This is a very old paper we wrote in Quantitative Strategies concerned with how to value options on stocks that settle in the old European style, where all stocks bought in the next (say) 30 days settle at some fixed date in the future, say 40 days from now. You can find it at
In some countries, for example France, stocks bought or sold during an account period have their settlement deferred to a designated settlement date. We explain how to value and hedge cash-settled European- or American-style options on stocks whose settlement is deferred. To do this we introduce the notion of “bare” (immediately settled) and “dressed” (deferred-settled) stock prices. It is the volatility of bare prices that is fundamental.
In France, options on the CAC-40 Index settle in cash and are hedged with stock or with futures contracts. At exercise or expiration, options settle in two business days. As far as stock settlement is concerned, the year is divided into account periods of several weeks; stock transactions occurring at any time within one account period all settle on a given account period settlement date. You can buy stock for hedging and hold it at no financ- ing cost, sometimes for several weeks, until the account period’s settlement date. Similarly, if you sell stock, you receive no cash or interest income until settlement.
These financing peculiarities affect hedging costs, which in turn affect options values, because the theory behind options valuation involves the cost of a riskless hedge. In this paper, we explain and evaluate the effects of periodic settlement on both European- and American-style cash-settled options.
A two-day delay between the exercise and settlement of options is negligible compared to the possibility of a delay of several weeks between the trade and settlement of stock. Therefore, to keep things simple, we’ll assume below that options settlement always occurs immediately on exercise or expiration.