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Financial Risk Management of Insurance Enterprises Interest Rate Caps/Floors

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Options on Interest Rates Last time, we discussed the basics of options Today, we apply our knowledge to options on interest rates –These are caps and floors We will see that insurance enterprises can greatly benefit from caps and floors

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Cap/Floor Terminology Strike rate is the rate which determines any cash flows of the cap or floor –Similar to the strike price or exercise price Underlying index is the interest rate that we want protection for or are speculating on Notional amount is the principal to which the interest rate will be applied to determine payoffs Up-front premium is the amount the buyer must pay to own the cap/floor

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How Caps Work Unlike a call or put option, a cap has multiple potential payoffs determined by a settlement frequency and a maturity At each settlement date, if the underlying index is below the strike rate, no payments are exchanged (aside from the premium) If the underlying index exceeds the strike rate, the seller of the cap must pay:

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An Example of a Cap A borrower has issued a floating rate note and is paying LIBOR quarterly over the next three years By purchasing a cap with a 10% strike rate, quarterly settlement frequency, a maturity of three years, and a notional amount equal to the amount of the note, the borrower can hedge its exposure to increasing LIBOR

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Using a Cap to Hedge Borrowing Costs As borrowing costs exceed the strike rate, the cap cash flows offset further increases in the underlying index Net effect is that interest expense is “capped” at 10% –This is why the option is called a “cap”

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How Floors Work Again, there are multiple settlement dates At each settlement date, if the underlying index exceed the strike rate, no payments are exchange (again, the premium is paid) If at a settlement date, the underlying index is below the strike rate, the seller of the floor must pay:

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Hedging An Asset’s Return If a security is earning a floating rate, the exposure is a drop in interest rates Buying a 6% floor puts a minimum value on the net return –Thus, the name “floor”

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Cap Values From our previous discussion, how does cap values change with respect to changes in: –Strike rate (as X increases, cap value decreases) –Current interest rate (as rates increase, cap value is higher) –Maturity (as T increases, cap value increases) –Index volatility (as F increases, caps increase) –Notional amount (value increases as amount at risk increases) –Settlement frequency (value increases as potential number of payments increase)

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The Up-Front Premium Premiums are based on percentage of notional principal This premium can be viewed as providing an annuity of interest rate protection –One policy per settlement period Net result of paying premium –Pay higher interest rate each period for protection against risk exposure (cap) –Receive lower interest for protection against low interest rates (floor)

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Methods to Lower/Eliminate the Up-Front Premium All methods give something back to lower up-front premium Interest rate collar –Protection against downside paid for by giving away some of the upside Interest rate corridor –Cap protection disappears in extreme scenarios Participating Cap/Floor –Premium paid when cap is not in the money

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Interest Rate Collar Sell floor to finance cap or sell cap to finance floor Net result is that interest expense will be between strike rates of cap and floor Can reduce premium to zero –Can even make profit

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Interest Rate Corridor Pay for cap 1 by selling cap 2 which has a higher strike rate –Sale of 2nd floor would have lower strike Protection disappears if rates move a lot Cannot reduce premium to zero

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Participating Cap Pay for cap by making payments when interest rate is below the cap Participation percentage is paid by cap “buyer” when rates decrease When index is above strike rate, same settlement as before When index is below strike, buyer pays: Participation % x(Strike-Index)x(Days/360) x(Notional Principal) As participation goes to 100%, it is a swap

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Participating Cap (60% Participation)

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Cap-Floor Parity Interest rate put-call parity is called cap- floor parity Suppose a collar strategy where strike rates on floor and cap are equal This locks in a fixed payment equal to the strike rate –This is essentially a fixed rate payor swap If this equivalent fixed swap rate is the market swap rate, then the collar strategy has zero cost (initially)

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Example 1 In the early 1980s, life insurers experienced disintermediation. Policyowners took out loans against their cash value at low rates and invested in higher yielding assets. As interest increased, the insurer had to take losses on their bond portfolios Life insurer could hedge this risk using interest rate caps –Payment on cap would be used to pay for withdrawals

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Example 2 Defined benefit pensions assume that contributions will earn an amount which will provide benefits in the future If the return on the assets is below the assumed return, the benefits are at risk Pension fund can buy a floor so that in periods of low returns, they will receive payments from the floor option

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Next Time Use of derivatives by US insurers What else insurers should be doing Reminder: Exam #1 is one week from today!

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Derivatives Workshop Actuarial Society October 30, 2007.

Derivatives Workshop Actuarial Society October 30, 2007.

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