Question

A Swap Contract: Assume that we are in a one-period arbitrage–free market with a a riskless asset (called MoneyMarket). Assume that all prices are given in units of MoneyMarket. Consider a swap contract that calls for the following:

(a) The buyer pays the seller an amount q to enter into the contract at time 0. (b) The seller agrees to exchange 1 unit of asset A for 1 unit of asset B at time 1.

TheunitvaluesofassetsAandBattimest=0andt=1areAt andBt,respectively. Asinall such problems, the values A1 and B1 of the underlying assets at the termination time t = 1 are subject to uncertainty. Determine the fair market value q of the contract (in terms of the initial share prices of A and A) .

Answer 1

An arbitrage is a way to make guaranteed profit from nothing, by short selling certain assets at time t=0, using the proceeds to buy other assets, and then settling accounts at time t=1. When an investor sells an asset short, he must borrow shares of the asset to sell in return of a promise to return the shares at a pre specified future time. In real markets there are constraints on short selling imposed by brokers and market regulators to assure that the shares borrowed for short sales can be repaid. Such contraints do not exist in idealized markets, nor are there interest payments on borrowed shares, nor are there transaction cost. Futhermore it is assumed that investors may buy or sell shares in any asset at the prevailing market price without affecting the share price.Hence the fair market value of Q is the difference between present values of assets A and B