Pricing financial derivatives with fuzzy algebraic models: A theoretical and computational approach

The thesis is comprised of seven chapters. The first chapter is introductory in nature and pertains to a brief review of the related work to the proposed study. It also contains the summary of the research work presented in this thesis.; Chapter 2 provides a literature survey of the work done by various researchers on triangular fuzzy numbers, trapezoidal fuzzy numbers and option pricing under fuzzy environment. Some of the work done by Carlsson and Fuller [30] on possibilitic mean and variance of fuzzy numbers is highlighted. The work done by Fuller and Majlender [53] on weighted possibilistic mean and variance of fuzzy numbers is also discussed to some extents. At the end of Chapter 2, a summary of the thesis is provided.; In Chapter 3, we introduce the O(m, n)-Trapezoidal Type Fuzzy Numbers, and establish some of their properties along with some examples.; In Chapter 4 for O(m, n)-Trapezoidal Type Fuzzy Numbers we derive expressions for possibilistic mean and possibilistic variance, weighted possibilistic mean and weighted possibilistic variance, expressions for possibilistic covariance and weighted possibilistic covariance. Some applications are provided in the form of examples using weighted functions.; In Chapter 5, we make use of O(m, n)-Trapezoidal Type Fuzzy Numbers to discuss the fuzzy binomial option pricing model and derive expression for the fuzzy risk neutral probabilities, along with fuzzy expression for the fuzzy call prices. As a consequence, we obtain weighted intervals for the risk neutral probabilities and for the expected fuzzy call price. Numerical examples are provided to illustrate the results.; In Chapter 6, we present the fuzzy binomial option pricing model using LR-Fuzzy numbers and obtain expressions for the fuzzy risk neutral probabilities and for the fuzzy call prices in terms of LR-fuzzy numbers.; In the last chapter of the thesis, we present the contributions made in the thesis and conclusion along with some recommendations for future directions on the problems considered in the thesis.