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Choosing Daily or Annual Volatility for Option Pricing and Hedging

Article Quant Q&A · Author: Trajan
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Summary

This brief exchange asks which volatility to use when pricing and hedging a European option, given conflicting daily and annual volatility figures. It mentions that Black–Scholes conventionally uses annualized volatility and asks whether a different measure is appropriate.

The reply recommends using the larger volatility as a conservative hedge input and says to annualize daily volatility using the square root of the number of trading days in a year. The document offers no derivation, data, or comparison of the inputs, and its stated daily and annual figures are internally inconsistent under the usual annualization relationship. The recommendation should therefore not be taken as a general rule: volatility estimates need consistent units and a model-appropriate horizon.

Key ideas

  • Option pricing inputs must be expressed on a time scale consistent with the model horizon.
  • Daily volatility is typically annualized by multiplying by the square root of trading days per year.
  • The exchange's suggestion to use the larger estimate is not supported by a derivation and is not established as a universal hedging rule.

Tags

OptionsVolatilityDerivatives pricing
Full text
# To use daily volatility or annual volatility


# To use daily volatility or annual volatility












From Joshi's Quant Interviews books:

> The statistics department from our tell you that the stock price has followed a mean reversion process for the last 10 years, with annual volatility 10% and daily volatility 20%. You want to sell a European option and hedge it, which volatility do you use?

Apparently the answer is daily volatiliy 20% as the option price is monotonically increasing in volatility.

I dont get this. I thought that the B-S price used annual volatility. Why should we deviate from this?

## Answer by Valometrics.com (score 0, accepted)

https://quant.stackexchange.com/a/50766

You should always use the biggest volatility to minimise the risk and hedge the option correctly. Don't forget to multiply daily volatility by square(252) to annualize it.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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