managing financial risk for insurers swaps options
TRANSCRIPT
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Managing Financial Risk for Insurers
Swaps
Options
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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
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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
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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
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Enter Swap Contracts
• Combine loan agreements into one contract
$Principal
$Principal
and Interest£Principal
£Principal
and Interest
0 1 2 T-1TTime
$Int $Int $Int
£Int £Int £Int
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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
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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
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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?
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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
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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
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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
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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
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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
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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
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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
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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
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Interest Rate Swap
NP*Rfix NP*Rfix NP*Rfix NP*Rfix
NP*Rfloat NP*Rfloat NP*Rfloat NP*Rfloat
Cash flows for fixed rate receiver
Time
0 1 2 T-1 T
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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
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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
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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
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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
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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
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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
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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
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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?)
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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
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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”
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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)
X
Asset Value
Cal
l Val
ue
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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)
X
Asset Value
Cal
l Val
ue
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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)
X
Asset Value
Pu
t V
alu
e
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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
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Payoff Diagram ExampleName two options strategies used
to get the following payoff
Long Straddle
-10
-5
0
5
10
15
20
25
10 20 30 40 50
Asset Value
Stra
ddle
Val
ue
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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
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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
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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 ( )
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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
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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
N = Normal distribution function
)()( 21 dNrtXedSNC
2/112
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ttrXSd
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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
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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%
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Answer
02.1
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)3768.(20)1768.(18
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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
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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
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Hedging Copper Prices
0
5
10
15
20
25
30
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Copper Price
Pri
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aid
CallCopperNet
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Additional Uses of Options
• Interest rate risk
• Currency risk
• Equity risk– Market risk– Individual securities
• Catastrophe risk
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Next
• Interest rate caps and floors