Applications of actuarial techniques in financial markets

Larry Marcus, FCAS, MAAA, CFA Chief Actuary Zurich Structured Solutions Group CAS Meeting November 13, 2007

Agenda – Three kinds of interactions between insurance and capital markets

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D&O pricing – using financial markets to assist in insurance pricing

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Mortgage wraps – insurance on the capital markets

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Contingent derivatives – hybrid of insurance and capital markets

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Insurance products

Using financial markets insights to price directors & officers insurance

Directors & officers insurance

• • • • • • © Zurich Although directors & officers (D&O) insurance covers a number of different claims, by far the largest cases are securities cases.

Large D&O losses are class actions that generally allege malfeasance, misrepresentations and non-disclosure of material facts as soon as any bad news is discovered or announced.

Generally these suits follow large stock drops.

The damages alleged are very closely related to the stock price drop.

Thus D&O awards claims payments can be thought of as “stock drop insurance.” Stock drop insurance is also known as a put option on a stock.

This option, unlike an ordinary put is dependent on alleged wrongdoing; a stock that fell due to a market crash probably would not be targeted.

The wrong doing must be sufficient to either win in court or at least produce a settlement.

Losses will be a fraction of the stock price drop since the affected class would not be all stockholder, but only those who bought after the alleged wrongdoing began.

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Using financial markets information to underwrite D&O insurance

• • • • • • • Based on the intuition above, the financial markets can provide much information to typical underwriting evaluations.

D&O underwriters may be financially astute, but they probably do not have the tools and insight of Wall Street analysts, and certainly not the entire financial market.

Wall Street may also have some inside information that is (in some cases illegally) being traded on.

Stock price volatility is a good indicator of D&O risk. High-flyers, and companies with wild stock prices, are more likely to have risky business models.

Put prices are a forward view of a company’s downward prospects.

Credit spreads and credit default swaps are also an assessment of riskiness.

Large bankruptcies almost inevitably lead to D&O suits Short interest is another measure of Wall Street skepticism.

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Damages determined by market cap drop

• • • Market cap drop = price drop x market cap Market cap is key to ILF’s The larger the account, the higher the ILF Very large companies should see very little price decrease by layer, since a price drop has to be relatively large to draw a suit.

The market cap intuition also tells you that a pre-existing drop in the stock price may give rise to a claim. Since policies are claims made, selling insurance on to a company with a large stock price is difficult.

Need to separate out market movements from unique company factors that may cause damages.

Note that looking at financial price indicators means pricing is not very stable, which does make customer and broker relations more difficult than a more stable rating.

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Zurich model

• • • • • • Developed by VJ Amstislavskiy, FCAS, MAAA Simulation based on Black-Scholes model and different indicators of volatility History, options implied volatility Claim probability dependent on price percentage drop relative to the size of the company Severity of losses are a function of market cap drop Additional component for bankruptcy based claims Adjusted Black-Scholes model from Harvard; gives the probability of market value of assets dropping below its liabilities Other models incorporate credit spreads and credit default swap pricings © Zurich 7

Structured finance

Mortgage insurance and financial guaranties

Mortgage insurance and financial guaranties

• • • Both mortgage insurers and financial guaranties are incorporated as property and casualty insurance companies, but require special licensing.

Reserves require actuarial opinions just like any other P&C company.

Primary mortgage insurance guarantees banks that individual borrowers will make good on their payments to banks. Usually required for most ordinary prime mortgages made with less than 20% down (known as 80% loan to value).

Most of these loans and the associated insurance go into pools which are securitized and get guaranteed by FNMA or FHMC (Fannie Mae and Freddie Mac).

But ordinary mortgage insurance can also be done on a pool of mortgages as an excess of loss contract.

Sometimes these pools are reinsured by captives of banks, again on a further excess of loss basis.

These will also go into mortgage securities and help support the rating of these bonds.

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Financial guaranties

• • Financial guaranties, also known as wraps, guarantee the full interest and principal of insured bonds to investors directly.

Considered better than ordinary mortgage insurance by investors and bond rating agencies because they pay the investors directly without fail since: They have no exclusions.

Claims can’t be denied.

Ordinary mortgage insurance has a number of exclusions, the most relevant one for property insurance type perils.

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Actuarial (type) analysis for insurance and guaranties

• • Need to analyze loss potential for mortgage defaults Default pattern varies with time rising from inception, peaking after a few years and then declining.

A default model needs to look at a large number of credit risk variables: Credit score Housing prices Loan to value ratio Interest coverage (interest/income) Primary residence or investment property Mortgage type and terms Multi-variate regressions are used to analyze default probabilities Stochastic methods are required to analyze pool policies since these are excess of loss.

Loss size given default need to be analyzed, as well, with similar variables © Zurich 11

The other key variable

• • • A second important variable that must be analyzed is mortgage prepayment rate.

Prepayments are an early return of principal due to refinancing, home sale or just the desire of borrowers to get rid of their mortgage.

Functions like lapse rates in life insurance.

Losses are avoided if the pool prepays early.

Prepayment pattern is slow at first, accelerates and then decelerates.

Key variables are: Mortgage rate Change in mortgage rates in the market Housing prices Mortgage type and terms © Zurich 12

Bond guaranties are much more complex

• • • • • • • • In addition to figuring in default, the structure of the bond is a key variable.

Bond payments are scheduled principal and interest, but also include prepayments of principal.

Bonds are generally tranched into a different number of smaller bonds with different credit ratings and different interest rates.

Senior bonds rated AAA are protected by a series of lower rated bonds.

Subordinated bonds (lower rated) are written off when defaults get too high.

Bonds are also protected by excess interest generated by the mortgages themselves above the promised bond interest rates.

Not a simple excess of loss calculation as prepayments and default losses all interact with the bonds structure Principal and interest are redirected to senior bonds if default rates get too high. Rules of allocating principle and interest are lengthy and complex.

Prepayments can help lower default costs, but also lower collected interest.

Thus bond guaranty models are as complex as virtually any insurance model, but can be understood by an actuary willing to devote the time and effort.

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Commodity markets

Using a mix of insurance and financial market insights to price a product for the power industry

Power markets

• • • • • Electrical power after years of being dominated by vertically integrated utilities was deregulated.

This created an open commodity market for wholesale power, where merchant generators build or buy power plants and sell the output to distribution utilities who provide it to end users.

Since power is a real time commodity that can not be stored, the price of wholesale power at any moment varies dramatically, depending on generation (supply) and load (demand).

In addition, the cost of blackouts is extremely prohibitive to distribution utilities, thus they need to buy enough power at virtually any price.

Power can be a dramatically volatile market.

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Power is a volatile commodity

NYC Hourly Power Prices - 5:00 PM

1,400 1,200 1,000 800 600 400 200 0 © Zurich 16

Power risk management

• • • • • Power suppliers have to be careful to have enough power for really hot (or potentially hot) days, by procuring enough supply.

The traditional way to do this was to buy extra power in advance in the commodity markets.

Power, like any actively traded commodity, can be bought in three ways: In the spot markets (hourly) As a forward or futures agreement (guaranteed constant delivery for a fixed price no matter what the spot price) As an options agreement (delivery for a fixed price at the option of the purchaser) Since power comes from real machines, it can be bought two ways – either: Financially firm (delivery guaranteed or liquidated damages paid) Unit contingent (delivery only if a power plant is up and running) Being guaranteed, financially firm power is considerably more expensive, because of the risk of non-performance.

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Power options

• • • • • • Buying power options is the traditional way to purchase power for peak demand times.

In reality, this “option” is a gas turbine (power plant) with a high fuel cost that can be turned on and off when needed.

However, this option isn’t always reliable since it can break down.

Thus, electricity suppliers buy (or often build) more options than they expect to need on average to have a margin of safety for breakdowns.

Ultimately this is inefficient, since some plants or options may never be needed.

Thus some other type of protection was needed.

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An insurance solution

• • Ordinary property insurance doesn’t work Waiting period for BI of 30 to 60 days Limits on reimbursement Exclusion for causes of loss Solution: Cover only the value of loss power, not value of the plant itself Dual trigger program Reimbursement only comes when: The power plant is out, subject to few systematic exclusions.

The value of lost power is greater than a preordained price.

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A more efficient solution

• Insurance offers a solution more efficient than a physical solution because financial instruments are generally more flexible than physical contracts.

© Zurich strike market price

Typical Call Option

strike market price no event no event

Insurance Solution

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How do you price this insurance

• • Typical property insurance rating plans are useless for a product this distinct.

Need to return to fundamentals of frequency and severity Simple answer: Premium = (percent of time plant is out) x (value of power xs strike) + markup = forced outage rate x option price + markup More complex technique: Time series simulations of both outages and power prices © Zurich 21

Outages

• • • • • • Good outage data is available.

This is a consequence of being a regulated industry.

Industry plant outage time readily available through industry data.

More complex statistics can be purchased from the NERC.

Outage calculations are purely actuarial Simulating outages Simulate plants going down (exponential waiting period – implies Poisson frequency) Outage time distributions are fit to industry data Plenty of interpretation and judgment is required.

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Power prices

• • • • • • Are trickier to estimate than outages.

Market is dynamic and depends highly on: Supply (new power plants built, old ones retired, extended repairs) Demand (population growth, increased use of electronics, weather) Can use historical data but need to adjust for above factors.

Better to use commodity market prices for modeling Better to use forward prices for expected prices Use options prices to determine volatility structure Need to estimate risk premium in commodity prices Look at the history to estimate stretches of high and low prices Match up outage sequences with price sequences in your simulation to determine cost of insurance With simulation results you can price innumerable structures © Zurich 23

Uses

• Utilities can buy these products to protect themselves from losses due to untimely plant outages.

• Merchant generators (independent power producers) can use these to sell their electricity at a premium price by guaranteeing deliver or liquidated damages.

• Energy traders can buy power from a generator on a unit contingent basis, buy the insurance and resell it financially firm and capture arbitrage profits.

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An insurance product or a capital markets product?

• Can be described as either © Zurich 25

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