Institute of Actuaries of India 2010 SA6 Investment Specialist Applications University - Question Paper

b)    The life insurance company has recently sold a large number of traditional deferred pension annuity contracts whereby premiums are paid annually during the accumulation phase and at retirement, in 10 to 15 years time, the customer has an open market option (OMO) to buy an annuity from another provider or to buy a level annuity from the company using the interest rates guaranteed (5% pa) at point of sale of the deferred pension annuity contract.

i)    Explain in detail the economic nature of the option which has been sold and how it could be hedged with a derivative assuming there is a sophisticated and developed financial markets    (6)

ii)    What are the risks with such a derivative hedging approach    (2)

iii)    Value the guarantee for a deferred pension annuity, expected to be 12 crore when it vests in 10 years, and the expected life expectancy of the individual is 10 years after vesting. The forward swap rate is 4%pa; the 11 year spot rate is 5%pa and 12 year and beyond the spot rate is 5.5%pa respectively (both compounded

continuously). Swap rate volatility is 0.3. You are given that    

3.2539485 where ii=5.5% . State other assumptions, if any.    (5)

c)    The insurance company has a large portfolio of immediate payment annuities. It is considering entering into a longevity swap with another insurance company in order to transfer the longevity risk. The longevity swap can be considered similar to a total return swap.

i) Explain the mechanics of an interest rate swap and indicate the risks associated with such an investment

ii) Define a total return swap and indicate how such an instrument might be used to

transfer longevity risk.    (3)

iii) How else might such a transaction be structured and explain the advantages and disadvantages of each approach.

d) The life company has recently sold a traditional with profits single premium product which has backing assets of 20% 5 year government bonds and 80% equities. The company has given a guarantee that the reversionary bonus will be 3% pa for this cohort of policies which mature in 5 years time and these policies have backing assets worth 20 crore currently. Government bonds gross redemption yield is 4%pa and equity index volatility o is 0.4.

i)    Explain in terms of Black-Scholes option pricing model how you would value the guarantee and then calculate the value of the guarantee for this cohort of policies.

State any assumptions underlying your calculations.    (4)

ii)    What assumptions underlie the Black-Scholes approach?    (3)

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Q. 2) RBI has come out with a draft paper on Introduction of Credit Default Swaps (CDS) for Corporate Bonds and has invited views from Bankers, Insurers, Mutual Funds, Primary Dealers, IRDA, SEBI etc. They are expecting to get views on many aspects related to the management of the CDS contracts.

The paper proposes to introduce plain vanilla OTC single-name CDS for corporate bonds issued by resident entities who are rated by credit rating companies or for those corporate bonds which are issued by SPV (special purpose vehicles) provided they are set up by rated infrastructure companies.

The paper mentions that credit derivatives market has seen very high growth from mid 1990s. This has happened due to the standardization of the contracts, increased number of participants and also the ability of participants to express credit views such as the credit volatility, shape of the companys credit curve, timing and pattern of defaults.

The Lehman Brothers and AIG had exposures to CDS contracts and when they failed as counterparty, it triggered a global financial crisis in which Lehman became bankrupt and AIG was bailed out by the US government. Most of the CDS contracts were written on sub-prime mortgages.

In the recent times the CDS spreads on Greek Sovereign debt had risen dramatically as a response to the fiscal problems in the country and it led to a steep increase in the cost of borrowing and rollover of the Greek Sovereign debt. In view of such corporate and sovereign troubles some countries are reconsidering the decision to introduce CDS.

The draft paper recommends two types of participants, Users and Market makers. The Users will only be allowed to hedge their exposure to corporate bonds by buying CDS but they cannot sell/write CDS to other buyers and cannot have short positions in CDS whereas the market-makers will be allowed to have both buy and sell position.

The paper also mentions that credit rating of reference entity is required but there is no requirement for the reference asset to be rated.

1.)

i)    What are credit derivatives and what is their use?

ii)    What are the other major credit derivatives products apart from CDS?

2.)

i)    What are the risks in OTC derivative products?    (2)

iii)What    are the main benefits of CDS instruments?    (3)