Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Stock Options and Arbitrage Problem

  1. Oct 6, 2011 #1
    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.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?