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IFM > Actuarial application on options > Flashcards

Actuarial application on options Flashcards

1
Q

What are the 5 guarantees on variable annuities ?

A

. Guaranteed minimum death benefit (GMDB)
. Earnings-enhanced death benefit
. Guaranteed minimum accumulation benefit (GMAB)
. Guaranteed minimum withdrawal benefit (GMWB)
. Guaranteed minimum income benefit (GMIB)

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2
Q

Describe the GMDB and the return of premium GMDB.

A

Pays when the account value < premium.
Upon death, the policyholder receives a minimum amount, regardless of the account value.
Typically that amount is the premium paid initially. When this is the case, the guarantee is called “return of premium GMDB”.

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3
Q

Describe the earnings-enhanced death benefit.

A

Pays when the account value > premium.

Upon death, the policyholder receives a percentage of the excess of the account value over the premium.

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4
Q

What is the embedded option in a return of premium GMDB?

A

Put option :
pays when the account value (St) < premium (K)
Payoff = max (K-St ; 0)

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5
Q

What is the embedded option in an earnings-enhanced death benefit?

A

Call option :
pays when the account value (St) > premium (K)
Payoff = p%[ max (K-St ; 0) ]

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6
Q

Describe the GMAB (also called guaranteed minimum maturity benefit - GMMB).

A

Guarantees a minimum value for the account at a specific time.

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7
Q

What is the embedded option in a GMAB?

A

Put option :
pays when the account value (St) < guaranteed amount (K) at the specified time
Payoff = max (K-St ; 0)

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8
Q

Describe the GMWB.

A

Guaranteed that after the policyholder reaches a certain age, he may withdraw a certain amount every year for life.

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9
Q

Describe the GMIB.

A

Provides a guaranteed whole life annuity purchase rate at specified ages (protects against raises in annuity rates).

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10
Q

Give an example of the application of the GMIB.

A

At the age of 65, the policyholder may purchase a whole life annuity of 750 $ / month for 100 K $.

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11
Q

What is a mortgage guaranty insurance (MGI)?

A

Pays the lender the outstanding balance of the loan plus these settlement costs :
. Interest on the loan
. Propriety taxes, insurance premiums and maintenance costs
. Condominium and related propriety management fees
. Legal costs associated with foreclosure
. Costs of repairs necessary to get the propriety into sellable conditions.

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12
Q

Who purchases the mortgage guaranty insurance?

A

The lender.

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13
Q

What is the embedded option in a MGI?

A 
Put option : 
B = balance of the loan
C = settlement costs 
R = foreclosure proceeds 
Payoff : max (B+C-R ; 0)
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14
Q

Who receives the proceeds of the foreclosure sale?

A

The insurance company.

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15
Q

What is the embedded option in a mortgage loan from the perspective of the lender?

A 
Put option : 
B = balance of loan
C = settlement costs (except insurance on loan)
R = foreclosure proceeds
Payoff : max (B+C-R ; 0)
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16
Q

What is the guaranteed replacement cost coverage?

A

A rider to a propriety insurance contract that provides for paying the replacement costs for the propriety rather than the actual cash value before the loss.

17
Q

What is the embedded option the guaranteed replacement cost coverage?

A

Call option :
St : costs of replacement
K : cash value of propriety before the loss
Payoff : max (St-K ; 0)

18
Q

What is inflation indexing?

A

Guaranteed that the pension payment is adjusted to CPI if CPI > 1. The pension payment never decreases if the index goes dow.

19
Q

What is the embedded option inflation indexing?

A

Can be seen as a call or a put.

Call payoff : max { P(t-1) ; P(0) * [CPI(t)/CPI(0)] }

20
Q

What is static headging?

A

Buying options and then doing nothing.

21
Q

What are 5 types of exotic options that are useful for static hedging?

A
  1. Lookback options
  2. Shout options
  3. Chooser options
  4. Forward start option
  5. Rainbow option
22
Q

What is a lookback option? What type of guarantee can we hedge using a lookback option?

A

Use for hedging guarantees that can be reset by the policyholder.
Payoffs are based on the maximum or minimum value of the underlying asset.

23
Q

What is the difference between the standard lookback option vs the extrema lookback option?

A

Standard lookback option : floating strike price
if m = min & M = max
Payoff call : max(St-m ; 0)
Payoff put : max (M-St;0)

Extrema lookback option
Payoff call : max (M-K ; 0)
Payoff put : max (K-m ; 0)

24
Q

What is a shout option?

A

Allows the purchaser to select a date on which the underlying price on that date is used for the calculation of the payoff if it is to the advantage of the policyholder.

25
Q

What is the payoff of a shout option?What type of guarantee can we hedge using a lookback option?

A

Hedges the policyholder’s right to reset the guarantee once.
Call : max (St-K ; S-K)
Put : max (K-St ; K-S)

26
Q

What is a chooser option?

A

Allows the policyholder to choose between a call and a put.

27
Q

What guaranteed can we hedge using a chooser option?

A

GMBDs (put) combined with earnings-enhanced death benefits (call).

28
Q

What is a forward start option?

A

Allow the purchaser to buy an option at a later time with strike price determined by the underlying price at that time.

29
Q

What guaranteed can we hedge using a forward start option?

A

Useful to hedge (during the accumulation period) a GMWB that will come into effect only during the payout period.

30
Q

What is a rainbow option?

A

Have a payoff that depends on 2 or more risky assets. Useful for variable annuities since the policyholder may invest in many funds.

31
Q

What is dynamic hedging?

A

Buying options and frequently updating the hedging portfolio.

32
Q

How can you hedge catastrophic risks?

A
  1. Reinsurance
  2. Weather derivatives. Ex: pays out in the event of a hurricane or an earthquake
  3. Catastrophe bonds.
33
Q

What is a catastrophe bond ?

A

Bond issued by an insurance company that pays interest and principal only if no catastrophe occurs. Pays higher interest because the insurance company will default if a catastrophe occurs.

34
Q

What are the options associated with each variable annuity guarantee? (GMDB, GMAB, GMWB, GMIB)

A

GMDB : put
GMAB : put
GMWB : put
GMIB : call

IFM (19 decks)

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