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Options portfolio optimization of exotic options written on Mini S\&P500 Index in an illiquid market with Conditional Value-at-Risk (CVaR)

Options portfolio optimization of exotic options written on Mini S\&P500 Index in an illiquid market with Conditional Value-at-Risk (CVaR) XlEkA
A new approach to optimizing a portfolio of financial instruments to reduce risk of high losses is considered and tested on application. It focuses on minimizing Conditional value-at-risk (CVaR). CVaR is frequently used risk measure in current risk management practice. For continuous distribution, CVaR is defined as the conditional expected loss under the condition that it exceeds Value-at-risk (VaR). We consider optimization portfolios for minimizing CVaR. In this work, this approach to the optimization problems with CVaR constraints. In particular, the approach can be used for maximizing expected returns under CVaR constraints. \\ Two main difficult tasks for an investor are (1) to find the optimal portfolio with the smallest amount of risk given a required expected return and (2) to determine buying or selling prices of the exotic options that suitable for optimal portfolio. In this work, we apply this approach to option markets. We consider standard put and call options which are written on S\&P 500 Mini Index. The quotes come with bid and ask prices as well as sizes. We first determine the optimal portfolio, the portfolio with the smallest CVaR given a required return. We also investigate the changes in optimized portfolios subject to various modeling parameters. The index is modeled by a variance gamma process which is a geometric Brownian motion with gamma-distributed random time implements.
A new
You use this word too often, consider replacing it with
approach
to optimizing a portfolio of financial instruments to
This phrase/word (depending on the context) can be potentially replaced with :
reduce
You use this word too often, consider replacing it with
risk
of high losses
is considered
and
This phrase/word (depending on the context) can be potentially replaced with :
tested
on application. It focuses on minimizing Conditional value-at-
This phrase/word (depending on the context) can be potentially replaced with :
risk
(
Possible spelling mistake found.
CVaR
).
Possible spelling mistake found.
CVaR
is
frequently
This phrase/word (depending on the context) can be potentially replaced with :
used
You use this word too often, consider replacing it with
risk
measure in
This phrase/word (depending on the context) can be potentially replaced with :
current
You use this word too often, consider replacing it with
risk
management practice. For continuous distribution,
Possible spelling mistake found.
CVaR
is defined
as the conditional
This phrase/word (depending on the context) can be potentially replaced with :
expected
loss under the condition that it exceeds Value-at-
This phrase/word (depending on the context) can be potentially replaced with :
risk
(
Possible spelling mistake found.
VaR
). We consider optimization portfolios for minimizing
Possible spelling mistake found.
CVaR
. In this work, this
You use this word too often, consider replacing it with
approach
to the optimization problems with
Possible spelling mistake found.
CVaR
constraints.
In particular
, the
You use this word too often, consider replacing it with
approach
can be
This phrase/word (depending on the context) can be potentially replaced with :
used
for maximizing
This phrase/word (depending on the context) can be potentially replaced with :
expected
returns under
Possible spelling mistake found.
CVaR
constraints. \\

Two main difficult tasks for an investor are (1) to find the optimal portfolio with the smallest amount of
You use this word too often, consider replacing it with
risk
This phrase/word (depending on the context) can be potentially replaced with :
given
a required
This phrase/word (depending on the context) can be potentially replaced with :
expected
return and (2) to determine buying or selling prices of the exotic options that suitable for optimal portfolio.

In this work, we apply this
You use this word too often, consider replacing it with
approach
to option markets. We consider standard put and call options which
are written
on S\
Possible spelling mistake found.
&P
500 Mini Index. The quotes
This phrase/word (depending on the context) can be potentially replaced with :
come
with bid and ask prices
as well
as sizes. We
first
determine the optimal portfolio, the portfolio with the smallest
Possible spelling mistake found.
CVaR
This phrase/word (depending on the context) can be potentially replaced with :
given
a required return. We
also
investigate the
This phrase/word (depending on the context) can be potentially replaced with :
changes
in optimized portfolios subject to various modeling parameters. The index
is modeled
by a variance gamma process which is a geometric Brownian motion with gamma-distributed random time implements.
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IELTS academic Options portfolio optimization of exotic options written on Mini S\&P500 Index in an illiquid market with Conditional Value-at-Risk (CVaR)

Academic
  American English
3 paragraphs
221 words
6.0
Overall Band Score
Coherence and Cohesion: 7.0
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Lexical Resource: 5.0
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Grammatical Range: 6.5
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Task Achievement: 5.0
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