Barrier Option Pricing under SABR Model Using Monte Carlo Methods

The project investigates the prices of barrier options from the constant underlying volatility in the Black-Scholes model to stochastic volatility model in SABR framework. The constant volatility assumption in derivative pricing is not able to capture the dynamics of volatility. In order to resolve the shortcomings of the Black-Scholes model, it becomes necessary to find a model that reproduces the smile effect of the volatility. To model the volatility more accurately, we look into the recently developed SABR model which is widely used by practitioners in the financial industry. Pricing a barrier option whose payoff to be path dependent intrigued us to find a proper numerical method to approximate its price. We discuss the basic sampling methods of Monte Carlo and several popular variance reduction techniques. Then, we apply Monte Carlo methods to simulate the price of the down-and-out put barrier options under the Black-Scholes model and the SABR model as well as compare the features of these two models

Numerical Study on the Thermal Performance of Embedded Heat Pipes for CPU Cooling

Thermal management of central processing units (CPU) becomes more challenging in the development and production of high performance computers with faster and smaller size CPUs. Heat pipes are two-phase cooling devices with an effective thermal conductivity over 200 times higher than that of a copper heat sink. In addition, heap pipes have light weight, low cost and the flexibility of many different sizes and shape options which can be embedded into the metallic heat sink to provide more efficient thermal management. In this project, CFD was used to study a heap pipe embedded CPU cooler. The simulated results is validated with the experimental data for the same CPU cooler. Golf ball fans were also introduced to replace the stock fans in the CPU cooler to enhance the heat transfer and lower the operating temperature. The detailed distributions of temperature, velocity, and pressure were used to analyze the performance of the CPU cooler in both cases and found the golf ball fans are more effective than the stock fans

Simulation of a Gas Tungsten Arc Welding Process in COMSOL

The purpose of this project is to model the transport phenomena (heat transfer, fluid flow, and current flow) in a gas tungsten arc welding (GTAW) process using COMSOL Multiphysics. The model development will start with developing two separate models - an arc model and a weld pool model and end with an integrated arc - weld pool model to simulate the interaction between the arc and the weld pool. The integrated arc-weld pool model will be used to study the effects of some welding process parameters, such as the anode materials, the arc length, and the shielding gas, on the final weld quality

Simulation of Droplet Impingement on Solid Surface by the Level Set Method and Phase Field Method

The simulation of multi-phase flow with moving interfaces is important in a wide range of applications, such as ink-jet printing, metal depositions, spray cooling, and biomedical engineering applications. Level Set and Phase Field methods are two well-known techniques for tracking the moving interfaces. Each model has its own strength and weakness. This paper compares the two surface tracking models in the simulation of droplet impingement process. The simulations are carried out by employing the Level Set and Phase Field models in COMSOL. The dynamic impingement processes is presented for a glycerin droplet impacting a non-wetting wax surface. The simulated spreading factor and apex height are compared with experimental results for the two surface tracking models

Analysis of A Counter Flow Parallel-Plate Heat Exchanger

Heat exchangers are used widely in many industries for heat recovery or cooling purposes. This paper developed a numerical model to simulate a counter flow parallel heat exchanger. A representative repeating unit cell of the multi-channeled heat exchanger was taken as the computational domain, which includes a cold channel and a hot channel separated by plates. The model was simulated in COMSOL for an oil to water heat exchanger. Higher temperature oil and relatively lower temperature water entered two separate parallel channels in opposite directions. The detailed distributions of temperature, velocity, and pressure were used to analyze the performance of the heat exchanger. It was found the model can be used to provide guidance for designing an optimal heat exchanger

Simulation of Turbulent Flow in an Asymmetric Air Diffuser

This research paper compared three k-ε family turbulence models; Standard k-ε, RNG k-ε and Realizable k-ε, and two k-ɷ family models; Standard k-ɷ and Stress-Strain Transport, SST k-ɷ. The turbulent flow characteristics were predicted in a two-dimensional of 10° half-angle diffuser using the five turbulence models with the ANSYS FLUENT 13.0 code. Numerical results were validated by comparing them to experimental fluid dynamics (EFD) results. Velocity profiles, turbulent kinetic energy profiles and skin friction coefficients were presented validate the numerical results. Contours velocity-streams functions were shown as well. One of the most interesting observations of comparing numerical solutions to EFD data was apparently that k-ε family models have a valid prediction of flow characteristics that are far away from wall effects, however, k-ɷ models have a significant prediction of flow behavior nearby the wall boundaries. In addition, the changes in the quality of meshing elements and its number have noticeable influences on computational fluid dynamics (CFD) results. Personally, the present CFD investigation obviously has given a deep insight of the most important fluid dynamics concepts that were studied in the computational fluid dynamics course

Study on Transient Thermal Analysis of a Disc Brake During Braking and Releasing Periods

Automobile braking system is considered as one of the most important safety systems in modern vehicles as its main intention is to stop or decelerate the vehicle. The frictional heat generated between the pads and disc during the braking application can cause various negative impacts, such as brake fade, thermal cracks, disc thickness variation and wear. This project studied the transient thermal behavior of a disc brake system during the braking phase and the followed releasing period. A three-dimensional finite element model with a moving heat source was developed with COMSOL Multiphysics to predict the temperature distribution in the disc braking system, including two pads, a rotor disc, bolts, and a section of the shaft. The maximum surface temperature on the contact surface has been found to increase in the braking period and then decrease as the rotor slows down and further decrease during the releasing period. The maximum temperature on the contact surface depends on both the car velocity and deceleration rate. The effects of convective and radiative heat transfer are also studied. It is found that heat is mainly dissipated through convective heat transfer at the disc surfaces

Droplet Acceleration in the Arc

This paper simulates the acceleration of the droplet in the arc during gas metal arc welding process. After a droplet is detached from the electrode, it is accelerated in the high temperature and high velocity arc to the workpiece. The droplet is subjected to several forces, such as the arc plasma shear stress, arc pressure force, surface tension force, gravity force, and electromagnetic force. A comprehensive model is used to simulate the changes of droplet shape, temperature, and velocity during the acceleration in the arc. The transient interaction of droplet and arc plasma is through coupled boundary conditions, thus, no assumptions are needed to simulate the droplet acceleration. The simulated results were compared with the published experimental data and an agreement was found

Engage Students in Engineering – using Everyday Engineering Examples

Fifty percent of students entering engineering programs do not earn an engineering degree. Many students leave engineering because unsatisfactory experiences in introductory engineering courses in their first and second years. Improving student engagement through the use of everyday examples is one key ENGAGE strategy because research indicates that this strategy has a powerful impact upon students’ satisfaction with and perseverance in engineering. This project implemented Everyday Engineering Examples (E^3s) in four engineering classes to teach technical concepts through a ENGAGE E^3s mini-grant. This paper introduces ENGAGE project and E^3s and shares the benefits of our E^3s mini-grant experience and strategies of using the E^3s examples in engineering classes