Replicating portfolios play a central role in the pricing of financial derivatives. Here is a brief summary of the replicating portfolio approach as it applies to forwards/futures; next Tuesday, we will further discuss various other forwards/futures pricing problems and also briefly consider how to price simple call and put options via replicating portfolio approaches.
- Buying forward is equivalent to buying the underlying on margin, and selling forward is equivalent to shorting the underlying and lending money. Like options, forwards and futures are priced by pricing the replicating portfolio and invoking the “no-arbitrage” condition. If the forward/futures price is too low, then one can earn positive returns with zero risk and zero net investment by buying forward, shorting the underlying, and lending money. Similarly, if the forward/futures price is too high, one can earn positive returns with zero risk and zero net investment by selling forward and buying the underlying with borrowed money. This is commonly referred to as “riskless arbitrage”; it’s riskless because you’re perfectly hedged, and it’s arbitrage because you are buying low and selling high.