The Black—Scholes model we have seen so far has a simple mathematical side but it has an even simpler financial side. The asset we considered was a stock which could be held without additional cost or benefit and was freely tradable at the price quoted. Even leaving aside the issues of transaction costs and illiquidity, not much of the financial market is like that. Even vanilla products — foreign exchange, equities and bonds — don't actually fit the simple asset class we devised. Foreign exchange involves two assets which pay interest, equities pay dividends, and bonds pay coupons.

Just retreading the same mathematics for each of these will be enough to keep us busy. The sophistication we have to peddle now is financial.

Foreign exchange

In the foreign exchange market, like the stock market, holding the basic asset, currency, is a risky business. The dollar value of, say, one pound sterling varies from moment to moment just as a US stock does. And with this risk comes demand for derivatives: claims based on the future value of one unit of currency in terms of another.

Forwards

Consider, though, a forward transaction: a dollar investor wanting to agree the cost in dollars of one pound at some future date T. As with stocks, the replicating strategy to guarantee the forward claim is static. We buy pounds now and sell dollars against them. But cash in both currencies attracts interest.