Introduction to
Derivative 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
Buy A Call
V
Buy A Put
P
V
P
V
Sell A Put
Sell A Call
P
P
Options
• Options have a Time Value and an Intrinsic Value
V
Call option value
Time value
Intrinsic value
P
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
Low Vol. Asset
Probability
High Vol. Asset
Fwd Strike
Price Price
Price of
Underlying
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
Gain/Loss
Cap
Interest
Rate
Premium
Strike
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
Interest Rates
Decrease
Increase
Yes
No Cover
Sell Assets, Pay Losses
Covered
Collect Reinsurance
No
No Cover, No Losses
Catastrophic
Event
No Cover, No Losses
• Reinsured pays a premium to purchase cover if two different
risk events occur
– The correlations between the two events are low or nonexistent
– 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
Double Trigger Cover
Equity Protection
Stock Market
Increase
Catastrophic
Event
Yes
No Cover
Sell Assets, Pay Losses
No
No Cover, No Losses
Decline
Covered
Collect Reinsurance
No Cover, No Losses
Falcon’s Integrated Risk Management Process
Step 1
Evaluation and Simulation of Economy(s)
and Capital Market(s)
Step 2
Evaluation and Simulation of Balance Sheet Items



Business mix
Reinsurance strategy
Mergers, Acquisitions and
Divestitures


Step 3

Surplus Optimization
(Efficient Frontier)
Step 4
Analysis of Results:
- Decomposition of Risk
- Downside Analysis
- RBC
- Solvency
Step 5
Sensitivity Testing
Strategic Business Decisions
Investment Strategy
Derivatives
Capital Allocation/Structure
PCIC Company Profile

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
Traditional Cover

Aggregate CAT cover: 300 x 100 calendar year loss
ratio from CATs

Price: 30% of subject earned premium

Placement: 50%

No reinstatements or rebates
Dual Trigger Cover
Income Smoothing

Aggregate CAT cover: 300 x 100 calendar year loss
ratio from CATs

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%

No reinstatements or rebates
Shareholder's Equity Efficient Frontier
3-Year Time Horizon
880.0
860.0
840.0
Shareholder's Equity ($mm)
820.0
800.0
780.0
760.0
Current Reinsurance
740.0
720.0
700.0
140.0
160.0
180.0
200.0
220.0
240.0
Standard Deviation of Shareholder's Equity ($mm)
Current
260.0
280.0
Shareholder's Equity Efficient Frontier
3-Year Time Horizon
880.0
860.0
840.0
Shareholder's Equity ($mm)
820.0
800.0
780.0
Current Reinsurance
760.0
740.0
Traditional Cover
720.0
700.0
110.0
130.0
150.0
170.0
190.0
210.0
230.0
Standard Deviation of Shareholder's Equity ($mm)
Current
Traditional Cover
Efficient Frontier
250.0
270.0
290.0
Shareholder's Equity Efficient Frontier
3-Year Time Horizon
880.0
860.0
840.0
Shareholder's Equity ($mm)
820.0
800.0
780.0
Current Reinsurance
760.0
Dual Cover
740.0
Traditional Cover
720.0
700.0
110.0
130.0
150.0
170.0
190.0
210.0
230.0
250.0
Standard Deviation of Shareholder's Equity ($mm)
Traditional Cover
Current
Dual Cover
Efficient Frontier
270.0
290.0
Myth Company Profile

Similar book to PCIC

More heavily reinsured

More aggressive investment strategy: 50% stocks, 50%
short-term bonds
Traditional Cover

Aggregate CAT cover: 300 x 100 calendar year loss
ratio from CATs

Price: 25% of subject earned premium

Placement: 50%

No reinstatements or rebates
Dual Trigger Cover
Catastrophe Protection

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%

No reinstatements or rebates
Shareholder Equity
End of Year: 3 out of 3
850,000
800,000
750,000
700,000
650,000
600,000
550,000
500,000
450,000
400,000
Current Reinsurance
1% to 5%
Traditional Cover
5% to 25%
Dual Cover
25% to 50%
50% to 75%