Given u$=1\mathrm{.}05,$ d$=0\mathrm{.}98,$ r$=0\mathrm{.}01,$ T$=1$

Suppose that we have the physical probability $P(S_T=S_{0}u)=P(S_T=S_{0}d)=\frac{1}{2}.$

a$)$ Compute the price of the call option $V_0=E(e^{-rT}{V}_T)$ where $E$ here denotes the expectation under the physical probability just described.

b$)$ Construct an arbitrage opportunity in this scenario if the price of the call option is the $V_0$ you found in part a$.$