# Stock Options and Arbitrage Problem

1. Oct 6, 2011

### Oragest

1. The problem statement, all variables and given/known data

I'm currently taking an introduction to mathematical finance and I'm not sure how to go about proving this inequality using arbitrage.

Consider a European call option with strike price K. Give an arbitrage argument which shows we must have V0 <= S0 - K(1+p)^-n.

2. Relevant equations

V0 is the price of the option at time t=0.
S0 is the price of the stock at time t=0.
Vn is the price of the option at t=n, given by max{S-K, 0}.
p is the risk-free interest rate.

3. The attempt at a solution

I've tried to solve this by buying a stock and putting an amount z in the bank at time t=0, then comparing the initial and final value of the portfolio with the option. I've set z = K(1+p)^-n so that at t=n z will equal K. I get stuck after that.

I've also tried to use the put-call parity but it takes away from the proof part of the assignment if I use that.

Any help would be greatly appreciated.