In this short paper, we study the simulation of a large system of stochastic processes subject to... more In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of financial entities. We then seek an efficient estimator for the probability of a default, indicated by a firm value below a certain threshold, conditional on common factors. We first analyse the convergence of the Euler--Maruyama scheme applied to the fast Ornstein--Uhlenbeck SDE for the volatility, and show that the first order strong error is robust with respect to the mean reversion speed (only) if the step size is scaled appropriately. Next, we consider approximations where coefficients containing the fast volatility are replaced by certain ergodic averages (a type of law of large numbers), and study a correction term (of central limit theorem-type). The accuracy of these approximations is assessed by numerical simulation of pathwise losses an...
We consider a class of stochastic path-dependent volatility models where the stochastic volatilit... more We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for the spot process with the full truncation Euler scheme or the backward Euler-Maruyama scheme for the squared stochastic volatility component. Under some mild regularity assumptions and a condition on the Feller ratio, we establish the strong convergence with order 1/2 (up to a logarithmic factor) of the approximation process up to a critical time. The model studied in this paper contains as special cases Heston-type stochastic-local volatility models, the state-of-the-art in derivative pricing, and a relatively new class of path-dependent volatility models. The present paper is the first to prove the convergence of the popular Euler schemes with a positive rate, which...
We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its E... more We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of stochastic differential equations arising in finance. We prove that both implicit and explicit Euler-Maruyama discretizations for the CIR process preserve the exponential integrability of the exact solution for a wide range of parameters, and find lower bounds on the explosion time.
In this thesis, we study the FX option pricing problem and put forward a 4-factor hybrid stochast... more In this thesis, we study the FX option pricing problem and put forward a 4-factor hybrid stochastic-local volatility model. The model, which describes the dynamics of an exchange rate, its volatility and the domestic and foreign short rates, allows for a perfect calibration to European options and has a good hedging performance. Due to the high-dimensionality of the problem, we propose a Monte Carlo simulation scheme that combines the full truncation Euler scheme for the stochastic volatility component and the stochastic short rates with the log-Euler scheme for the exchange rate. We analyze exponential integrability properties of Euler discretizations for the square-root process driving the stochastic volatility and the short rates, properties which play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a large class of stochastic differential equations in finance, including the ones studied in this thesis. Hence, we pro...
This article discusses Analog Devices’ new broad market LIDAR prototyping platform and how it hel... more This article discusses Analog Devices’ new broad market LIDAR prototyping platform and how it helps shorten the customers’ product development time by providing a complete hardware and software solution that customers can use to prototype their algorithms and custom hardware solutions. It goes over the details of the modular hardware design, including the light receive and transmit signal chains, FPGA interface, and optics for long range sensing. The system partitioning decisions that were made are explained, helping highlight the importance of good system design, interface definition, and right level of modularity. The components of the open source LIDAR software stack and the platform specific API are described showing how customers can benefit from these during product development and integrate them in their final solutions. Introduction As autonomous vehicles and robots continue to move from science fiction to reality, automotive and industrial customers are seeking new environm...
In this short paper, we study the simulation of a large system of stochastic processes subject to... more In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of financial entities. We then seek an efficient estimator for the probability of a default, indicated by a firm value below a certain threshold, conditional on common factors. We first analyse the convergence of the Euler--Maruyama scheme applied to the fast Ornstein--Uhlenbeck SDE for the volatility, and show that the first order strong error is robust with respect to the mean reversion speed (only) if the step size is scaled appropriately. Next, we consider approximations where coefficients containing the fast volatility are replaced by certain ergodic averages (a type of law of large numbers), and study a correction term (of central limit theorem-type). The accuracy of these approximations is assessed by numerical simulation of pathwise losses an...
We consider the Heston-CIR stochastic-local volatility model in the context of foreign exchange m... more We consider the Heston-CIR stochastic-local volatility model in the context of foreign exchange markets, which contains both a stochastic and a local volatility component for the exchange rate combined with the Cox-Ingersoll-Ross dynamics for the domestic and foreign interest rates. We study a full truncation scheme for simulating the stochastic volatility component and the two interest rates and derive the exponential integrability of full truncation Euler approximations for the square root process. Under a full correlation structure and a realistic set of assumptions on the so-called leverage function, we prove strong convergence of the exchange rate approximations and then deduce the convergence of Monte Carlo estimators for a number of vanilla and path-dependent options.
People recognition is a relevant subset of the generic image based recognition task with many pos... more People recognition is a relevant subset of the generic image based recognition task with many possible application areas such as security, surveillance, human-robot interaction or recently the social security in a pandemic context. In this work we present a light-weight recognition pipeline for time-of-flight cameras based on deep learning techniques tailored to this specific type of camera with registered infrared and depth images. By combining the maturity of the 2D image based recognition techniques with the custom depth sensing we achieved effective solutions for a number of relevant industrial applications. In particular, our focus was on automatic door-control and people counting applications.
When external overvoltage conditions are applied to an amplifier, ESD diodes are the last line of... more When external overvoltage conditions are applied to an amplifier, ESD diodes are the last line of defense between your amplifier and electrical over stress. With proper understanding of how an ESD cell is implemented in a device, a designer can greatly extend the survival range of an amplifier with the appropriate circuit design. This article aims to introduce readers to the various types of ESD implementations, discuss the characteristics of each implementation, and provide guidance on how to utilize these cells to improve the robustness of a design. Introduction In many applications where the input is not under system control but rather connects to the outside world, such as test equipment, instrumentation, and some sensing equipment, it is possible for input voltages to exceed the maximum rated voltage of a front-end amplifier. In these applications, protection schemes must be implemented to preserve the survival range and robustness of the design. The front-end amplifier’s inter...
In this paper, the valuation of European and path-dependent options in foreign exchange (FX) mark... more In this paper, the valuation of European and path-dependent options in foreign exchange (FX) markets is considered when the currency exchange rate evolves according to the Heston model combined with the Cox-Ingersoll-Ross dynamics for the stochastic domestic and foreign short interest rates. The mixed Monte Carlo/PDE method requires that we simulate only the paths of the squared volatility and the two interest rates, while an "inner" Black-Scholes-type expectation is evaluated by means of a PDE. This can lead to a substantial variance reduction and complexity improvements under certain circumstances depending on the contract and the model parameters. In this work, we establish the uniform boundedness of moments of the exchange rate process and its approximation, and prove strong convergence in $L^p$ ($p\geq1$) of the latter. Then, we carry out a variance reduction analysis and obtain accurate approximations for quantities of interest. All theoretical contributions can be e...
The previous parts of this article series introduced the Zynq SDR rapid prototyping platform,1 pr... more The previous parts of this article series introduced the Zynq SDR rapid prototyping platform,1 presented the steps of using MATLAB and Simulink to develop an algorithm that can successfully process and decode ADS-B transmissions,2 and showed how to verify the algorithm both in simulation and with live data acquired from the SDR platform.3 The ultimate goal of all stages is to create a verified model that can be translated into C and HDL code and is ready to be integrated in the SDR platform’s software and hardware infrastructure.
®the next natural step is to verify the algorithm’s functionality using real data acquired from t... more ®the next natural step is to verify the algorithm’s functionality using real data acquired from the actual SDR hardware system that it is going to run on. As a first step, the verification of the algorithm is done using different sets of input data captured from the system. This helps validate the algorithm’s functionality, but does not guarantee that the algorithm will perform as expected in environmental conditions other than the ones used to make the data captures, or what the behavior and performance will be for different settings of the analog front end and digital blocks of the SDR system. In order to verify all of these aspects, it is very beneficial if the algorithm can be run online to receive live data as input and to tune the settings of the SDR system for optimal performance. This part of the article series discusses the software tools provided by Analog Devices to allow direct interaction between MATLAB and Simulink models with the FMCOMMSx SDR platforms and shows how t...
In this paper we discuss a workflow for softwaredefined radio development, which uses modern soft... more In this paper we discuss a workflow for softwaredefined radio development, which uses modern software and hardware tools to accelerate the design process. Specifically, this work addresses the historical disconnects in the flow from initial algorithm design and conception, through to final HDL and hardware deployment. This flow is demonstrated through an example modem design and custom hardware for deployment, utilizing the Analog Devices AD9361-Z7035 System-on-Module. The main advantages of this proposed workflow is that it provides traceability in a design and naturally segments tasks to an engineer’s domain of expertise, but also provides convenient areas of convergence between disjoint group members.
.................................................................................................... more ......................................................................................................... Preface............................................................................................................
Used in a wide range of industrial, automotive, and commercial applications, electric motors are ... more Used in a wide range of industrial, automotive, and commercial applications, electric motors are controlled by drives that vary the electrical input power to control the torque, speed, and position. High-performance motor drives can increase efficiency and deliver faster, more accurate control. Advanced motor-control systems combine control algorithms, industrial networks, and user interfaces, so they require additional processing power to execute all tasks in real time. Multichip architectures are typically used to implement modern motor-control systems: a digital signal processor (DSP) executes motor-control algorithms, an FPGA implements high-speed I/O and networking protocols, and a microprocessor handles executive control.1
We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid loca... more We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance reduction techniques in order to accelerate convergence. We use control variates derived from a calibrated pure local volatility model, a two-factor Heston-type LSV model (both with deterministic rates), and the stochastic (CIR) short rates. Our numerical experiments show that because of the dramatic variance reduction we are able to calibrate the four-factor model at almost no extra computational cost when the corresponding calibrated two-factor model is at our disposal. The method can be applied to a large class of hybrid LSV models and is not restricted to our particular choice of the diffusion. The calibration procedure is performed on real-world market data for...
This paper presents the design of a system intended to be used for automatic control applications... more This paper presents the design of a system intended to be used for automatic control applications. The system consists of a signal acquisition module, a programmable high speed Digital Signal Processing (DSP) core, a Microcontroller Unit (MCU), an output module and a communication module. Both analog and digital signals can be given as input to the system. The analog signals are digitized by a high speed analog to digital converter, while the digital signals are read through an I2C bus. The programmable DSP core can perform basic arithmetic operations, finite and infinite impulse response filtering and fuzzy logic operations at high speed and with a high degree of parallelism on the data received from the signal acquisition module. The MCU is a soft processor core with a RISC instruction set and it is used for controlling the operation of all the other modules and for implementing more complicated control algorithms that cannot be performed by the DSP core. The output module contain...
FPGA-Based Systems Increase Motor-Control Performance Powering ICs On and Off Design a PLL Loop F... more FPGA-Based Systems Increase Motor-Control Performance Powering ICs On and Off Design a PLL Loop Filter when Only the Zero Resistor and Capacitor Are Adjustable Quickly Implement JESD204B on a Xilinx FPGA Power Management for Integrated RF ICs Design Reliable Digital Interfaces for Successive-Approximation ADCs 2 3 11 15 21 25 31 A forum for the exchange of circuits, systems, and software for real-world signal processing • Volume 49, Number 1, 2015 Analog Dialogue
In this short paper, we study the simulation of a large system of stochastic processes subject to... more In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of financial entities. We then seek an efficient estimator for the probability of a default, indicated by a firm value below a certain threshold, conditional on common factors. We first analyse the convergence of the Euler--Maruyama scheme applied to the fast Ornstein--Uhlenbeck SDE for the volatility, and show that the first order strong error is robust with respect to the mean reversion speed (only) if the step size is scaled appropriately. Next, we consider approximations where coefficients containing the fast volatility are replaced by certain ergodic averages (a type of law of large numbers), and study a correction term (of central limit theorem-type). The accuracy of these approximations is assessed by numerical simulation of pathwise losses an...
We consider a class of stochastic path-dependent volatility models where the stochastic volatilit... more We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for the spot process with the full truncation Euler scheme or the backward Euler-Maruyama scheme for the squared stochastic volatility component. Under some mild regularity assumptions and a condition on the Feller ratio, we establish the strong convergence with order 1/2 (up to a logarithmic factor) of the approximation process up to a critical time. The model studied in this paper contains as special cases Heston-type stochastic-local volatility models, the state-of-the-art in derivative pricing, and a relatively new class of path-dependent volatility models. The present paper is the first to prove the convergence of the popular Euler schemes with a positive rate, which...
We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its E... more We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of stochastic differential equations arising in finance. We prove that both implicit and explicit Euler-Maruyama discretizations for the CIR process preserve the exponential integrability of the exact solution for a wide range of parameters, and find lower bounds on the explosion time.
In this thesis, we study the FX option pricing problem and put forward a 4-factor hybrid stochast... more In this thesis, we study the FX option pricing problem and put forward a 4-factor hybrid stochastic-local volatility model. The model, which describes the dynamics of an exchange rate, its volatility and the domestic and foreign short rates, allows for a perfect calibration to European options and has a good hedging performance. Due to the high-dimensionality of the problem, we propose a Monte Carlo simulation scheme that combines the full truncation Euler scheme for the stochastic volatility component and the stochastic short rates with the log-Euler scheme for the exchange rate. We analyze exponential integrability properties of Euler discretizations for the square-root process driving the stochastic volatility and the short rates, properties which play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a large class of stochastic differential equations in finance, including the ones studied in this thesis. Hence, we pro...
This article discusses Analog Devices’ new broad market LIDAR prototyping platform and how it hel... more This article discusses Analog Devices’ new broad market LIDAR prototyping platform and how it helps shorten the customers’ product development time by providing a complete hardware and software solution that customers can use to prototype their algorithms and custom hardware solutions. It goes over the details of the modular hardware design, including the light receive and transmit signal chains, FPGA interface, and optics for long range sensing. The system partitioning decisions that were made are explained, helping highlight the importance of good system design, interface definition, and right level of modularity. The components of the open source LIDAR software stack and the platform specific API are described showing how customers can benefit from these during product development and integrate them in their final solutions. Introduction As autonomous vehicles and robots continue to move from science fiction to reality, automotive and industrial customers are seeking new environm...
In this short paper, we study the simulation of a large system of stochastic processes subject to... more In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of financial entities. We then seek an efficient estimator for the probability of a default, indicated by a firm value below a certain threshold, conditional on common factors. We first analyse the convergence of the Euler--Maruyama scheme applied to the fast Ornstein--Uhlenbeck SDE for the volatility, and show that the first order strong error is robust with respect to the mean reversion speed (only) if the step size is scaled appropriately. Next, we consider approximations where coefficients containing the fast volatility are replaced by certain ergodic averages (a type of law of large numbers), and study a correction term (of central limit theorem-type). The accuracy of these approximations is assessed by numerical simulation of pathwise losses an...
We consider the Heston-CIR stochastic-local volatility model in the context of foreign exchange m... more We consider the Heston-CIR stochastic-local volatility model in the context of foreign exchange markets, which contains both a stochastic and a local volatility component for the exchange rate combined with the Cox-Ingersoll-Ross dynamics for the domestic and foreign interest rates. We study a full truncation scheme for simulating the stochastic volatility component and the two interest rates and derive the exponential integrability of full truncation Euler approximations for the square root process. Under a full correlation structure and a realistic set of assumptions on the so-called leverage function, we prove strong convergence of the exchange rate approximations and then deduce the convergence of Monte Carlo estimators for a number of vanilla and path-dependent options.
People recognition is a relevant subset of the generic image based recognition task with many pos... more People recognition is a relevant subset of the generic image based recognition task with many possible application areas such as security, surveillance, human-robot interaction or recently the social security in a pandemic context. In this work we present a light-weight recognition pipeline for time-of-flight cameras based on deep learning techniques tailored to this specific type of camera with registered infrared and depth images. By combining the maturity of the 2D image based recognition techniques with the custom depth sensing we achieved effective solutions for a number of relevant industrial applications. In particular, our focus was on automatic door-control and people counting applications.
When external overvoltage conditions are applied to an amplifier, ESD diodes are the last line of... more When external overvoltage conditions are applied to an amplifier, ESD diodes are the last line of defense between your amplifier and electrical over stress. With proper understanding of how an ESD cell is implemented in a device, a designer can greatly extend the survival range of an amplifier with the appropriate circuit design. This article aims to introduce readers to the various types of ESD implementations, discuss the characteristics of each implementation, and provide guidance on how to utilize these cells to improve the robustness of a design. Introduction In many applications where the input is not under system control but rather connects to the outside world, such as test equipment, instrumentation, and some sensing equipment, it is possible for input voltages to exceed the maximum rated voltage of a front-end amplifier. In these applications, protection schemes must be implemented to preserve the survival range and robustness of the design. The front-end amplifier’s inter...
In this paper, the valuation of European and path-dependent options in foreign exchange (FX) mark... more In this paper, the valuation of European and path-dependent options in foreign exchange (FX) markets is considered when the currency exchange rate evolves according to the Heston model combined with the Cox-Ingersoll-Ross dynamics for the stochastic domestic and foreign short interest rates. The mixed Monte Carlo/PDE method requires that we simulate only the paths of the squared volatility and the two interest rates, while an "inner" Black-Scholes-type expectation is evaluated by means of a PDE. This can lead to a substantial variance reduction and complexity improvements under certain circumstances depending on the contract and the model parameters. In this work, we establish the uniform boundedness of moments of the exchange rate process and its approximation, and prove strong convergence in $L^p$ ($p\geq1$) of the latter. Then, we carry out a variance reduction analysis and obtain accurate approximations for quantities of interest. All theoretical contributions can be e...
The previous parts of this article series introduced the Zynq SDR rapid prototyping platform,1 pr... more The previous parts of this article series introduced the Zynq SDR rapid prototyping platform,1 presented the steps of using MATLAB and Simulink to develop an algorithm that can successfully process and decode ADS-B transmissions,2 and showed how to verify the algorithm both in simulation and with live data acquired from the SDR platform.3 The ultimate goal of all stages is to create a verified model that can be translated into C and HDL code and is ready to be integrated in the SDR platform’s software and hardware infrastructure.
®the next natural step is to verify the algorithm’s functionality using real data acquired from t... more ®the next natural step is to verify the algorithm’s functionality using real data acquired from the actual SDR hardware system that it is going to run on. As a first step, the verification of the algorithm is done using different sets of input data captured from the system. This helps validate the algorithm’s functionality, but does not guarantee that the algorithm will perform as expected in environmental conditions other than the ones used to make the data captures, or what the behavior and performance will be for different settings of the analog front end and digital blocks of the SDR system. In order to verify all of these aspects, it is very beneficial if the algorithm can be run online to receive live data as input and to tune the settings of the SDR system for optimal performance. This part of the article series discusses the software tools provided by Analog Devices to allow direct interaction between MATLAB and Simulink models with the FMCOMMSx SDR platforms and shows how t...
In this paper we discuss a workflow for softwaredefined radio development, which uses modern soft... more In this paper we discuss a workflow for softwaredefined radio development, which uses modern software and hardware tools to accelerate the design process. Specifically, this work addresses the historical disconnects in the flow from initial algorithm design and conception, through to final HDL and hardware deployment. This flow is demonstrated through an example modem design and custom hardware for deployment, utilizing the Analog Devices AD9361-Z7035 System-on-Module. The main advantages of this proposed workflow is that it provides traceability in a design and naturally segments tasks to an engineer’s domain of expertise, but also provides convenient areas of convergence between disjoint group members.
.................................................................................................... more ......................................................................................................... Preface............................................................................................................
Used in a wide range of industrial, automotive, and commercial applications, electric motors are ... more Used in a wide range of industrial, automotive, and commercial applications, electric motors are controlled by drives that vary the electrical input power to control the torque, speed, and position. High-performance motor drives can increase efficiency and deliver faster, more accurate control. Advanced motor-control systems combine control algorithms, industrial networks, and user interfaces, so they require additional processing power to execute all tasks in real time. Multichip architectures are typically used to implement modern motor-control systems: a digital signal processor (DSP) executes motor-control algorithms, an FPGA implements high-speed I/O and networking protocols, and a microprocessor handles executive control.1
We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid loca... more We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance reduction techniques in order to accelerate convergence. We use control variates derived from a calibrated pure local volatility model, a two-factor Heston-type LSV model (both with deterministic rates), and the stochastic (CIR) short rates. Our numerical experiments show that because of the dramatic variance reduction we are able to calibrate the four-factor model at almost no extra computational cost when the corresponding calibrated two-factor model is at our disposal. The method can be applied to a large class of hybrid LSV models and is not restricted to our particular choice of the diffusion. The calibration procedure is performed on real-world market data for...
This paper presents the design of a system intended to be used for automatic control applications... more This paper presents the design of a system intended to be used for automatic control applications. The system consists of a signal acquisition module, a programmable high speed Digital Signal Processing (DSP) core, a Microcontroller Unit (MCU), an output module and a communication module. Both analog and digital signals can be given as input to the system. The analog signals are digitized by a high speed analog to digital converter, while the digital signals are read through an I2C bus. The programmable DSP core can perform basic arithmetic operations, finite and infinite impulse response filtering and fuzzy logic operations at high speed and with a high degree of parallelism on the data received from the signal acquisition module. The MCU is a soft processor core with a RISC instruction set and it is used for controlling the operation of all the other modules and for implementing more complicated control algorithms that cannot be performed by the DSP core. The output module contain...
FPGA-Based Systems Increase Motor-Control Performance Powering ICs On and Off Design a PLL Loop F... more FPGA-Based Systems Increase Motor-Control Performance Powering ICs On and Off Design a PLL Loop Filter when Only the Zero Resistor and Capacitor Are Adjustable Quickly Implement JESD204B on a Xilinx FPGA Power Management for Integrated RF ICs Design Reliable Digital Interfaces for Successive-Approximation ADCs 2 3 11 15 21 25 31 A forum for the exchange of circuits, systems, and software for real-world signal processing • Volume 49, Number 1, 2015 Analog Dialogue
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