the coreactant was studied in acetonitrile solution. The ECL emission spectra of the mixed solution including the above three ECL labels were investigated. The ECL maximum emissions at ~440 nm for DPA, ~560 nm for RUB, and ~630 nm for Ru(bpy)3 2+ were linearly proportional to the concentration of each individual ECL labels in mixed solutions, suggesting that multiplexing detection and quantification of biomolecules with ECL technology is feasible

Pricing American derivatives and interest rates derivatives based on characteristic function of the underlying asset returns

PhDIn this thesis I introduce a new methodology for pricing American options when the underlying model of the asset price allows for stochastic volatility and/or it has a multi-factor structure. Our approach is based on a decomposition of an American option price into its European options counterpart price and the early exercise premium, paid by the option holder in order to keep the right of exercising the option at any time-point before its expiration date. Based on closed form solutions of the joint characteristic function of the state variables driving the underlying model, the thesis provides analytic, integral solutions of the early exercise premium (and hence of the American option price) which enable us to build up fast and accurate numerical approximation procedures for calculating options prices. The analytic solutions that I derive express the optimal early exercise boundary in terms of prices of Arrow-Debreu type of securities reflecting the values of the options additional payoffs if they are exercised earlier, or not. Numerical results reported in the thesis show that our approach can price American options on stocks, bonds and interest rates derivatives efficiently and very fast, compared with existing methods. The efficiency gains of our method stem from the fact that it involves only one step of approximation, as the European prices embodied in the American option prices can be calculated analytically. The gains of computational speed come from the fact that our method can reduce the integral dimensions of the early exercise premium considerably

Optimum buckling design of composite stiffened panels using ant colony algorithm

Optimal design of laminated composite stiffened panels of symmetric and balanced layup with different number of T-shape stiffeners is investigated and presented. The stiffened panels are simply supported and subjected to uniform biaxial compressive load. In the optimization for the maximum buckling load without weight penalty, the panel skin and the stiffened laminate stacking sequence, thickness and the height of the stiffeners are chosen as design variables. The optimization is carried out by applying an ant colony algorithm (ACA) with the ply contiguous constraint taken into account. The finite strip method is employed in the buckling analysis of the stiffened panels. The results shows that the buckling load increases dramatically with the number of stiffeners at first, and then has only a small improvement after the number of stiffeners reaches a certain value. An optimal layup of the skin and stiffener laminate has also been obtained by using the ACA. The methods presented in this paper should be applicable to the design of stiffened composite panels in similar loading conditions