Options: fundamentals and arbitrage

No-arbitrage bounds on a call

The range a European call price must sit in, whatever the model.

max⁡(S0−Ke−rT, 0)≤C≤S0\max(S_0 - Ke^{-rT},\ 0) \le C \le S_0

Where

S0S_0
Spot. A call can never be worth more than the asset it buys.
Ke−rTKe^{-rT}
Discounted strike.

Assumptions

  • Model-free: violating either bound is an executable arbitrage, not a mispricing.

Sanity check. The lower bound exceeds intrinsic value whenever rates are positive.

Where this is taught