Introduction to Derivative Products and DFA

Introduction toDerivative Products

and DFA • Lawrence A. Berger, Ph.D.

– Swiss Re New Markets• Daniel B. Isaac, FCAS

– Falcon Asset Management Division of Swiss Re

• DFA Seminar: Managing Risk in a Portfolio Context

What Is A Derivative?

• Financial instrument whose value is derived from the performance of an “underlying asset”

• Refer to “cash price,” or “spot price” of the underlying

What Is An Underlying Asset?

• Can be anything

• Performance should be quantifiable

• Some examples are:

– Interest Rates

– Equities

– Foreign Exchange Rates

– Commodities

– Indices

– Loss Ratios

How Is A Derivative Created?

• Derivative product is a contractual agreement between two parties to either:

– exchange cash flows, or

– have one party assume a risk of the other party for a price

• Derivative product uses the “underlying asset” as a basis for the exchange

Options

• An Option Contract gives the owner the right, but not the obligation, to buy or sell an underlying asset at an exercise price on or before an agreed date

– Call = Right to buy at X

– Put = Right to sell at X

Options

V

P

V

P

Buy A PutV

P

V

P

Buy A Call

Sell A Put Sell A Call

Options

• Options have a Time Value and an Intrinsic Value

Call option value

Time value

P

V

Intrinsic value

Options Summary

• Intrinsic Value

– Call = Max(P-X,0)

– Put = Max(X-P,0)

• Option Premium = Intrinsic value plus time value

Pricing an Option

• Calculations dependent on several factors

– Spot price of underlying asset

– Strike price - price at which option allows owner to purchase or sell underlying asset

– Interest rates

– Volatility - measure of frequency and relative size of changes in price of underlying asset

– Time to expiration

Volatility

Probability

Price of UnderlyingAsset

StrikePrice

FwdPrice

Low Vol. Asset

High Vol. Asset

Interest Rate Cap

• An agreement where the seller agrees to pay the buyer, in return for a premium, the difference between the reference rate and an agreed strike rate should the reference rate rise above the strike

Cap Payoff Profile

Cap

Interest Rate

Gain/Loss

Strike

Premium

Cap = Hedge High Rates

• An interest rate cap is essentially an insurance policy against interest rates rising

• A cap buyer is protected against rates rising beyond the strike

• A cap seller receives a fee and gives up return if rates rise beyond strike

Double Trigger Cover

• Reinsured pays a premium to purchase cover if two different risk events occur

– The correlations between the two events are low or non-existent

– Lack of correlation allows for lower premiums

• Example: interest rate option with catastrophe trigger

– Option protects against losses on portfolio of fixed income instruments

– Option is exercisable only after Cat event

Interest Rates

CatastrophicEvent

No

Yes

IncreaseDecrease

No Cover Sell Assets, Pay Losses

No Cover, No Losses

CoveredCollect Reinsurance

No Cover, No Losses

Double Trigger CoverEquity Protection

Stock Market

CatastrophicEvent

No

Yes

DeclineIncrease

No Cover Sell Assets, Pay Losses

No Cover, No Losses

CoveredCollect Reinsurance

No Cover, No Losses

Falcon’s Integrated Risk Management Process

Evaluation and Simulation of Economy(s)and Capital Market(s)

Evaluation and Simulation of Balance Sheet Items

Surplus Optimization(Efficient Frontier)

Sensitivity Testing

Strategic Business Decisions

Step 1

Step 2

Step 3

Step 4

Step 5

Business mix Reinsurance strategy Mergers, Acquisitions and

Divestitures

Analysis of Results:- Decomposition of Risk- Downside Analysis- RBC- Solvency

Investment Strategy Derivatives Capital Allocation/Structure

Primarily short-tailed property business

Large portion (~50%) of book is CAT exposed

As a result of large liability risk, very conservative investment strategy: 20% cash, 80% bonds

PCIC Company Profile

Aggregate CAT cover: 300 x 100 calendar year loss ratio from CATs

Price: 30% of subject earned premium

Placement: 50%

No reinstatements or rebates

Traditional Cover


Recovery reduced based on S&P 500 return: Below 0%: No reduction Above 20%: Zero recovery Between 0% and 20%: Pro-rata reduction

Price: 12.5% of subject earned premium

Placement: 100%


Dual Trigger CoverIncome Smoothing

Shareholder's Equity Efficient Frontier3-Year Time Horizon

Current Reinsurance

700.0

720.0

740.0

760.0

780.0

800.0

820.0

840.0

860.0

880.0

140.0 160.0 180.0 200.0 220.0 240.0 260.0 280.0

Standard Deviation of Shareholder's Equity ($mm)

Sh

are

ho

lde

r's

Eq

uit

y (

$m

m)

Current


Current Reinsurance

Traditional Cover

700.0

720.0

740.0

760.0

780.0

800.0

820.0

840.0

860.0

880.0

110.0 130.0 150.0 170.0 190.0 210.0 230.0 250.0 270.0 290.0


Sh

are

ho

lde

r's

Eq

uit

y (

$m

m)

Current Traditional Cover Efficient Frontier


Traditional Cover

Current Reinsurance

Dual Cover

700.0

720.0

740.0

760.0

780.0

800.0

820.0

840.0

860.0

880.0

110.0 130.0 150.0 170.0 190.0 210.0 230.0 250.0 270.0 290.0


Sh

are

ho

lde

r's

Eq

uit

y (

$m

m)

Traditional Cover Current Dual Cover Efficient Frontier

Similar book to PCIC

More heavily reinsured

More aggressive investment strategy: 50% stocks, 50% short-term bonds

Myth Company Profile


Price: 25% of subject earned premium

Placement: 50%


Traditional Cover

Notional Amount: 75% of earned premium

Trigger: Calendar year loss ratio of at least 75%

Recovery based on S&P 500 return: Below -20%: 100% of notional Above 0%: Zero recovery Between 0% and -20%: Pro-rata reduction

Price: 3% of earned premium

Placement: 100%


Dual Trigger CoverCatastrophe Protection

400,000

450,000

500,000

550,000

600,000

650,000

700,000

750,000

800,000

850,000

Current Reinsurance Traditional Cover Dual Cover

1% to 5% 5% to 25% 25% to 50% 50% to 75%

End of Year: 3 out of 3Shareholder Equity

Introduction to Derivative Products and DFA

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