Title: Hedging parameters estimation for American options and its application in upper bound algorithms
Authors: Zhang, Bingfeng (張炳鋒)
Abstract: Upper bound algorithms for pricing American-style options (also called
American options) usually rely on the approximations of the optimal
martingale. Tightness of the estimated upper bounds highly depends on the
construction of the martingale. The nested simulation method constructs
the martingale with the aid of an estimated lower bound process. It can be
easily implemented. However, a limitation of the nested simulation method
is its requirement of large computational effort.
Several non-nested upper bound algorithms for pricing American-style
options have been proposed in recent years. They are computationally
attractive where nested simulations are not necessary. The computational cost
is linear in the number of exercise dates. To incubate non-nested upper bound
algorithms, researchers study the characteristics of the optimal martingale
from various aspects, such as stability, martingale representation theorem,
analytical representation and connection with delta hedging. For the ideas
of analytical representation and connection with delta hedging, the
construction of the martingale comes down to the estimation of delta process.
It is well known that delta is one of the most important hedging parameters
for American-style options. However, estimating hedging parameters at any
date efficiently is not an easy task.
In this thesis, based on the dynamic-programming representation of the
value process, a least-squares method (LSM) is proposed to estimate the
hedging parameters backwardly. With this method, estimation of the delta
process can be done in an efficient way. Based on the delta estimates, two
ideas are implemented to generate non-nested upper bounds. The first one
is that the delta estimates can be included into the basis functions of the
regression procedure when estimating the martingale. The other one is that
the martingale can be constructed directly with no sub-simulation and no
optimization. Through numerical experiments, it is found that the latter
one is a better choice.
Notes: CityU Call Number: HG6024.A3 Z426 2015; xiii, 87 pages : illustrations 30 cm; Thesis (Ph.D.)--City University of Hong Kong, 2015.; Includes bibliographical references (pages 84-87)
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