On the efficacy of Fourier series approximations for pricing European options

This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the halfrange cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together,these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

Improving ultrasound excitation systems using a flexible power supply with adjustable voltage and frequency to drive piezoelectric transducers

The ability of a piezoelectric transducer in energy conversion is rapidly expanding in several applications. Some of the industrial applications for which a high power ultrasound transducer can be used are surface cleaning, water treatment, plastic welding and food sterilization. Also, a high power ultrasound transducer plays a great role in biomedical applications such as diagnostic and therapeutic applications. An ultrasound transducer is usually applied to convert electrical energy to mechanical energy and vice versa. In some high power ultrasound system, ultrasound transducers are applied as a transmitter, as a receiver or both. As a transmitter, it converts electrical energy to mechanical energy while a receiver converts mechanical energy to electrical energy as a sensor for control system. Once a piezoelectric transducer is excited by electrical signal, piezoelectric material starts to vibrate and generates ultrasound waves. A portion of the ultrasound waves which passes through the medium will be sensed by the receiver and converted to electrical energy. To drive an ultrasound transducer, an excitation signal should be properly designed otherwise undesired signal (low quality) can deteriorate the performance of the transducer (energy conversion) and increase power consumption in the system. For instance, some portion of generated power may be delivered in unwanted frequency which is not acceptable for some applications especially for biomedical applications. To achieve better performance of the transducer, along with the quality of the excitation signal, the characteristics of the high power ultrasound transducer should be taken into consideration as well. In this regard, several simulation and experimental tests are carried out in this research to model high power ultrasound transducers and systems. During these experiments, high power ultrasound transducers are excited by several excitation signals with different amplitudes and frequencies, using a network analyser, a signal generator, a high power amplifier and a multilevel converter. Also, to analyse the behaviour of the ultrasound system, the voltage ratio of the system is measured in different tests. The voltage across transmitter is measured as an input voltage then divided by the output voltage which is measured across receiver. The results of the transducer characteristics and the ultrasound system behaviour are discussed in chapter 4 and 5 of this thesis. Each piezoelectric transducer has several resonance frequencies in which its impedance has lower magnitude as compared to non-resonance frequencies. Among these resonance frequencies, just at one of those frequencies, the magnitude of the impedance is minimum. This resonance frequency is known as the main resonance frequency of the transducer. To attain higher efficiency and deliver more power to the ultrasound system, the transducer is usually excited at the main resonance frequency. Therefore, it is important to find out this frequency and other resonance frequencies. Hereof, a frequency detection method is proposed in this research which is discussed in chapter 2. An extended electrical model of the ultrasound transducer with multiple resonance frequencies consists of several RLC legs in parallel with a capacitor. Each RLC leg represents one of the resonance frequencies of the ultrasound transducer. At resonance frequency the inductor reactance and capacitor reactance cancel out each other and the resistor of this leg represents power conversion of the system at that frequency. This concept is shown in simulation and test results presented in chapter 4. To excite a high power ultrasound transducer, a high power signal is required. Multilevel converters are usually applied to generate a high power signal but the drawback of this signal is low quality in comparison with a sinusoidal signal. In some applications like ultrasound, it is extensively important to generate a high quality signal. Several control and modulation techniques are introduced in different papers to control the output voltage of the multilevel converters. One of those techniques is harmonic elimination technique. In this technique, switching angles are chosen in such way to reduce harmonic contents in the output side. It is undeniable that increasing the number of the switching angles results in more harmonic reduction. But to have more switching angles, more output voltage levels are required which increase the number of components and cost of the converter. To improve the quality of the output voltage signal with no more components, a new harmonic elimination technique is proposed in this research. Based on this new technique, more variables (DC voltage levels and switching angles) are chosen to eliminate more low order harmonics compared to conventional harmonic elimination techniques. In conventional harmonic elimination method, DC voltage levels are same and only switching angles are calculated to eliminate harmonics. Therefore, the number of eliminated harmonic is limited by the number of switching cycles. In the proposed modulation technique, the switching angles and the DC voltage levels are calculated off-line to eliminate more harmonics. Therefore, the DC voltage levels are not equal and should be regulated. To achieve this aim, a DC/DC converter is applied to adjust the DC link voltages with several capacitors. The effect of the new harmonic elimination technique on the output quality of several single phase multilevel converters is explained in chapter 3 and 6 of this thesis. According to the electrical model of high power ultrasound transducer, this device can be modelled as parallel combinations of RLC legs with a main capacitor. The impedance diagram of the transducer in frequency domain shows it has capacitive characteristics in almost all frequencies. Therefore, using a voltage source converter to drive a high power ultrasound transducer can create significant leakage current through the transducer. It happens due to significant voltage stress (dv/dt) across the transducer. To remedy this problem, LC filters are applied in some applications. For some applications such as ultrasound, using a LC filter can deteriorate the performance of the transducer by changing its characteristics and displacing the resonance frequency of the transducer. For such a case a current source converter could be a suitable choice to overcome this problem. In this regard, a current source converter is implemented and applied to excite the high power ultrasound transducer. To control the output current and voltage, a hysteresis control and unipolar modulation are used respectively. The results of this test are explained in chapter 7.

Le infrastrutture viarie dismesse o declassate ed il progetto di paesaggio

Paesaggio ed infrastrutture viarie sono un binomio molto forte: il primo ha insito il concetto di accessibilità, in quanto non può esistere senza la presenza di un osservatore; la strada, invece, trova i fattori che la connotano nel suo rapporto con la morfologia su cui insiste. Le infrastrutture viarie sono elemento strutturale e strutturante non solo di un territorio, ma anche di un paesaggio. Le attuali esigenze di mobilità portano oggi a ripensare ed adeguare molte infrastrutture viarie: laddove è possibile si potenziano le strutture esistenti, in diversi casi si ricorre a nuovi tracciati o a varianti di percorso. Porsi il problema di conservare itinerari testimoni della cultura materiale ed economica di una società implica considerazioni articolate, che travalicano i limiti del sedime: una via è un organismo più complesso della semplice linea di trasporto in quanto implica tutta una serie di manufatti a supporto della mobilità e soprattutto il corridoio infrastrutturale che genera e caratterizza, ovvero una porzione variabile di territorio definita sia dal tracciato che dalla morfologia del contesto. L’evoluzione dei modelli produttivi ed economici, che oggi porta quote sempre maggiori di popolazione a passare un tempo sempre minore all’interno del proprio alloggio, rende la riflessione sulle infrastrutture viarie dismesse o declassate occasione per la progettazione di spazi per l’abitare collettivo inseriti in contesti paesaggistici, tanto urbani che rurali, tramite reti di percorsi pensate per assorbire tagli di mobilità specifici e peculiari. Partendo da queste riflessioni la Tesi si articola in: Individuazioni del contesto teorico e pratico: Lo studio mette in evidenza come la questione delle infrastrutture viarie e del loro rapporto con il paesaggio implichi riflessioni incrociate a diversi livelli e tramite diverse discipline. La definizione dello spazio fisico della strada passa infatti per la costruzione di un itinerario, un viaggio che si appoggia tanto ad elementi fisici quanto simbolici. La via è un organismo complesso che travalica il proprio sedime per coinvolgere una porzione ampia di territorio, un corridoio variabile ed articolato in funzione del paesaggio attraversato. Lo studio propone diverse chiavi di lettura, mettendo in luce le possibili declinazioni del tema, in funzione del taglio modale, del rapporto con il contesto, del regime giuridico, delle implicazioni urbanistiche e sociali. La mobilità dolce viene individuata quale possibile modalità di riuso, tutela e recupero, del patrimonio diffuso costituito dalle diversi reti di viabilità. Antologia di casi studio: Il corpo principale dello studio si basa sulla raccolta, analisi e studio dello stato dell’arte nel settore; gli esempi raccolti sono presentati in due sezioni: la prima dedicata alle esperienze più significative ed articolate, che affrontano il recupero delle infrastrutture viarie a più livelli ed in modo avanzato non concentrandosi solo sulla conversione del sedime, ma proponendo un progetto che coinvolga tutto il corridoio attraversato dall’infrastruttura; la seconda parte illustra la pratica corrente nelle diverse realtà nazionali, ponendo in evidenza similitudini e differenze tra i vari approcci.