Globally Optimum Trading Positions for Path-Dependent Options

A computer-implemented method for evaluating trading positions for a path-dependent European Contingent claim (ECC), wherein the method comprises:

• receiving a plurality of trading time instances from a trader;
• retrieving ECC data and market data associated with the path-dependent ECC from a database, wherein the ECC data comprises data associated with the path-dependent ECC and an underlying asset of the path-dependent ECC, and the market data comprises annualized volatility of the underlying asset and risk-free interest rate of market;
• computing a current option price and a shifted option price of the path-dependent ECC at a trading time instance, selected from amongst the plurality of trading time instances based on the ECC data, the market data, and at least one discrete-monitoring time instance occurring before the trading time instance;
• and
• evaluating a trading position in the underlying asset at each of the plurality of trading time instances based on the current option price and the shifted option price, wherein the trading position minimizes global variance of profit and loss to the trader.

A non-transitory computer-readable medium having embodied thereon a computer program for executing a method comprising:

• receiving a plurality of trading time instances from a trader;
• retrieving ECC data and market data associated with a path-dependent ECC from a database, wherein the ECC data comprises data associated with the path-dependent ECC and an underlying asset of the path-dependent ECC, and the market data comprises annualized volatility of the underlying asset and risk-free interest rate of market;
• computing a current option price and a shifted option price of the path-dependent ECC at a trading time instance, selected from amongst the plurality of trading time instances based on the ECC data, the market data, and at least one discrete-monitoring time instance occurring before the trading time instance;
• and
• evaluating a trading position in the underlying asset at each of the plurality of trading time instances based on the current option price and the shifted option price, wherein the trading position minimizes global variance of profit and loss to the trader.