Box Spread - Background

Background

An arbitrage operation may be represented as a sequence which begins with zero balance in an account, initiates transactions at time t = 0, and unwinds transactions at time t = T so that all that remains at the end is a balance whose value B will be known for certain at the beginning of the sequence. If there were no transaction costs then a non-zero value for B would allow an arbitrageur to profit by following the sequence either as it stands if the present value of B is positive, or with all transactions reversed if the present value of B is negative. However, market forces tend to close any arbitrage windows which might open; hence the present value of B is usually insufficiently different from zero for transaction costs to be covered. This is considered typically to be a "Market Maker/ Floor trader" strategy only, due to extreme commission costs of the multiple-leg spread. If the box is for example 20 dollars as per lower example getting short the box anything under 20 is profit and long anything over, has hedged all risk .

A present value of zero for B leads to a parity relation. Two well-known parity relations are:-

• Spot futures parity. The current price of a stock equals the current price of a futures contract discounted by the time remaining until settlement:

• Put call parity. A long European call c together with a short European put p at the same strike price K is equivalent to borrowing and buying the stock at price S. In other words, we can combine options with cash to construct a synthetic stock:

Note that directly exploiting deviations from either of these two parity relations involves purchasing or selling the underlying stock.