Catastrophic risks and the pricing of catastrophe equity put options

Area of Science:

• Quantitative Finance
• Risk Management
• Actuarial Science

Background:

• Insurance companies utilize financial strategies to hedge catastrophic risks.
• Catastrophe equity put options (CatEPuts) are crucial financial instruments in this hedging context.
• Existing models often lack practical application with real-world data.

Purpose of the Study:

• To develop and implement a practical option pricing model for CatEPuts.
• To calibrate the model using historical financial data.
• To evaluate CatEPuts on a major Italian insurance company's stock during a volatile period.

Main Methods:

• A novel option pricing model is developed, incorporating a compound Poisson process with negative jumps to represent catastrophic events.
• A calibration framework is proposed, utilizing historical log-returns, market capitalization, and option implied volatilities.
• The calibrated model is applied to price CatEPuts on a specific stock during January-April 2020.

Main Results:

• The study presents a pricing approach for CatEPuts that can be implemented with real data.
• The ratio of plain-vanilla put options to CatEPuts is found to be dependent on the implied volatility smile's shape.
• This ratio exhibits significant variation over the observed high-volatility period.

Conclusions:

• The developed CatEPut pricing model offers a practical tool for the insurance industry.
• Implied volatility smiles are key determinants in the relative pricing of CatEPuts versus standard put options.
• Dynamic market conditions, particularly volatility, significantly influence the effectiveness and pricing of CatEPut strategies.