# 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?

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 $\frac{\sigma}{\sqrt{3}}$.