Scribd
Upload
65 views2 pages

Advanced Variance Swap Insights

Variance swaps allow investors to bet on the realized variance of an underlying asset over a period of time. Traditional option pricing models assume stock prices follow a diffusion process and see variance swaps as redundant to vanilla options. However, variance swaps are truly a bet on potential jumps in the underlying's price. The document argues that variance swaps should be priced independently from vanilla options using a model that allows for stochastic volatility and jumps. This recognizes variance swaps provide additional information about the asset beyond diffusion models and sees them as marking a new era in volatility trading.

Uploaded by

yukiyuriki
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
65 views2 pages

Advanced Variance Swap Insights

Variance swaps allow investors to bet on the realized variance of an underlying asset over a period of time. Traditional option pricing models assume stock prices follow a diffusion process and see variance swaps as redundant to vanilla options. However, variance swaps are truly a bet on potential jumps in the underlying's price. The document argues that variance swaps should be priced independently from vanilla options using a model that allows for stochastic volatility and jumps. This recognizes variance swaps provide additional information about the asset beyond diffusion models and sees them as marking a new era in volatility trading.

Uploaded by

yukiyuriki
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
You are on page 1/ 2

Variance Swaps

The variance swap is an equity derivative with payoff the realized variance of the underlying
equity or index. The Black-Scholes-Merton tradition of continuous delta hedging under
diffusion confuses it with the log contract. As a consequence, it suggests the variance swap is
redundant with the vanilla options.

However, what the variance swap truly is (what it is, over and above the vanillas) is a play on
the possible underlying jumps. Learn why, here.

We believe variance swaps mark a new age in volatility arbitrage. For this reason, we price
them from scratch, independently of the diffusion assumption or even the idea that vanilla
options may have ever been a play on variance:
 We price the variance swaps under our generalized jump-diffusion model with
stochastic volatility and stochastic jumps, also known as the “regime-switching
model.”

 We also price the log contract. This way, you can measure the difference due to the
jumps.

 It doesn't matter whether jumps (in the equity or the index) have been known to occur
or not to occur in the past. (A jump to default couldn't have occurred in the past.)
What matters is whether the market anticipates such jumps.

 The empirical disconnect between the market price of the variance swap and the
theoretical price of the log contract (a.k.a. the strip of vanillas), apparent even on the
index, points in that direction.

 We even calibrate the regime-switching model against the market prices of variance
swaps of different starting dates and maturity dates, independently of the vanillas.
Indeed, the variance swap is not redundant with the vanillas and its price carries
additional information on the underlying process (as does the price of any path-
dependent option, generally).

 People should be suspicious, anyway, of any methodology that is incapable of valuing


an instrument as natural and simple and homogeneous as the variance swap directly
and says it requires a full strip of known vanilla options prices in order to do so!

 On top of vanilla variance swaps, our all-numerical solving techniques enable us to


price the following payoffs:
o volatility swaps
o capped volatility and variance swaps
o gamma swaps
o corridor variance swaps
o up and down corridor variance swaps
o conditional variance swaps
o variance options
o variance swaptions

 All this is achieved in our general equity-to-credit framework, of which dividends


and default risk are an integral part.

You might also like