1. Financial Risk Management of Insurance Enterprises
Options 1

2. 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 2

3. 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 3

4. 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 4

5. 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?) 5

6. 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 6

7. 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” 7

8. 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 8

9. 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 9

10. 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 10

11. Combining Options and Underlying Securities
Call options, put options and positions in the underlying securities can be combined to generate specific payoff patterns

12. Payoff Diagram Example Name two options strategies used to get the following payoff11

13. 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 12

14. 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 13

15. 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 14

16. 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?) 15

17. 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

18. 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

19. Using the Black-Scholes Model
Only variables required
Underlying stock price
Exercise price
Time to expiration
Volatility of stock price
Risk-free interest rate

20. 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%

21. Answer

22. 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 16

23. 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 17

24. Hedging Copper Prices 18

25. Additional Uses of Options
Interest rate risk
Currency risk
Equity risk
Market risk
Individual securities
Catastrophe risk

26. 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