Digital Security Tokens and Their Derivatives

Applied cryptography and network security could bring a new commerce architecture for valuable but uncertain digital objects in an open network. This paper models the digital objects as security token, which is abbreviated into a word coinage setok. Each setok has its price, values, and timestamp on it as well as the main contents. Not only the price but also the values can be uncertain and may cause risks. A number of properties of the setok are defined. They include value response to compromise, price response to compromise, refundability, tradability, online divisibility, and offline divisibility. Then, in search of risk-hedging tools, a derivative written not on the price but on the value is introduced. The derivative investigated is a simple European call option. Based on the common no-arbitrage condition, several option-pricing formulae are derived in discrete-time and continuous-time models. These formulae do not require any divisibility of the underlying setok. With respect to applications, an inverse estimation of compromise probability is studied. Assuming a systematic risk of compromise, the no-arbitrage theory gives a partial differential equation (PDE) to price the call option; given a set of parameters including the compromise probability, the PDE can tell us the option price. By making an inverse use of this, we are able to estimate the risk of compromise.