Abstract
Given a Black stochastic volatility model for a future F, and a function g, we show that the price of can be represented by portfolios of put and call options. This generalizes the classical representation result for the variance swap. Further, in a local volatility model, we give an example based on Dupire’s formula which shows how the theorem can be used to design variance related contracts with desirable characteristics.
Highlights
The variance swap, and its derivatives such as the VIX index, have become the instruments of choice to trade a view on volatility
These products experience extreme volatility during market distress, and a short position typically incurs dramatic losses. To circumvent this practical problem, we generalize in this paper the concept of the variance swap
We include an example where we apply Dupire’s formula in a Black local volatility model to choose a g such that V is independent of F
Summary
OPEN ACCESS Citation: Lindberg C (2017) A note on contracts on quadratic variation. Data Availability Statement: All relevant data are within the paper. Given a Black stochastic volatility model for a future F, and a function g, we show that the price of 1 2. RT g ðt; FðtÞÞF2 ðtÞs2 ðtÞ dt can be represented by portfolios of put and call options. This generalizes the classical representation result for the variance swap. In a local volatility model, we give an example based on Dupire’s formula which shows how the theorem can be used to design variance related contracts with desirable characteristics
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