Understanding financial derivatives during the South Sea Bubble: the case of the South Sea subscription shares

South Sea Company subscription shares were compound call options on the firm's own fully-paid shares. From the description of shares found in 6 Geo. 1, c. 4, a theory of their pricing is developed. A method for computing subscription share values is also developed. Calculated theoretical values for subscription shares are compared to the shares' historical values and a close correspondence between the two is demonstrated. The prices of the subscriptions relative to fully-paid share prices thus appear to be explainable using simple financial economic theory and to have been formed quite rationally. There is no obvious evidence of barriers to arbitrage or inefficiencies in the markets for fully-paid shares and subscription shares during the financial crisis known as the South Sea Bubble.