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Risk and Hedging Questions for Options with Realized-Volatility Barriers

Article Quant Q&A · Author: fwd_T
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Summary

The document raises a risk-management problem for a vanilla option that terminates if realized volatility over the option’s life exceeds a preset barrier. Such a condition could reduce the option’s price, but it also makes the payoff depend on the path of realized volatility as well as the underlying option outcome.

The question asks how to hedge the instrument and how its exposures respond to mean-reversion speed, mean-reversion level, and possibly time-varying volatility of variance. No answer, model, hedge prescription, references, or empirical results are provided. The text is therefore useful as a statement of a derivatives-pricing problem, but it does not establish how the parameter sensitivities behave or how a hedge should be constructed.

Key ideas

  • A realized-volatility barrier can cause a vanilla option to terminate when volatility crosses a preset threshold.
  • The barrier introduces path dependence into the option’s payoff and risk exposures.
  • The question identifies mean reversion and volatility of variance as parameters of interest.
  • The document provides no proposed hedge, model, or evidence about parameter effects.

Tags

OptionsVolatilityRisk managementDerivatives pricing
Full text
# Barrier on realized volatility


# Barrier on realized volatility












I am trying to understand the risk exposures of vanilla options that also have a European barrier on realized volatility. For example, the option could knock out if the realized volatility over the time of the option exceeds a certain value (which could be set to be relatively low in order to cheapen the option). How would one do hedging for such instruments? How do risk exposures look like? Most of all, I am interested in understanding how such an instrument is influenced by the mean reversion speed, mean reversion level and especially by the (possibly time-dependent) volatility-of-variance.

Any reference would be much appreciated. Until now I could not find anything relevant, which is probably because I am using the wrong terms.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.