Alexandria Digital Research Library

Asymptotic Behavior of Worst Case Scenario Prices in Uncertain Volatility Models

Author:
Ren, Bin
Degree Grantor:
University of California, Santa Barbara. Statistics and Applied Probability
Degree Supervisor:
Jean-Pierre Fouque
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2013
Issued Date:
2013
Topics:
Economics, Finance, Statistics, and Mathematics
Keywords:
Worst case scenario
Uncertain volatility
Asymptotic
Genres:
Online resources and Dissertations, Academic
Dissertation:
Ph.D.--University of California, Santa Barbara, 2013
Description:

Financial derivatives have been widely used for investments or transfer risks among different parties. It has been an important topic to determine their prices.

The celebrated model by Fisher Black, Robert Merton and Myron Scholes is the progenitor to modern finance. However, its application is restricted due to the constant volatility assumption. Therefore, the uncertain volatility models and worst case scenario analysis are introduced [4] and [32] to consider the amount of risk in derivative pricing.

In this dissertation, we discuss the asymptotic behaviors of the worst case scenario price under an uncertain volatility model. We are mainly interested in how the worst case scenario price behaves as the degree of model uncertainty vanishes. We derive the derivative of the worst case scenario price with respect to the interval size: epsilon at epsilon = 0. This study produces an approximation of the worst case scenario price or the worst case scenario volatility process. If the volatility interval is small in the model, we need only to solve two linear PDEs to approximate the solution of a fully nonlinear PDE: Black-Scholes-Barenblatt equation.

Physical Description:
1 online resource (112 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3ww7fmx
ISBN:
9781303052712
Catalog System Number:
990039788300203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Bin Ren
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