Tuesday, March 29th, 2:30 pm, 115 Armes Hall

1. Dr. Ruppa K. Thulasiram Department of Computer Science University of Manitoba As the title suggests, this is a cross-disciplinary area of research known as "Computational Finance". We will start from a problem in business (especially finance), apply engineering techniques to solve it with sound mathematical approaches and bring out some computational issues. There are several problems in finance and the one we focus on is "option pricing". This problem forms backbone to many other problems such as risk management. We start the talk with a background introduction of option pricing problem. While there are several numerical techniques employed to solve option pricing problem, a traditional method known as binomial lattice approach, is intuitive and popular. Due to fluctuation in the financial market, some parameters (such as risk free rate) may not always be evaluated precisely in the classical binomial risk neutral option pricing model and hence limits the model's capabilities in capturing the uncertainties in the market place. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into model formulation and solution process. In this work, we propose a systematic method of transforming usual financial concepts into fuzzy numbers. Moreover, we propose a crisp risk free rate assisted by Capital Asset Pricing Model (CAPM) return in our fuzzy option pricing model. Our model is geared towards a more natural and intuitive way to deal with uncertainty and arbitrariness using fuzzy algebra. We highlight our theoretical model with a numerical example and show that the classical binomial option pricing model becomes a special case of our model. We will then move on to extend the technique to real options where many possible exercise boundaries are introduced. This will turn the option pricing problem into a compute intensive problem that drives high performance computing. We will mention our current effort in algorithm design and implementation of this problem in two directions (i) with many possible exercise boundaries (ii) for basket options with multiple underlying assets. This research is supported by a recent URGP grant of University of Manitoba. Department of Computer ScienceInstitute for Industrial Mathematics and StatisticsJoint IIMS and CS Seminar "From Drake Center to Machray Hall via EITC - A Cross Campus Stroll" or: Option Pricing with Fuzzy Algebra that drives High Performance Computing Tuesday, March 29th, 2:30 pm, 115 Armes Hall