Math 489/889
Stochastic Processes and
Advanced Mathematical Finance
Homework 2

Steve Dunbar

Due Monday, Sept 13, 2010
  1. Consider the hypothetical country of Elbonia, where the government has declared a “currency band” policy. This means exchange rate between the domestic currency, the Elbonian Bongo Buck, denoted by EBB, and the US Dollar is guaranteed to fluctuate in a prescribed band, namely: 0.95 USD  EBB 1.05 USD

    for at least one year. Suppose also that the government has issued 1-year bonds denominated in the EBB. The government is so shaky that it must pay a continuously compounded interest rate of 20%. Assuming that the corresponding continuously compounded interest rate for US lending and borrowing is 4%, show that there is an arbitrage opportunity. In a sentence explain the risk associated with this transaction.

  2. Consider a market that has
    1. a stock (also called a security or asset), current price S
    2. a loan market so that money (also called a bond) can be borrowed or loaned at an annual interest rate of r compounded continuously.

    At the end of a time period T, the security will either increase in value by a factor U to SU, or decrease in value by a factor D to value SD. Show that a forward contract with strike price k that, is, a contract to buy the security at time T with potential values SU k and SD k should have the strike price set at Sexp(rT) to avoid an arbitrage opportunity.