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Why Averaging Reduces Volatility in Asian Call Options

Article Quant Q&A · Author: user32226
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Summary

The document gives an intuition for why averaging can reduce the volatility exposure of an Asian call option with an average-strike payoff. It uses the fact that the time average of standard Brownian motion over a fixed horizon has standard deviation proportional to the square root of time, with a smaller scale than a single terminal Brownian observation. For a geometric Brownian motion spot price, the answer then gives an approximate volatility for the average spot price that is lower than the spot process volatility.

This is a compact approximation, not a full option-pricing derivation. It does not specify market parameters or quantify the option's price impact, and the stated volatility relationship should not be treated as an exact result for the average of a lognormal price process. The explanation supports the general effect of averaging while leaving payoff valuation and modeling assumptions open.

Key ideas

  • A time average smooths some of the fluctuations in a price path.
  • The time average of Brownian motion has a lower standard deviation scale than its terminal value.
  • The answer approximates average spot volatility under a geometric Brownian motion model.
  • The volatility approximation does not itself provide a complete Asian option valuation.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Asian Call Option


# Asian Call Option












An Asian call option with the average strike payoff, uses the “averaging” to reduce the effect of volatility. Why is this so?

## Answer by Antoine Conze (score 3)

https://quant.stackexchange.com/a/38737

If $W$ is a standard Brownian motion then $\frac{1}{T}\int_0^T W_t dt$ has standard deviation $\sqrt{\frac{T}{3}}$. For this reason if $S_t=S_0e^{(\alpha -\frac{1}{2}\sigma^2)t + \sigma W_t}$ is the GBM spot price then the average spot price $\frac{1}{T}\int_0^T S_t dt$ has approximate volatility $\frac{\sigma}{\sqrt{3}}$.

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.