Systems, computer-implemented methods, and computer medium to determine premiums for supplemental crop insurance

A supplemental crop insurance machine comprising:

• a supplemental insurance server including one or more processors, being in communication with one or more databases, being positioned to communicate through an electronic communications network to one or more user devices positioned remote from the supplemental insurance server, and being configured to:
• serve, to the one or more user devices through the electronic communications network, a supplemental crop insurance policy information content page comprising one or more policy parameter fields adapted to be populated by a user with a corresponding set of supplemental crop insurance policy parameters;
• receive input of the set of supplemental crop insurance policy parameters to populate the one or more policy parameter fields, the set of supplemental crop insurance policy parameters including:
• (1) one or more of coverage level, insurance plan elected, expected yield, approved yield, acres, type, practice, county, share, and liability adjustment factor, (2) one or more of risk adjusted revenue probability, and premium rate, and (3) a liability based on one or more of expected yield, approved yield, coverage level, deductible, co-pay, acres, share, inventory value, and liability adjustment factor, the determination of the premium configured to include summing the premium amount per acre for a potential insured's selected coverage level for all alternative price discovery periods elected, multiplying the sum by a selected liability adjustment factor to obtain a result, and multiplying the result by the number of insured acres and by the potential insured's share of such acres;
• use vectorized code to simulate a plurality of potential price trajectories spanning a time period, the time period including a plurality of months, potential price trajectories simulated by:
• determining one or more stochastic up-down price movement multipliers, wherein a stochastic up price movement multiplier is determined by the equation
• u=eσP√{square root over (2Δt)}
• and a stochastic down price movement multiplier is determined by the equation
• d=e−σP√{square root over (2Δt)}
• in which σP represents a futures price annualized implied volatility associated with the set of supplemental crop insurance loss parameters and Δt represents an inverse of a determined number of trading days per year, determining one or more risk-adjusted price movement probabilities, and generating greater than 10,000 potential price trajectories based at least in part upon the one or more up-down price movement multipliers and the one or more risk-adjusted price movement probabilities;
• determine a premium for a non-reinsured supplemental crop insurance policy responsive to the set of supplemental crop insurance policy parameters and the plurality of potential price trajectories;
• transmit via the supplemental insurance server, data representing the premium for the non-reinsured supplemental crop insurance policy over the electronic communications network to one or more user devices;
• and
• serve, to the one or more user devices, supplemental crop insurance policy information content including the premium for the non-reinsured supplemental crop insurance policy to one or more users.