Financial Risk Management of Insurance Enterprises

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Financial Risk Management of Insurance Enterprises

• Options

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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
• PCLifes 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 owners point of view)
• For calls, max(S-X,0) X exercise price
• For puts, max(X-S,0) Scurrent 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 XgtS, option expires worthless
• If SgtX, option value is S-X
• Read call options left to right
• Only affects payoffs to the right of X

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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

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Basic Option Values Puts

• At maturity
• If SgtX, option expires worthless
• If XgtS, option value is X-S
• Read put options right to left
• Only affects payoffs to the left of X

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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
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Payoff Diagram Example

• Reading with calls (left to right)
• Buy one call with X10
• Sell two calls with X30
• Buy one call with X50
• Reading with puts (right to left)
• Buy one put with X50
• Sell two puts with X30
• Buy one put with X10

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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

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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?)

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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

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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
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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
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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 Lecture

• Combining the building blocks with each other to
  create new risk management products
• Combining the building blocks with debt or equity
  to create hybrid securities