Introduction on Volatility Derivatives

Volatility derivatives have payoffs that depend explicitly on the volatility of the underlying assets on which they are written.

They provide investors a way to take a clean view on volatility without being exposed to underlyings' movements.

There is now a liquid OTC market for products such as the variance swap, the volatility indices. 


16.1 The need for Volatility Derivatives


The demand for such products comes from the generally negative correlation often seen between an index and its volatility. 

This negative correlation makes a volatility product an excellent choice for diversification. 

Volatility generally increases as the market declines --> possibility to buy vol as a downside hedge definitely has appeal.

This demand has been met with supply from the sell side in certain contracts, particularly the variance swap.

This is attributed to the existence of robust hedges for such contracts. 


Following the VS, investors’ appetites have increased for more tailored views --> New generation of volatility derivatives. 

New generation of volatility derivatives: 

- Corridor VS

- Conditional VS

- Gamma Swaps

- Options on RV


Volatility derivatives can be tailored to hedge specific volatility risks and can also be customized investments in volatility.

With the increase in the liquidity and range of products, it is fair to consider volatility derivatives as an asset class.


16.2 Traditional Methods for Trading Volatility


Here we review some of the strategies seen before and study their potential as a means to trade volatility.

We start by showing that the traditional methods do not provide a pure exposure to volatility. 

It justifies the necessity fro the VS and subsequent volatility derivatives. 


Traditional methods = delta-hedged options --> hedging exposure to movements in S to isolate volatility exposure. 

One buys (sells) options whose IV is less (greater) than the anticipated RV. 


1) ATM Straddle = ATM Call + ATM Put

- initial cost can be quite high.

- view on future RV and also on changes in IV. 

- initial delta = 0.


As S moves --> pick up Delta --> can incur high transaction costs + liquidity issues while keeping delta neutral. 

To see only the volatility risk --> we would have to consistently Delta hedge the position. 


2) Strangle = OTM Call + OTM Put

- cheaper than straddle but need larger move to make money


Neither of these strategies provide a pure exposure to volatility. 


3) Call option


If the investor delta hedges --> a large proportion of P&L comes from difference between RV and IV used to price and hedge. 

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- σi = implied volatility that was used to price the option

- σ= volatility the trader uses when computing his Delta

-Gamma copie(t,σh) = Gamma at time t computed using the volatility σ--> it is function of the underlying. 



- The integral implies that this P&L is still a function of the path of the underlying and the transition of time.

- Vega decreases when S moves away from K in either direction

- It lowers the potential as a way to gain exposure to volatility without taking a view on the path of the underlying. 



We need a vehicle that will provide pure exposure to the volatility

- irrespectively of the underlying's path

- with no requirement of Delta hedging 


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