Managing Financial Risk for Insurers

Swaps

Options

Overview• What is a swap contract?• Which swap contracts are most popular?• How is an interest rate swap structured?• How does a swap contract differ from forwards and

futures?• What are some applications of swaps?• Options - puts and calls• What is the difference between options and other

derivative contracts?• Applications of option contracts

Why Did Swap Contracts Evolve?

• Breakdown of the Bretton Woods system of fixed exchanged rates occurred in the early 1970s

• Companies were exposed to exchange rate volatility if they had foreign subsidiaries

• Profits produced by subsidiary, when translated to dollars, produced losses– e.g., the dollar price of foreign currencies was uncertain

• Wanted a hedge to protect against FX volatility

Before Swaps

• Companies used parallel back-to-back loans

• Interest paid on borrowing is in foreign currency, interest received is in dollars– Principal amount of loans selected so that interest

payments equal income of subsidiary

• Problems with back-to-back loans– Default of counterparty did not release obligation– Inflated balance sheet amount of debt

Enter Swap Contracts

• Combine loan agreements into one contract

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Currency Swap

• On each settlement date, the US company pays a fixed pound interest rate on a notional amount of pounds and receives a dollar amount of interest on a notional amount in dollars

• Since the interest rate is fixed, the only change in value is due to change in FX rate

• Using netting, only one party pays the difference between cash flow values

Currency Swap Example• A pension fund holds a 1,000,000 DM face value,

5-year German bond and is exposed to a decrease in the value of DM. The bond pays a coupon of 20,000 quarterly

• To hedge the risk, the pension fund uses a currency swap where it pays 20,000 DM every quarter including a 1,000,000 DM payment in 5 years

• The pension fund receives $30,000 quarterly and will receive $1,500,000 at maturity

Currency Swap Example (p.2)• The pension fund has essentially locked in an

exchange rate of 0.6667 DM/$1• If in 3 months, the spot exchange rate has changed

to 0.65DM/$1, the pension fund pays (20,000/0.65-30,000)=$769 or (20,000-30,000 x 0.65)=500 DM

• A similar settlement occurs every 3 months for 5 years based on the prevailing spot price

• At maturity, include the principal payments– Why did we ignore the principal at initiation?

Swap Contract Provisions

• An agreement between two parties to exchange (or swap) periodic cash flows

• At each payment date, only the net value of cash flows is exchanged

• The cash flows are based on a notional principal or notional amount

• The notional amount is only used to determine the cash flows

Other Swaps

• Although concerns of foreign currency volatility were the primary force behind the evolution in swaps, other swaps are commonly used

• Currency-coupon or cross-currency interest rate swap– Still two different currencies– One interest rate is a fixed rate, one rate is floating

Other Swaps (p.2)

• Interest rate swap– Special case of currency-coupon swap: there is only

one currency– Two interest rates: one fixed and one floating– Interest rate swaps are now the most actively traded

type of swap contract– We will see its usefulness to insurers

• Basis-rate swap or basis swap– Interest rate swap with two floating rates

Other Swaps (p.3)

• Commodity swap (e.g., oil swap)– Notional principal is in units of a commodity

– Over the entire life of the swap, one party pays a fixed price per commodity unit, the other party pays a floating price

• Equity swap– One party pays the return on an equity index (such as

the S&P 500) while receiving a floating interest rate

– Really a type of basis swap

Commodity Swap Example• P/L insurer expects to pay claims over the next 4 years

on existing policies. A portion of the claims are based on lumber costs. Insurer estimates that it will require 80,000 board-feet of lumber every 6 months.

• Insurer is exposed to increasing lumber prices

• Forward contracts are liquid for short-term only. Insurer can lock in a fixed price by entering into a swap with a notional amount of 80,000 board-feet of lumber at a price of $350 per 1,000 board-feet

Commodity Swap Example (p.2)• In 6 months, if the spot price of lumber increases to $400

per 1,000 board-feet, the insurer receives (400-350) x 80 =$4,000– The gain on the swap will offset the higher cash prices that the

insurer pays on lumber

• Now, one year into the swap, scientists invent a seed for a quick-growing tree which increases the supply of lumber, and the price of lumber drops to $250 per 1,000 board-feet, the insurer must pay $8,000

• Net effect is fixed price for 80,000 board-feet

A Closer Look at Interest Rate Swaps

• One party pays a fixed interest rate while receiving a floating rate payment

• Typical contract:– Floating rate is LIBOR (note, this has credit

risk)– Settlement is quarterly

• However, interest rate swaps are privately negotiated so anything goes

A Closer Look at Interest Rate Swaps (p. 2)

• Assume a quarterly settlement• At the first settlement date (in three months),

the floating rate is (current) spot 3-month LIBOR

• For future periods, the floating side is determined by the future level of LIBOR

• At settlement, the payment is based on the difference of LIBOR and the fixed rate times the notional principal

Interest Rate Swap

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Cash flows for fixed rate receiver

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Why Use Interest Rate Swaps?• Essentially translates a fixed cash flow into a

floating cash flow (or vice versa)

• Companies with interest rate exposure can adjust their interest rate risk

• Insurers with long term assets and shorter term liabilities can enter a swap in which they pay a fixed rate and receive a floating rate– This swap provides cash inflows if interest rates rise

Pricing Swap Contracts• The value of a swap can be calculated from

spot rates and forward rates

• Swap contracts have an initial value of zero

• Set fixed rate so that NPV of swap is zero

• Example: what is the required fixed swap rate if the 6-month spot rate is 8% per year and the 1-year spot rate is 10% per year– Assume semi-annual settlements

Pricing an Interest Rate Swap

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Interest Rate Swap Market• Evolution of market based on hedging opportunities

available to broker• Initially, market was slow

– Swaps are privately negotiated– Finding counterparty with exact notional amount, maturity,

etc. took time

• Now, brokers hedge fixed/floating swaps with Eurodollar futures until counterparty is found– Underlying rate of future is quarterly LIBOR– Eurodollar futures is most active futures market

Credit Risk of Swap Contracts• Swap is portfolio of forward contracts

– Long-term forwards are illiquid, however

• Credit risk of swaps is between forwards and futures due to performance period

• Notional principal is not good for measuring risk exposure

• Default risk must take into account:– Risk is only percentage of notional amount– Netting reduces risk to difference of payments– Some of the time you are a net receiver

What is an Option Contract?• Options provide the right, but not the obligation, to buy or

sell an asset at a fixed price– Call option is right to buy

– Put option is right to sell

• Key distinction between forwards, futures and swaps and options is performance– Only option sellers (writers) are required to perform under the

contract (if exercised)

– After paying the premium, option owner has no duties under the contract

Some Terminology

• The exercise or strike price is the agreed on fixed price at which the option holder can buy or sell the underlying asset

• Exercising the option means to force the seller to perform– Make option writer sell if a call, or force writer to

buy if a put

• Expiration date is the date at which the option ceases to exist

More Terminology

• American options allow holder to exercise at any point until expiration

• European option only allows holder to exercise on the expiration date

• The premium is the amount paid for an option

A Simple Example• Suppose PCLife owns a European call option on IBM

stock with an exercise price of $100 and an expiration date of 3 months

• If in 3 months, the price of IBM stock is $120, PCLife exercises the option– PCLife’s gain is $20

• If at the expiration date the price of IBM is $95, PCLife lets the option expire unexercised

• If the price of IBM in one month is $3,000, PCLife will not exercise (Why not?)

Option Valuation Basics• Two components of option value

– Intrinsic value– Time value

• Intrinsic value is based on the difference between the exercise price and the current asset value (from the owner’s point of view)– For calls, max(S-X,0) X= exercise price– For puts, max(X-S,0) S=current asset value

• Time value reflects the possibility that the intrinsic value may increase over time– Longer time to maturity, the higher the time value

In-the-Moneyness

• If the intrinsic value is greater than zero, the option is called “in-the-money”– It is better to exercise than to let expire

• If the asset value is near the exercise price, it is called “near-the-money” or “at-the-money”

• If the exercise price is unfavorable to the option owner, it is “out-of-the-money”

Basic Option Value: Calls

• At maturity– If X>S, option expires

worthless

– If S>X, option value is S-X

• Read call options left to right– Only affects payoffs to

the right of X

Call Value at Maturity(Long Position)

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Basic Option Value: Calls (p.2)

• Of course, for the option writer, the payoff at maturity is the mirror image of the call option owner

Call Value at Maturity(Short Position)

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Basic Option Values: Puts

• At maturity– If S>X, option expires

worthless

– If X>S, option value is X-S

• Read put options right to left– Only affects payoffs to

the left of X

Put Option(Long Position)

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Combining Options and Underlying Securities

• Call options, put options and positions in the underlying securities can be combined to generate specific payoff patterns

Payoff Diagram ExampleName two options strategies used

to get the following payoff

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Payoff Diagram Example

• Reading with calls (left to right)– Buy one call with X=10– Sell two calls with X=30– Buy one call with X=50

• Reading with puts (right to left)– Buy one put with X=50– Sell two puts with X=30– Buy one put with X=10

Determinants of Call Value• Value must be positive

• Increasing maturity increases value

• Increasing exercise price, decreases value

• American call value must be at least the value of European call

• Value must be at least intrinsic value

• For non-dividend paying stock, value exceeds S-PV(X)– Can be seen by assuming European style call

Determinants of Call Value (p.2)

• As interest rates increase, call value increases– This is true even if there are dividends

• As the volatility of the price of the underlying asset increases, the probability that the option ends up in-the-money increases

Thus, )C C S X T r

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Put-Call Parity• Consider two portfolios

– One European call option plus cash of PV(X)– One share of stock plus a European put

• Note that at maturity, these portfolios are equivalent regardless of value of S

• Since the options are European, these portfolios always have the same value– If not, there is an arbitrage opportunity (Why?)

Therefore, C PV X P S ( )

Fisher Black and Myron Scholes• Developed a model to value European options on stock• Assumptions

– No dividends– No taxes or transaction costs– One constant interest rate for borrowing or lending – Unlimited short selling allowed– Continuous markets– Distribution of terminal stock returns is lognormal

• Based on arbitrage portfolio containing stock and call options

• Required continuous rebalancing

Black-Scholes Option Pricing Model

C = Price of a call option

S = Current price of the asset

X = Exercise price

r = Risk free interest rate

t = Time to expiration of the option

= Volatility of the stock price

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Using the Black-Scholes Model

• Only variables required– Underlying stock price

– Exercise price

– Time to expiration

– Volatility of stock price

– Risk-free interest rate

Example

• Calculate the value of a call option with– Stock price = $18– Exercise price = $20– Time to expiration = 1 year– Standard deviation of stock returns = .20– Risk-free rate = 5%

Answer

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Use of Options

• Options give users the ability to hedge downside risk but still allow them to keep upside potential

• This is done by combining the underlying asset with the option strategies

• Net position puts a floor on asset values or a ceiling on expenses

Hedging Commodity Price Risk with Options

• P/C insurer pays part of its claims for replacing copper plumbing

• Instead of locking in a fixed price using futures or swaps, the insurer wants to get a lower price if copper prices drop

• Insurer can buy call options to protect against increasing copper prices

• If copper prices increase, gain in option offsets higher copper price

Hedging Copper Prices

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Additional Uses of Options

• Interest rate risk

• Currency risk

• Equity risk– Market risk– Individual securities

• Catastrophe risk

Next

• Interest rate caps and floors