Question

(2.3) C >= S-Ee^(-rT)

**Give an argument based on the no arbitrage assumption that justifies (2.3).

Answer 1

C >= S-Ee^(-rT)

Put-Call Parity-
C + PV(E) = P + S
where:
C = price of the European call option
PV(E) = the present value of the strike price (x), discounted from the value on the expiration date at the risk-free rate
P = price of the European put
S = spot price or the current market value of the underlying asset

Term- Ee^(-rT) is the PV of strike price (with slightly different notation).

Rearranging terms in Put-Call Parity-
C= P + S - PV(E)
i.e.
C= P + S - Ee^(-rT)

The minimium price of Put option for any given underlying asset can be zero but not negative. Hence, the RHS in above equation can be equal to LHS or lower. Hence, we get an inequality-
C >= S-Ee^(-rT)
Here, if the put option price is zero, then the 2 sides are equal. In case the put option has a +ve value, the LHS is greater than RHS