Research Contributions by Yongmin Zhang
Capital Market Research
- Built fallout models for rate locks in mortgage pipeline.
- Developed hedging strategies for mortgage pipeline management.
- Developed cash flow models for reverse mortgage products.
- Developed look back option models with hurdle adjustments.
- Created various mortgage rates forecasting models using time series analysis.
- Built mortgage prepayment models which use loan attribution to forecast the probability of prepayment for every month of a loan’s remaining term. Calibrated to millions of loan records and carried out forward prepayment speed test.
- Created and streamlined hedging strategies for mortgage backed securities using TBA, swap, swaption based on risk matrices of key rate durations, mortgage spread duration, Vega and convexity.
American Option Pricing Models
- Variational inequalities formulation for American options.
- Investigated sensitivity of the option price to the final payoff change.
- Designed accurate methods to determine the optimal exercise boundary.
Finite Element Models for Free Boundary Problems
- Developed fast algorithms for solving a class of free boundary problems called obstacle problems which arise from the filtration dam problem, the Stefan problem, and the American option pricing models.
- Derived a general condition for the convergence of free boundaries of discrete
solutions to the free boundary of the continuous solution.
The interface between wetted and unwetted regions in dam problem and early exercise
boundary of American options are typical free boundaries.
- Established a monotonicity principle for a finite element approximation of obstacle problem. Obtained an optimal error estimate under maximum norm which improved two well-known results established by Nitsche and Baiocchi thirty years ago.
- Developed a numerical model for a Bingham fluid flow in a cylindrical pipe using
a regularization method.
Stochastic Models and Monte Carlo Simulations
- Developed and implemented numerical algorithms for
a stochastic multiphase fluid mixing model.
- Discovered an asymmetry effect ("North Pole Effect") on axisymmetric flow analyzed
this effect on various statistics of the chaotic fluid mixing by
carrying out Monte Carlo simulations.
Finite Difference Models for Multiphase Supersonic Flow and Shock Waves
- Developed front tracking algorithms in curved geometries. Implemented these
algorithms into a flow simulation package "FronTier" in C/C++. The code has been
applied to various fluid instability problems: Gravity and shock driven
instabilities, turbulent mixing and combustion, and diesel jet flow.
- Conducted a quantitative error and efficiency analysis for the FronTier code.
- Analyzed a scaling law for the shock strength in spherical shock driven
Computer Simulations for Radiation and Combustion Processes in Star Explosions
- Conducted front tracking simulations for the first spherically diverging,
hydrodynamically unstable laboratory experiments of relevance to
supernova. Front tracking gave a better agreement with laser experiments
than other codes. This work has gained recognition from several leading groups
on laser experiments including Lawrence Livermore National Laboratory and
University of Michigan.
- Developed radiation-coupled front tracking algorithms in collaboration
with laser researchers in University of Michigan.
- Conducted numerical measurement of impact of laser preheat on interface
structure and instability.
- Developed numerical models for turbulent combustion in Type Ia supernova. .