The valuation of self-funding instalment warrants

© 2017 World Scientific Publishing Company. We present two models for the fair value of a self-funding instalment warrant. In both models we assume the underlying stock process follows a geometric Brownian motion. In the first model, we assume that the underlying stock pays a continuous dividend yield and in the second we assume that it pays a series of discrete dividend yields. We show that both models admit similarity reductions and use these to obtain simple finite-difference and Monte Carlo solutions. We use the method of multiple scales to connect these two models and establish the first-order correction term to be applied to the first model in order to obtain the second, thereby establishing that the former model is justified when many dividends are paid during the life of the warrant. Further, we show that the functional form of this correction may be expressed in terms of the hedging parameters for the first model and is, from this point of view, independent of the particular payoff in the first model. In two appendices we present approximate solutions for the first model which are valid in the small volatility and the short time-To-expiry limits, respectively, by using singular perturbation techniques. The small volatility solutions are used to check our finite-difference solutions and the small time-To-expiry solutions are used as a means of systematically smoothing the payoffs so we may use pathwise sensitivities for our Monte Carlo methods

The evaluation of discrete barrier options in a path integral framework

The pricing of discretely monitored barrier options is a difficult problem. In general, there is no known closed form solution for pricing such options. A path integral approach to the evaluation of barrier options is developed. This leads to a backward recursion functional equation linking the pricing functions at successive barrier points. This functional equation is solved by expanding the pricing functions in Fourier-Hermite series. The backward recursion functional equation then becomes the backward recurrence relation for the coefficients in the Fourier-Hermite expansion of the pricing functions. A very efficient and accurate method for generating the pricing function at any barrier point is thus obtained. A number of numerical experiments with the method are performed in order to gain some understanding of the nature of convergence. Results for various volatility values and different numbers of basis functions in the Fourier-Hermite expansion are presented. Comparisons are given between pricing of discrete barrier option in the path integral framework and by use of finite difference methods

Performance of a Balanced Portfolio With Active Covered-Call Strategies

This study investigates the performance of local and global investments with and without covered call option strategies over the period from January 2000 to December 2015. The Covered Call Strategy (CCS) is a common return enhancing strategy used in portfolio management. The strategy consists of simultaneously holding a long position in an asset and writing call options on that asset. The local investment are on the top twenty stocks from Australian market while the global investment is an international balanced portfolio. For covered call strategies, market option data from Australian Stock Exchange is used. The results show that under some constraints, using covered call strategies in general improves the risk-adjusted returns

3D Woven Composites: From Weaving to Manufacturing

Manufacturing near-net shape preforms of fibre-reinforced composites has received growing interest from industry. Traditionally, a preform was made from 2D fabrics, but recently, it has been shown that 3D textiles can be used with success; with weaving being the predominant technology for carbon fibre composites. In 3D weaving, weft, warp and binder fibres run across, along and through the fabrics in the X, Y and Z directions, respectively. Producing a unitised single-piece fabric and subsequently reducing the takt time required for rapid composite manufacturing are two of the main advantages of using 3D woven preforms. Weaving of 3D fabrics, manufacturing of 3D composites, physical characterisation and mechanical testing of infused composites samples are discussed in this chapter. Finally, a large automotive composite made of single-piece 3D woven preform was manufactured and presented for demonstration

Energija vezanja donora u paraboličkoj kvantnoj jami

We solved the impurity problem in a parabolic quantum well. The binding energy of a neutral donor in GaAs-Alx Ga1!xAs parabolic quantum well is determined variationally. For a dopant at the well center, and at the edge of the well in the interface region, the changes in the binding energy of donors are calculated, for different well sizes and depths. The 2s excited state is reported.Riješili smo problem primjese u paraboličkoj kvantnoj jami. Energija vezanja neutralnog donora u GaAs-Alx Ga1−xAs paraboličkoj kvantnoj jami se rješava varijacijski. Izračunali smo energije vezanja donora ako je u sredini jame i ako je uz rub u međusloju, za različite širine i dubine jame. Izvješćujemo o uzbuđenom stanju 2s

Energija vezanja donora u paraboličkoj kvantnoj jami

We solved the impurity problem in a parabolic quantum well. The binding energy of a neutral donor in GaAs-Alx Ga1!xAs parabolic quantum well is determined variationally. For a dopant at the well center, and at the edge of the well in the interface region, the changes in the binding energy of donors are calculated, for different well sizes and depths. The 2s excited state is reported.Riješili smo problem primjese u paraboličkoj kvantnoj jami. Energija vezanja neutralnog donora u GaAs-Alx Ga1−xAs paraboličkoj kvantnoj jami se rješava varijacijski. Izračunali smo energije vezanja donora ako je u sredini jame i ako je uz rub u međusloju, za različite širine i dubine jame. Izvješćujemo o uzbuđenom stanju 2s