Multi-asset Spread Option Pricing and Hedging

We provide two new closed-form approximation methods for pricing spread options on a basket of risky assets: the extended Kirk approximation and the second-order boundary approximation. Numerical analysis shows that while the latter method is more accurate than the former, both methods are extremely fast and accurate. Approximations for important Greeks are also derived in closed form. Our approximation methods enable the accurate pricing of a bulk volume of spread options on a large number of assets in real time, which offers traders a potential edge in a dynamic market environment.multi-asset spread option, closed-form approximation

Control circuits for avalanche photodiodes

Avalanche Photodiodes (APDs) have been used in a wide range of low light sensing applications such as DNA sequencing, quantum key distribution, LIDAR and medical imaging. To operate the APDs, control circuits are required to achieve the desired performance characteristics. This thesis presents the work on development of three control circuits including a bias circuit, an active quench and reset circuit and a gain control circuit all of which are used for control and performance enhancement of the APDs. The bias circuit designed is used to bias planar APDs for operation in both linear and Geiger modes. The circuit is based on a dual charge pumps configuration and operates from a 5 V supply. It is capable of providing milliamp load currents for shallow-junction planar APDs that operate up to 40 V. With novel voltage regulators, the bias voltage provided by the circuit can be accurately controlled and easily adjusted by the end user. The circuit is highly integrable and provides an attractive solution for applications requiring a compact integrated APD device. The active quench and reset circuit is designed for APDs that operate in Geiger-mode and are required for photon counting. The circuit enables linear changes in the hold-off time of the Geiger-mode APD (GM-APD) from several nanoseconds to microseconds with a stable setting step of 6.5 ns. This facilitates setting the optimal `afterpulse-free' hold-off time for any GM-APD via user-controlled digital inputs. In addition this circuit doesn’t require an additional monostable or pulse generator to reset the detector, thus simplifying the circuit. Compared to existing solutions, this circuit provides more accurate and simpler control of the hold-off time while maintaining a comparable maximum count-rate of 35.2 Mcounts/s. The third circuit designed is a gain control circuit. This circuit is based on the idea of using two matched APDs to set and stabilize the gain. The circuit can provide high bias voltage for operating the planar APD, precisely set the APD’s gain (with the errors of less than 3%) and compensate for the changes in the temperature to maintain a more stable gain. The circuit operates without the need for external temperature sensing and control electronics thus lowering the system cost and complexity. It also provides a simpler and more compact solution compared to previous designs. The three circuits designed in this project were developed independently of each other and are used for improving different performance characteristics of the APD. Further research on the combination of the three circuits will produce a more compact APD-based solution for a wide range of applications

A dual-rail charge pump bias circuit for avalanche photodiodes

In this paper, a dual-rail charge pump bias circuit for avalanche photodiodes is presented. The proposed circuit was fabricated and measured on a printed circuit board (PCB). Experimental measurements show that it is capable of providing up to 50 V bias voltage and delivering more than 40 mW of power for shallow-junction planar APDs that operate between 25 V and 40 V, allowing avalanche currents in the mA range. The circuit requires only a dual supply rail at ± 5 V which makes it useful for reducing the system complexity and the cost of using additional external power supplies in an APD-based sensing system. With the shunt regulators in the circuit, the bias voltage can be accurately controlled and easily adjusted

Active quench and reset integrated circuit with novel hold-off time control logic for Geiger-mode avalanche photodiodes

This Letter presents an active quench-and-reset circuit for Geiger-mode avalanche photodiodes (GM-APDs). The integrated circuit was fabricated using a conventional 0.35 μm complementary metal oxide semiconductor process. Experimental results show that the circuit is capable of linearly setting the hold-off time from several nanoseconds to microseconds with a resolution of 6.5 ns. This allows the selection of the optimal afterpulse-free hold-off time for the GM-APD via external digital inputs or additional signal processing circuitry. Moreover, this circuit resets the APD automatically following the end of the hold-off period, thus simplifying the control for the end user. Results also show that a minimum dead time of 28.4 ns is achieved, demonstrating a saturated photon-counting rate of 35.2  Mcounts/s

High resolution hold-off time control circuit for Geiger-mode avalanche photodiodes

A high-resolution hold-off time control circuit for Geiger-mode avalanche photodiodes (GM-APDs) that enables linear changes to the hold-off time from several nanoseconds to microseconds is presented. The resolution of the hold-off time can be varied from nanoseconds to tens of nanoseconds with a range up to 1.2 μs to cater for a variety of GM-APDs. This circuit allows setting of the optimal `afterpulse-free' hold-off time for any GM-APD through digital inputs or additional signal processing circuitry. The layout area is 95 μm × 55 μm which makes it suitable for use with APD arrays. The APD is automatically reset following the end of the hold-off period

A compact bias and gain control circuit for avalanche photodiodes

An integrable solution for stable bias control of avalanche photodiodes up to 30 V is presented. This circuit enables gain control to an accuracy of 3% for values of multiplication gain up to 100

Design of a hold-off time control circuit for geiger-mode avalanche photodiodes

A high-resolution hold-off time control circuit for Geiger-mode avalanche photodiodes (GM-APDs) that enables linear changes to the hold-off time from several nanoseconds to microseconds is presented. The resolution of the hold-off time can be varied from nanoseconds to tens of nanoseconds with a range up to microseconds to cater for a variety of GM-APDs. This circuit allows setting of the optimal 'afterpulse-free' hold-off time for any GM-APD through digital inputs or additional signal processing circuitry. With this circuit, the APD is automatically reset following the end of the hold-off period that further simplifies the end-user’s control. A layout of this circuit is designed using a conventional 0.15 μm complementary metal oxide semiconductor (CMOS) process, resulting a area of 95 μm × 55 μm which makes it suitable for use with APD arrays

Integrable bias solution for avalanche photodiodes

A bias circuit for avalanche photodiodes (APDs) based on a dual-rail charge pump configuration operating from a 5 V supply that is capable of supplying a bias voltage in excess of 50 V is presented. For shallow-junction planar APDs that operate between 25 and 45 V this circuit is capable of delivering more that 50 mW of power, allowing avalanche currents in the mA range. The circuit design requires only two external capacitors, while the rest of the circuit can be implemented as an application-specific integrated circuit which makes the circuit highly integrable. The bias voltage can be accurately controlled and easily adjusted by the end user using the shunt regulator incorporated for voltage control

Real-time dark count compensation and temperature monitoring using dual SPADs on the same chip

Dual single-photon avalanche photodiodes (SPADs) integrated on the same chip enable the effective compensation of dark count rate (DCR) in the SPAD and also the real-time monitoring of the chip temperature. In the design, two identical SPA Ds are fabricated on the same chip. one operating normally and the other one covered by a metal layer to be kept in the dark. The two SPADs are identically biased and connected to identical active quench and reset integrated circuits. As both detectors are identical in structure. the dark count is expected to be similar for both. Experimental measurements show that the two SPADs exhibit similar DCR performance over a range of bias voltages and temperatures. By measuring the DCR from the covered SPAD, the DCR from the normally operated SPAD can be accounted for directly. This can he particularly useful for SPADs, where the DCR is high. Experiments under illumination show that the shaded SPAD is immune to illumination over a wide range of incident light power. This enables the real-time monitoring of the temperature on the sensor chip using the counting rate from the dark operated avalanche photodiode (APD)

Design of an adjustable bias circuit using a single-sided CMOS supply for avalanche photodiodes

A charge pump circuit operating from a single-sided CMOS supply, capable of biasing avalanche photodiodes up to 40 V with load currents in the mA range is presented. This circuit introduces new design elements that overcome previously published limitations. These elements include pass-gate voltage regulators and a mechanism for linking the negative voltage regulator to the positive voltage output. This design allows linear adjustment of the output voltage from a single control voltage. The circuit has compact dimensions of 1.55 mm × 1 mm, including bond pads, which makes it suitable for hybrid integration in a single package with an APD and two surface-mount capacitors