Tail Coverage Calculator

This calculator estimates the tail coverage needed for an insurance policy based on loss severity data, helping determine the additional coverage required beyond standard policy limits to protect against extreme losses.

Input Parameters

Enter historical loss values separated by commas

Calculation Results

Tail Coverage Results

Results will appear here after calculation

Calculation Formula

Tail Coverage = P(X > L)

Where:
P(X > L) = Probability of a loss exceeding the policy limit
L = Policy Limit
The calculation uses extreme value theory (Gumbel distribution) for large loss estimation

Tail Coverage Calculator Usage Guide

Learn how to use the Tail Coverage Calculator and understand its working principles

How to Use This Calculator

  1. Enter your policy limit: Input the maximum amount your policy will pay out per claim (e.g., $1,000,000).
  2. Input loss data: Enter historical loss values separated by commas. These should be the largest losses you've experienced. More data points provide more accurate results.
  3. Select confidence level: Choose your desired confidence level (common options are 95%, 99%, or 99.5%). Higher confidence levels require more tail coverage.
  4. Click Calculate: The calculator will determine the probability of exceeding your policy limit and estimate the expected shortfall.

Understanding Tail Coverage

Tail coverage is additional insurance that kicks in when a loss exceeds your policy limit. It's crucial for businesses with exposure to catastrophic events that could exceed standard policy limits.

Calculation Methodology

This calculator uses the Gumbel distribution, a common method for modeling extreme values. It calculates:

  • The probability of a loss exceeding your policy limit
  • The expected shortfall (ES) - the average amount by which claims exceed the policy limit in the upper tail of the distribution

Disclaimer: This calculator provides an approximation based on historical data and statistical models. Actual tail coverage needs may vary based on specific risk factors, industry standards, and underwriting considerations. Consult with an insurance professional for comprehensive coverage planning.