Question: All Black-Scholes assumptions hold. Assume no dividends. The stock price is $100. The riskless interest rate is 5% per annum. Consider a one-year European call option struck at-the-money (i.e. strike equals current spot).
$(1)$ If the volatility is zero (i.e. σ=0), what is the call worth?
$(2)$ After valuing the call, how to hedge the call (assuming you sold it).
My attempt to $(1)$:
Since volatility is zero, it means that return does not deviate from riskless return, that is, $$$100 \times 1.05 = $105.$$ So the call worth $\$105.$
But I have no idea on how to hedge the call.
Any idea would be appreciated.