Volatility as an Asset Class
Lecture Note 4.1: Volatility as an Asset Class
Introduction:
Today we begin a new phase of our course in which we move beyond
pricing options. Our goal is to study derivative products that allow in-
investors to gain or hedge exposure to factors that are not literally asset
prices. This exposure may sometimes be embedded in an instrument
that looks like an option (or a forward or a swap). We will also see
examples of unique new payoff structures.
To get started with the subject, we can build on our study of options
pricing with stochastic volatility to think about securities whose payoff
is tied to volatility itself. We’ll discuss why people might be interested
in such products. We’ll also see some amazing results about how we
can price them.
Outline:
I. Why Trade Volatility?
II. Risk-Neutral Expectations
III. Volatility and the Log Contract
IV. Model-Free Implied Volatility
V. VIX
VI. Extensions
VII. Summary
I. Why Trade Volatility?
� The volatility of a financial asset is driven by the rate of infor-
mation flow about the asset, or the degree of uncertainty about
its future value.
� It is not at all uncommon for investors to have opinions – or
feelings – about the level of uncertainty in the economy or in
their personal wealth that is not necessarily connected to an
opinion about whether future news is likely to be good or bad.
� Times of high uncertainty feel very different.
· Prices are likely to be lower due to risk aversion.
· Also importantly, market illiquidity is strongly correlated with volatility.
� So, at least for non-diversifiable risk, it’s natural to see why
people might want to “buy volatility” as insurance.
� We have learned that if we are long a delta-hedged option on
an asset, S, that is effectively a bet on volatility.
· If continuously delta hedge it, you will have no exposure to
S and the total amount of money you make will depend on
realized volatility between now and expiration.
� But if this is what you want, then this strategy is not going to
be very efficient.