Stander Symposium abstract book - University of Dayton

POSTER SESSION 1
question-by-question analysis of each participants’ responses was completed. Results indicate that most of the participants had good experiences
in high school and college, in general, but their responses varied greatly in how they viewed those experiences.
Numerical Algorithm to Value American Call Option
Presenter(s): Junyao Zhang
Advisor(s): Paul W Eloe
Mathematics - Graduate Research
A numerical algorithm is developed to produce a numerical solution of a boundary value problem for the Black-Scholes partial differential equation
on a certain region that includes a free boundary. In this algorithm, an artificial boundary is introduced and a method to find the free boundary
is developed. This algorithm is introduced by H. Han and X.Wu, A Fast Numerical Method for the Black-Scholes Equation of American Option,
SIAM J. Numer. Anal., 41 (2003), pp. 2081-2095.
Numerical Investigation into a Computational Approximation of Bifurcation Curves
Presenter(s): Joshua R Craven
Advisor(s): Muhammad Usman
Mathematics - Independent Research
In this project, I use computational tools to study the bifurcations in nonlinear oscillators. Matlab is first used to determine the slow flow phase
portrait of each region and the characteristics of each critical point. Next, the parameters are discretized and for each set of values we find the
locations of the real critical points and the eigenvalues of the Jacobian matrix. With this knowledge, we can approximate the bifurcation diagram.
These results are compared with results from preexisting software.
Option pricing based on Regime-Switching Recombining Tree
Presenter(s): Tao Tian
Advisor(s): Paul W Eloe
Mathematics - Graduate Research
Our goal is to design an efficient Regime-Switching recombining tree (RS-tree) to calculate the option price based on the condition that the underlying
stock price fits the regime-switching model. The RS-tree is efficient if it grows linearly as the time steps increases; as a result, we can use
many more time steps to calculate the option price. Both European and American options will be calculated in this Regime-Switching model. The
next step is to design the RS-tree to two regimes (here m=2), and use the Regime-Switch model to calculate the option price for both European
and American option. Finally, we will compared the result with others method. II.MethodAt first, we extend the Cox, Ross and Rubinstein Tree
for the Black-Scholes-Merton option pricing model. Then we employ the method developed by Liu to construct an efficient RS-tree for European
and American options. We begin with a 2-regime model. For the Transfer probability based on the two regimes, we use the method from Yin and
Zhang. We construct a RS-tree which grows linearly and accomplish this by a recombination of nodes at each time step. As a result, we adjust
the up factor U in a reasonable way; also, it is necessary to match the local mean and variance calculated from the tree to that implied by the
continuous regime-switching diffusion in order for the discrete tree approximation to converge to the continuous process as the time step h goes
to zero. Upon successful development of the 2-regime algorithm, we shall extend the algorithm to m >2 regimes and extend the applications to
exotic options in the future.
Road Travel Time Estimation with GPS Floating Car Data
Presenter(s): Jieai Zheng
Advisor(s): Ruihua Liu
Mathematics - Graduate Research
The objective of this research is to provide reliable estimation of urban roadway travel time in time for traffic managing departments and travelers
based on floating car data. Travel time data collection and estimation is an important technology method to achieve the Intelligent Transportation
Systems (ITS) information services. Poor-quality information leads mistrust and un-ease of traffic congestion. Thus the accuracy of travel
time prediction must meet certain requirements. GPS floating car collection method accesses the data source by ordinary vehicles equipped with
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