Passport Option

A call option on the trading account of an individual trader, giving the holder the amount in his trading account at expiration if it is positive, or zero if it is negative. They are also called perfect trader options. The terms of the contract will specify what the underlying asset is that the trader is allowed to trade, his maximum long and short position, how frequently he can trade and for how long. To price these contracts requires knowledge of stochastic control theory. The governing partial differential equation is easily solved by finite differences.