Ӧ�ø���ͳ�� 2011, 27(3) 232-240 DOI:      ISSN: 1001-4268 CN: 31-1256

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(Assets-to-Liabilities)�����ж��������Դ����\,--\,��ɢ����
(Jump-Diffusion Process)���н�ģ.
�ü���Brown�˶������䳣̬�����˶�������,
�ö����ͬǿ�ȵ�Poisson�����������ܸ�������Ϣ��ϡ��ż���¼��������ĸ����������ļ�������,
�ö����ͬ�Ķ�����̬���������������������Ӧ��������,
���ٶ��������ǿɷ�ɢ��. ��ģ���޶���,
����Ӧ��It\^{o}����͵ȼ�����ȱ任,
�����˹�˾��ֵ�����÷���ŷʽ��Ȩһ�㻯�ķ����ʽ�Ľ������۹�ʽ,
�ƹ��˾���Ľṹ���÷�����Ȩ�����Լ�״̬��������������\,--\,��ɢ����,
ͬʱҲ�Ӷ����ĽǶ�������Zhou\,(2001)��Lobo\,(1999)�Ĺ���.

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Multiple Jumps-Diffusion Model and Vulnerable European Option Pricing
Wei Zhengyuan,Gao Hongxia
Chongqing University of Technology
Abstract:

A mixed diffusion process involving various
sources of jumps is introduced to characterize both the price of
underlying asset and the ratio of firm's assets to liabilities.
Continuous component is modeled as geometric Brownian motion to
describe their ``normal'' revolution, and discontinuous component is
modeled as jumps with several Poisson arrival processes in
conjunction with corresponding random jump size to characterize
their sudden increase or drop in a surprising manner
instantaneously. This may be due in part to the impact of rare
events and new information, such as technological innovation,
regulatory effects, catastrophic rare events and so on $\ldots$
These jumps are assumed independent of each other, with each type
having a log-normally distributed jump size, we also supposed that
all jumps risk is diversifiable and hence not priced in equilibrium.
By applying It\^{o} lemma and equivalent martingale measure
transformation within the framework of our model, we derived a
closed form of analytic solution for vulnerable European option, and
therefore generalized classical formula for vulnerable European
option with jump and quantified the works by Zhou\,(2001) and
Lobo\,(1999).

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