hi my name is Patrick Boyle welcome back to my youtube channel. Today's video is
on the topic of volatility swaps. I am back to my usual video format today
which is shorter videos that quickly explain financial topics. I aim to
keep them 5 to 10 minutes long with no filler material in them. Last week I
posted a series of 6 longer slideshow style lectures each one was about an
hour long that I put together as a playlist.
I think it's called revision lectures. A few people had emailed me asking for
longer lectures they basically felt it was easier for them to study that way so
I put those ones together um you know as revision aids for students who are
preparing we'll say for an exam or something like that. let me know what you
think of those videos and of these videos tell me which style you prefer
because obviously the more feedback I get the better I can make these videos
and my goal is of course for you guys to find them as helpful as possible. Anyhow
on to today's topic, which is volatility swaps. If you want to have a long
position in future realized volatility (or to be long vol as option traders say)
Delta hedging a single option is not always a perfect approach as soon as the
stock price changes your sensitivity to further changes in volatility is altered
because of gamma - in theory the returns associated with Delta hedging an option
are fixed and are entirely based on the difference between the implied
volatility of the option when it was purchased or sold and the realized
volatility of the underlying over the life of the option. In the real world
with discrete rather than continuous Delta hedging (which means that traders
occasionally re-hedge rather than constantly rehedging at every second
throughout the life of the option) this turns out not to be the case. Variance
and volatility swaps were created to allow investors
to hedge volatility risk or to speculate on implied volatility in a clean manner
without the need for continuous Delta hedging which can be both expensive and
inefficient. The naming of these products as swaps is somewhat misleading as
they're more like forwards this is because their payoff occurs at maturity
where swaps have intermediate payouts over the the life of the contract. So
what are volatility swaps? A volatility swap is an over-the-counter financial
derivative which allows investors to trade future realized volatility against
current implied volatility. It acts like a forward contract on the future
realized volatility of a given underlying asset. Volatility swaps allow
investors to trade the volatility of an asset directly much as they would trade
a stock or an index. At inception of the trade the strike is usually chosen such
that the fair value of the swap is zero. The volatility notional is the notional
amount paid or received per volatility point or per 1% shift in realized
standard deviation. The payout of a volatility swap is the notional
multiplied by the difference between the realized volatility and the volatility
strike agreed at inception. The profit and loss on a volatility swap relates
only to the realized volatility of the underlying and is unaffected by any
directional moves thus it gives you a simpler and more
pure volatility exposure than Delta hedging an option does. So how do we
replicate and hedge volatility swaps? Well there's no simple replication
strategy for a volatility swap. Variance rather than the volatility exposure is
what you get from hedged options trading. From a derivatives point of view
variance can be viewed as the primary underlying and volatility swaps are best
regarded as derivative securities on variance
volatility being the square root of variance is a nonlinear function and is
therefore more difficult both theoretically and practically to value
and hedge the main difficulty with pricing and hedging volatility swaps is
that they require a volatility of volatility (or vol of vol) model and if
this model is not representative of the real world your pricing will be wrong.
Volatility swaps are very difficult to hedge and so market participants moved
towards trading variance swaps as variance swaps can be statically
replicated. Volatility swaps cannot be hedged by a static portfolio of options
but they can be hedged with variance swaps for small moves the payouts of
volatility and variance swaps can be similar. On screen right now you can see
the payoff of a volatility swap and a variance swap as a function of realized
volatility. For more on this topic take a look at the textbook for this course a
link to it is in the description below hopefully you found the video helpful if
so click the like button and click the subscribe button if you'd like to see
more videos like this. Tomorrow's video will be on the topic of variance swaps
see you then and have a great day bye