Lower Bound for a European Call

Compare a portfolio long the call and holding cash $K{e}^{-rT}$ against holding the stock outright.

The bound is $\max (S_0-K{e}^{-rT},0)$.

1. 1. State the standard no-arbitrage bound

   A European call on a non-dividend stock must be worth at least the discounted intrinsic value, otherwise buying the call and shorting the replicating portfolio is a free profit.

   $$C\ge \max (S_0-K{e}^{-rT},0)$$

2. 2. Plug in numbers

   Discount the strike and subtract from the spot price.

   $$C\ge \max (100-95e^{-0.05},0)\approx 9.6332$$

Answer: max(100-95e^{-0.05},0)