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What are Variance Swaps? Financial Derivatives - Trading Volatility - YouTube
Channel: Patrick Boyle
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Hi my name is Patrick Boyle welcome to
my YouTube channel today we're going to
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learn about variance swaps new
derivatives that we'll be looking at
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today so a variance swap is an
over-the-counter financial derivative
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which allows investors to trade future
realized variance against current
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implied variance. Today
we're talking about variance while
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yesterday we did talk about volatility
swaps so you can watch that video as well
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but how variance swaps work is they act
like a forward contract on the future
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realized variance of a given underlying
asset. The reason that variance is used
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rather than volatility is because
variance which is volatility squared can
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be replicated with a static hedge and so
essentially these things are more traded
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than volatility swaps because they're
easier to hedge. At inception of the
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trade the strike is usually chosen such
that the fair value of the swap is zero
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variance swaps allow investors to
speculate on or to hedge risks
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associated with volatility one leg of
the swap will pay an amount based upon
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the realized variance of the price
changes of the underlying product.
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Usually these price changes will be
daily log returns based upon daily
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closing prices. The other leg of the swap
will pay a fixed amount which is the
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strike quoted at the deals inception.
Thus the net payoff to the
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counterparties will be the difference
between these two levels, and will be
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settled in cash at the expiration of the
deal. The long party receives realized
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variance and pays the strike variance at
maturity and a short party receives the
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strike variance and pays realized
variance at maturity. The annualized
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realized variance is calculated based on
a pre specified set of sampling points
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over the life of the swap. normally an
investment
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Bank is the calculation agent for any
variance swaps traded. The calculation
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agent usually has some discretion over
whether a market disruption event occurs
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or the treatment of situations such as
if a stock is delisted. This can lead to
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issues if an investor is long and short
identical products versus two different
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investment banks. These problems are less
of an issue if the counterparties are
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joint calculation agents. The profit and
loss on a volatility swap relates only
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to the realized variance (which is
volatility squared) of the underlying and
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is unaffected by any directional moves,
thus much like volatility swaps it gives
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you a simpler and more pure volatility
exposure than Delta hedging an option
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does. The payoff of a variant swap is
convex in volatility as you can see on
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the screen right now. This means that an
investor who is long a variance swap
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will benefit from boosted gains and
discounted losses, this bias is reflected
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in slightly higher strike prices for
variance swaps when compared to
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volatility swaps, a phenomenon which is
amplified when volatility skew is steep.
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The fair value of a variance swap is
determined by the cost of the
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replicating portfolio of options. This
cost especially for index options is
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significantly affected by the volatility
smile or skew. I've made videos on those
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as well which are linked to above. The
return calculation for a variance swap
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on an index does not adjust for any
dividend payments that are paid. This
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means that the dividend modeling method
can affect pricing. Long-dated dividends
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are usually modeled as flat yield and
near dated and hence either known or
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relatively certain dividends are modeled
discretely so they're essentially one by
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one modeled. The payoff of a variance swap
is variance notional times that
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difference between the realized variance
and the strike variance. Returns are
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computed on a logarithmic basis for
variance swaps. Instead of using the
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standard calculation for variance the
contract terms usually set the mean
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return at zero. The reason for this is
that its impact on the price is minimal
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the expected average daily return is 1/ 252 of the money market rate while
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it's omission has the benefit of making
the payoff perfectly additive. That means
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that 3-month variance plus nine-month
variance in three months time would be
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equal to 1 year variance. So it's sort of
it's just that simplification in the
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formula just makes everything a little
bit easier. So how do we replicate
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variance swaps? Well in order to price
variance swaps we should first look at
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the replicating portfolio that captures
realized variance. The cost of that
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portfolio should be the fair value of
future realized variance. To achieve such
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a portfolio you need to combine options
of many different strikes. A portfolio of
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options of all strikes, weighted in
inverse proportion to the square of the
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strike level. Each option weighted by 1
divided by its own strike squared gives
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an exposure to variance that is
independent of stock price. Intuitively
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as the stock price moves up to higher
levels, each additional option of higher
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strike in the portfolio provides an
additional contribution to variance
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proportional to that strike. It takes an
infinite number of strikes appropriately
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weighted to replicate a variance swap. In
practice this is neither possible nor
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practical, there are only a certain
number of options available at any
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maturity and if the stock price moves
outside the range of available strikes
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the reduced Vega of the imperfectly
replicated contract will make it less
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responsive than a true variance swap. As
long as the stock price remains within
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the strike range trading the imperfectly
replicated contract will allow variance
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to accrue at the correct rate. So it's
worth noting that when these things
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first came out, you were able to trade
variance swaps both on indexes and on
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single stocks. Now during the credit
crunch markets were extremely extremely
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volatile and so even indexes were
swinging around at movements of 10% a
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day. Single stocks were even more
volatile than that, and so what was
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happening was that banks who had sold or
bought but were hedging variance swaps
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using this approach were finding that on
single stocks, on a daily basis the
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market was moving past the available
strike prices at least for the static
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hedge when it was first implemented and
so these hedges weren't working very
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well for single stock variance swaps and
for that reason these single stocks
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variance swaps aren't really available
anymore. it's much easier to trade index
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variantce but not really to trade these
simply because the the banks that were
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selling them really just didn't want to
to be on the other side of that because
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the hedge doesn't work very well in
extreme markets. So anyhow how do we
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price variance swaps?
Variance swaps can theoretically be
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hedged as I just described and thus
priced as a portfolio of European Call and
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put options with weights inversely
proportional to the square of the strike.
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Care must however be taken with regard
to the volatility smile, as the wings (and
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by that I mean deep in and out of the
money option prices) can have a
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disproportionate effect on the price. A
volatility smile model is needed to
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correctly price variance swaps. If we use
the Heston model a closed
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form solution can be derived for the
fair variance swap rate. To learn more
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about this take a look at chapter 12 of
my book Trading and Pricing Financial
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Derivatives which is linked to in the
description below. Okay well you made it
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all the way to the end of the video so
the rules are, as you know, that you have
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to hit the like button. If you would like
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Tune in tomorrow and we will be starting
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a series on interest rate swaps. See you
then, bye
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