The current price of a stock paying no dividend is $$50.$ The stock return has a mean

of $10\%$ and variance of $20\%$ per annum. The risk$-$free interest rate is $r=ln1\mathrm{.}05$ per

annum continuously compounded. A European average strike call option has a payoff

of max$(S_T-(\frac{?}{\text{b}\text{a}\text{r}}(S)),0)$ at the maturity, where $\frac{?}{\text{b}\text{a}\text{r}}(S)$ is the arithmetic average of the underlying

asset $S_t$ over the lifetime of the option, discretely sampled at $t=[0,1,2,$cdots$].$ The

option starts at time $t=0$ and expires at time $t=3.$