Counterparty Credit Exposures for Interest Rate Derivatives using Stochastic Grid Bundling Method and Change of Measure

Abstract

The notional amounts outstanding of over-the-counter (OTC) derivatives had
grown exponentially for almost two decades and its rapid growth were mainly
due the increase in OTC interest rate derivatives. As of december 2014, the
total notional amounts outstanding in the global OTC market was 630 trillions USD and the OTC interest rate derivatives represents about 80% of the
market.
Trading with OTC derivatives can lead to signicant risks. Especially counterparty credit risk has gained particular emphasis due to the credit crisis in
2007. The aim of this thesis is to determine if it is possible to get realistic
estimations of counterparty credit risk measures as Expected Exposure (EE)
and Potential Future Exposure (PFE) that re
ects the "real world" market.
In order to do simulations under the historical P-measure, attempts are made
to approximate the market price of risk and then calculate exposure proles
for the interest rate derivative Bermudan swaption. The Hull and White
one-factor short rate model is used and all calculations are done using the
Stochastic Grid Bundling Method(SGBM).

Popular Abstract

Due to the exponential growth amongst OverThe-Counter derivatives and the aftermaths
of the credit crises in 2007, a need for better
or more realistic estimations of counterparty
credit exposures has emerged.
Is it possible to get realistic estimations of
counterparty credit exposure that reflects the
“real world” market?
In this thesis I will try to answer that question.
Counterparty credit exposure is a part of the
concept counterparty risk and specifies the
amount of money that could be lost in case of
a counterparty default. The Over-The-Counter
contract that is investigated in this thesis is an
interest rate derivative, a Bermudan swaption.
The method used for computations is a Monte
Carlo method called Stochastic Grid Bundling
method. All the short rates used in
computations are simulated with the HullWhite one-factor model.
During the last decades, the focus of research
has been on the pricing of derivatives which is
done with risk-neutral probabilities under the
assumption that investors have neutral
mindset towards risk.
There has been a tendency of underestimating
counterparty risk amongst financial
institutions and this were partly because of a
general market view which were that large
companies were “too-big-to-fail”. This general
market view was shown to be far from true
during the credit crisis back 2007 when some
of those “too-big-to-fail” companies went
bankrupt.
During the last decade, due to the events
during the crisis, the Basel Committee on
Banking Supervision has published new
standards containing stricter regulations on
risk management. This has led to thatfocus of
research has started to change direction
towards risk management and that have led to
the realization that the impact from the real
world market should be given more attention,
i.e. the real world probabilities.
So how does one simulate counterparty credit
exposure impacted by the real market?
As mentioned in the beginning, these
estimations need to be computed using real
world probabilities instead of the risk neutral
probabilities. In order to change probabilities
one need to approximate a stochastic process,
often referred to as market price of risk, which
fulfills certain conditions stated by Girsanov’s
theorem.
Combining contents of Girsanov’s theorem
with the facts that most of these investments
and most risk related measures are long-term
implies that approximating the market price of
risk actually means trying to approximate the
real world drift of the market.
I have analyzed three different attempts to
approximate the market price of risk. The first
one is a constant, referred to as the historical
market price of risk. The other two
approximations are referred to as local prices
of risk since they are time-dependent.
When analyzing the results I detected
drawbacks for all of the three approximations.
For the historical market price of risk, it was
the inability to adapt to changes through time
and spreading the extra risk evenly over time.
For both the local prices of risk the main
drawback were that it lacked presence in the
long-term perspective and were only active for
a couple of years. Since most of the interest
rate derivatives are long-term investments this
is a significant drawback.
My conclusion is that these approximations of
the market price of risk are not complex
enough to capture all the market factors that
impacts on both short-term and long-term.
This might be possible to achieve in a multifactor model, where one could try to capture
and combine multiple of the market factors
that can impact both on short-term and longterm interest rates. The three approximations
that were analyzed in this thesis could be used
in combination as an extra safety margin
towards exposure or as an indicator, a way of
gaining more insight of how the impact from
the market is changing.

• author: Gustavsson, Johan
• supervisor: Magnus Wiktorsson
• organization: Mathematical Statistics
• course: FMS820 20171
• year: 2017
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• keywords: OTC, Counterparty credit risk, HW1F, Market price of risk, CVA, Potential Future Exposure, Expected Exposure, Bermudan swaption, Stochastic Grid Bundling Method, SGBM.
• language: English
• id: 8923335
• date added to LUP: 2017-08-21 14:06:56
• date last changed: 2017-08-21 14:06:56