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Volatility as an Asset Class


Lecture Note 4.1: Volatility as an Asset Class


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.


I. Why Trade Volatility?

II. Risk-Neutral Expectations

III. Volatility and the Log Contract

IV. Model-Free Implied Volatility


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.