Anticipated Events’ Impact on FX Options’ Implied Volatility

Abstract

Understanding events’ impact on financial instruments are crucial for the
participants in the financial markets. Here we propose an approach to model
an anticipated event’s impact on the prices of FX options, represented in
implied volatility. The model is implemented for anticipated event’s with
both Black and Scholes and SABR as the assumed underlying dynamic. The
model generates an implied volatility frown, for both dynamics. Hence it
contributes to the area regarding concave implied volatility functions, which
at the time of writing has little published literature related to it.

Popular Abstract

Big anticipated event’s, e.g. Brexit, impact on
financial markets have an increased importance
in today’s society. We have introduced a model
to better understand and measure said impact.
The derived model is flexible and practical
and can be used to understand event’s impact on
foreign exchange options at a low calculation cost.
A mixture model of two different scenarios can
generate a lot of different option values, and may
be adjusted to adapt different market scenarios.
One can with this model produce a frown shaped
volatility, in contrast to the more traditional smile
shape which some models are limited to. The
model varies between two and four parameters,
and it is clear that the four parameter model is
more flexible than the one with only two. However,
the increased flexibility comes with a cost and
the model is now more difficult to calibrate
to market data. One need to keep this in mind
since it is important from a practical point of view.
Since the complexity of the financial markets
are rapidly increasing, the risk management tool
box need to be expanded in a similar pace. The
model presented can be used as such a tool. It can
namely be used to perform a sensitivity analysis,
to measure how different potential outcomes of
an event effect a bank’s balance sheet.
The consensus view of the market participants
may also be of interest for investment firms and
the like. With the model one can extract the
market priced probabilities over large events, and
hence get a view of the average opinion. This is
useful since often one can think of the market as
working like a herd. This model may give you
a sense of whether you would like to follow the
herd or stroll away in another direction, following
your own contrarian view.
The model generates a price, which is a mixture
of option prices in two different scenarios, called
up and down. The two scenarios represent a
jump, caused by an anticipated event, in the
exchange rate between two currencies, see Fig.
1 for an illustration. Each scenario is assigned
a specific so called risk-neutral probability (a
risk-neutral world is a world in which a person
does not keep the risk in mind when evaluating
an investment opportunity). These probabilities
are used as weights, and from the resulting price
we are able to draw conclusions, discussed in the
previous parts of this article.

• author: Håkansson, Frej and Nilsson, Björn
• supervisor: Magnus Wiktorsson
• organization: Mathematical Statistics
• course: FMS820 20181
• year: 2018
• type: H2 - Master's Degree (Two Years)
• subject: Mathematics and Statistics
• keywords: Volatility frown, implied volatility, jump model, anticipated event, SABR, FX Options
• publication/series: Master's Theses in Mathematical Sciences
• report number: LUTFMS-3349-2018
• ISSN: 1404-6342
• other publication id: 2018:E44
• language: English
• id: 8949377
• date added to LUP: 2018-06-14 10:58:52
• date last changed: 2024-09-24 14:45:01