26.3 Approaches to Modeling the Cycle

3 approach:

  1. Soft approach

  2. Technical approach

  3. Behavioral modeling (Econometric)

Below show the importance of the dimension to each style:

  • Data quantity, variety and complexity

    Soft > Behavioral > Technical

  • Recognition of human factors

    Soft > Behavioral > Technical

  • Mathematical formalism and rigor

    Technical > Behavioral > Soft

Before we model, first we define what it is we want to know and look for leading indicators that foretell the turn in the cycle:

Criterion Variable

  • What variable we are interested in?

  • Conceptually we want price

    • e.g. Price to coer a standard risk

    • But impossible to define in insurance

  • Use loss ratio or combined ratio etc as a proxy

    • Maybe with adjustments for TVM (e.g. include investment income)

Predictor Variable:
Information available to calculate the current period criterion and also forecast the forward period criterion

  • Historical criterion variable and it’s components:

    (e.g. loss, expense)

  • Internal financial variables:

    (e.g. reserve, capital, capital flow, reinsurance cessions)

  • Regulatory rating variables:

    (e.g. downgrades and upgrades)

  • Reinsurance sector financials:

    (e.g. capital held by reinsurers)

  • Econometric variable:

    (e.g. inflation, unemployment, GDP)

  • Financial market variables:

    (e.g. interest rates, stock market returns)

Competitor Intelligence:
Gather information on customers at renewal time and competitors (e.g. Firm’s own agents, customere surveys at renewal, trade publications/news, rate filing)

  • Provides more detailed information on the state of the u/w cycle

  • Need to beware of antitrust and legal issues (e.g. industrial spying)

  • Goal is to look for leading indicatiors that foretell the turn in the cycle

26.3.1 Soft Approach

Starts with intense focus on data gathering and intelligence

Goal: Give analysts insight into the complex u/w cycle

  • Collect as much information as we can

This is a human approach, focused on three methods:

  1. Scenarios

    Detailed written statement describing a possible future state of the world

    • Help company think about how it might respond to different future states

    • Goal is to have a detailed description of the environment and analyzed by minds

  2. Delphi Method

    Gather expert opinion without biasing the group to the opinion of the most senior persons

    Process:

    1. Give background to participants

    2. Gather opinions using questionnaire

    3. Results are summarized and distributed

    4. Allow participants to reconsider and articulate reason for disagreeing

    5. Repeat until consensus is reached

  3. Formal Competitor Analysis

    • First determine current state, motives, and likely behavior for the main competitors

    • Need database of competitor information that has key financials, new items, and behavioral metrics

    • Overtime, distinction between normal and abnormal statistics becomes evident

    • Key to predicting turns in the u/w cycle is unusually profitable or distressed financial conditions reproduced over a large number of firms

26.3.2 Technical Approach

Focus here is on a small number of industry financial statistics (possibly only 1)

  • We have at best only a rudimentary theory underlying the model

Autoregressive Model

Research shown cycle can be modeled with \(AR(2)\) or \(AR(3)\) model

For \(AR(2)\):

\[X_t = b_o + b_1 X_{t-1} + b_2 X_{t-2} + \sigma \epsilon_t\]

Use autoregressive model to model P&C industry combined ratios

  • Results showed weak mean regression with lag 1 but strong mean regression at lag 2

  • Model can be used to forecast a few periods into the future and estimate the distribution for those forecasts

VARMAX

Generalized multivariate time series that can handle multiple simultaneous variable and utilize external variables

General Factor Model

  • Looks like \(AR(1)\) but with non-normal mean and a moving temporary mean (determined by \(z_{t-1}\))

\[X_t = c + d(Z_{t-1} - X_{t-1}) + \tau \delta_t\]

  • \(Z_t = a + b \cdot Z_{t-1} + \sigma \epsilon_t\)

  • \(Z_t\) maybe an unknown or unobservable variable

  • Neither error term needs to be normal

Complicated to fit this model

  • Generalized method of moments or efficient method of moments

26.3.3 Behavioral Modeling

Econometric Modeling

  • Sit between soft and technical model’s concern for structural insight (soft) and statistical validity (technical)

  • Same as soft approach:

    • Where we need large quantity, variety and complexity of data

    • Recognize human factors

  • Same as technical approach:

    • Require mathematical formalism

    • Tehcnical \(\Rightarrow\) statistical validity

Can be done at an industry level or company level

  • Industry level can be more detailed

  • Company level requires maintaining many individual models and their interactions

    • Can lead to insight from emergent properties (See ERA 4.2)