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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
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