PAK Study Manual Risk Neutral Dynamic Hedging

Transcription

PAK Study Manual
Foundations of CFE (CFE) Exam
Fall 2014 Edition
CTE
Hull-White
Ito’s Lemma
Agency Theory
Reinsurance
Risk Neutral
Corporate Finance
Stochastic Simulation
Efficient Market Hypothesis
Regime Switching Lognormal
Dynamic Hedging
Economic Capital
Behavioral Finance
Martingale
Value at Risk
Dividend
WACC
Delta
PAK Study Manual
for CFE Fall 2014
PRODUCT FEATURES
Purposes
Features
PAK
Study
Manual
PAK
Exam
Aid
PAK
Memorization
Aid
PAK
PAK Study
Test Aid Manual Package
Study
Summaries
X
X
Study
Relevant Past Questions (List)
X
X
Study
150+ Practice Questions
X
X
Study
5 Mock Questions
X
X
Study
Suggested Schedule (Detailed)
X
X
Study
Email Support
X
X
Practice
Mock Questions
X
X
Practice
Past Questions (Sorted PDFs)
X
X
Review
Condensed Summary
X
X
Review
Electronic Flash Cards
X
X
Evaluation Mock Exam
X
PAK Online
Seminar
X
Bonus
Bonus materials
X
Study
Online Video Seminar
X
Study
Past Exam Questions
X
1
PAK STUDY MANUAL
1. Summary
The PAK Study Manual covers the entire Foundations of CFE (CFE) syllabus. Not only
does it give you the detailed explanations on conceptual, calculation, and exam materials,
but it also fills in the gaps among the topics that are not covered in the source readings. It
helps you better understand and master the confusing logics and difficult materials.
In addition, it links the similar topics across readings together and connects them to the
syllabus so that you can see the whole picture of this exam.
2. Relevant Past CFE/FETE SOA Exam Questions (List)
For each reading, we compose a list of relevant past exam questions (if any) so that you
can locate the questions quickly and practice them immediately. This saves your time on
searching what materials are relevant to this exam.
3. 150+ Practice Questions
One key point to pass this exam is to "practice" (Practice makes perfect!). Due to this
reason, we create a set of practice questions (150+ in total) to refresh the materials just
learnt and to strengthen your knowledge. More practice will be available in the PAK Exam
Aid.
4. Mock Exam Questions
The mock exam questions mimic the same difficulty level of the real exam questions. 5
mock exam questions and solutions are included in the PAK Study Manual to challenge
your understandings. More practice will be available in the PAK Exam Aid.
5. Suggested Study Schedule (Detailed)
The syllabus is huge. It is very easy to lose track on your study. A clearly defined study
schedule and some useful tips are included to help you better manage your schedule.
6. Email Support
Get questions? Please send me an email
NOTE
The study manual will be released on 5/12 and 7/1
“I passed my AFE exam on my first attempt with 10. I give my credit to Eddy. Thank
you Eddy. ” By Su (Charlie) Yang—NJ
Read the whole story
PAK MEMORIZATION AID
DO YOU KNOW?
The PAK Study Manual and
related aids are updated EVERY
exam sitting.
You will see the most updated
materials, examples, and explanations to help you master the
concepts and pass this exam in
the first attempt.
1. Electronic Flash Cards
 Summarize the key points (with mnemonics) (PDF version is also available)

Work best for any big-screen cellular phone or mp3 player (e.g. iPhone, HTC,
Android, Nook, etc)
2. Condensed Summary
 Summarize the key points in outline format

Quickly refresh all the important topics in the readings
PAK TEST AID
1. Mock Exam
 This set of mock exam is different from those mock questions available in the
PAK Exam Aid. You can write down your answers and send them to me. I will
give you detailed feedbacks on how to improve your exam score
2
PAK EXAM AID
1. 30 Mock Exam Questions and Solutions (New)
The mock exam questions mimic the same difficulty level of the real exam questions. 30 mock
exam questions and solutions are included to challenge your understandings.
2. Case Study Analysis (New)
This set connects the case study materials to the study materials so that you can see the picture
on how they can be tested.
3. Past SOA Exam Questions (from All FSA Tracks) Relevant to This Exam
This set not only includes the past exam questions from the CFE/FETE exam, but also includes
the past exam questions from all the other FSA exam tracks (e.g. FETE, APM, CSP, DP, etc). It
helps you better understand how the materials were tested and gets you familiar with the SOA
exam question style.
NOTES
1. The availability date of the 1st and 2nd items above may be different. It depends on when the SOA
releases the new case study.
2. 1st release will contain item #3 and will be released on 7/30. The 2nd release will contain item #1
-#2 and will be released on 9/1.
3. If the SOA do not release the case study, an additional 5 mock questions will be used to replace
the case study analysis.
DO YOU KNOW?
You can find the most updated information about the
PAK Study Manual and related aids under the
“Announcement” section on
the front page of the PAK
website.
“I can unequivocally say that it is the best study guide that I have used as I've made
my way through the SOA exam system ” By David
Read the whole story
RELEASE SCHEDULE
Purposes
Features
PAK
Study
Manual
PAK
PAK
PAK
Memorization
Exam Aid
Test Aid
Aid
PAK Study
Manual Package
5/12 and
7/1
5/12 and 7/1
Relevant Past Questions (List)
7/1
7/1
Study
150+ Practice Questions
7/1
7/1
Study
5 Mock Questions
7/1
7/1
Study
Suggested Schedule (Detailed)
5/12
5/12
Study
Email Support
Anytime
Anytime
Study
Summaries
Study
Practice
Mock Questions
9/1
9/1
Practice
Syllabus Questions
9/1
9/1
Practice
Past Questions (Sorted PDFs)
7/30
7/30
Review
Condensed Summary
8/15
8/15
Review
Electronic Flash Cards
8/15
8/15
Evaluation Mock Exam
9/15
PAK Online
Seminar
9/15
Bonus
Bonus materials
To Be Announced
Study
Online Video Seminar
6/15 and 7/30
Study
Past Exam Questions
9/1
3
PAK STUDY MANUAL PACKAGE
1.
2.
3.
4.
5.
PAK Study Manual
PAK Exam Aid
PAK Memorization Aid
PAK Test Aid
Bonus materials
(Release on 5/12 and 7/1)
(Release on 7/30 and 9/1)
(Release on 8/15)
(Release on 8/15)
PAK ONLINE SEMINAR (NEW)
1. Clarify and explain the key concepts/calculations in each reading in the syllabus
2. Discuss the past exam questions (e.g. exam techniques, how to score)
3. Review the new case study
4. Contain condensed outlines for each reading on the syllabus
5. Review the lectures and study at your own pace
6. Email support
7. Free access for 2nd attempt (only for those who scored 2-5)
8. Practice Question Set (150+ in total)
9. PAK Study Manual is included
NOTE
1.
The online seminar will be released on 6/15 and 7/30. The videos related to the past
questions will be released on 9/1.
SAMPLES?
You can find more samples on the PAK website.
IMPORTANT NOTES
DO YOU KNOW?
If you are not sure which
exam track to take, or how it
can advance your career, you
can send an email to Eddy
and discuss your situation
with him. He will share his
work experience with you so
that you can make your decision informatively.
1.
Please note that all products are in electronic (PDF) format. No hard copy is provided.
2.
Once you make a purchase (please use your work email address), we will send you a confirmation email within 1 business days Once the files are available, we will send them to you
through email. Please make sure that you put the correct email address when you purchase
the PAK products. If you do not receive the confirmation email, please send me an
email.
3.
Please check your “junk” mailbox. Sometimes, my email is blocked.
MORE INFORMATION
Want more information? Please contact me at paul.peterson@pakstudymanual.com
or eddy.chan@pakstudymanual.com or visit www.pakstudymanual.com
COMMENTS FROM THE PAST CANDIDATES
You can find more comments from the past candidates here: PAK Testimonials.
WHERE TO PURCHASE PAK PRODUCTS
The PAK products are available at Actex, Actuarial Bookstore, and SlideRule Books.
4
PAK Study Manual for CFE Fall 2014
Frequent Answer Questions
Do You Need to Read the Source Readings?
Unlike the preliminary exams, reading the source readings (textbooks, SOA study notes, and online readings) is a
must in the FSA exams. PAK Study Manual can help you understand the materials faster and memorize them
quickly so that in the time-limited environment, you can be well-prepared for the exam.
How Much Time is Needed to Study for This Exam?
This varies by person. Usually it will take one 350-400 hours to study for a FSA exam (5-hour). Please expect to
spend the same amount of time for the CFE exam.
Study Schedule
From the date the SOA release the new syllabus to the exam date, there are around 4 months to study. How to
plan your study schedule?
T=2.5 months
T=0
Read the Source Readings
T=3.5 months
Review Again
T=4 months
Practice
Read the Source Readings
Assume you take the CFE exam in this exam sitting. In general, it will take one 2 to 2.5 months to finish them. To
study more efficiently, I highly suggest you following the steps below:
Step 1: Define Your Own Study Schedule
- Use the suggested study schedule as a reference
- Prepare your own study schedule (Target 20-30 pages @weekday and 50-60 pages @weekend)
- Expect to read the whole syllabus and the past exams 2 or 3 times before the exam
Step 2: Read the Source Readings Together with the PAK Study Manual
- Write down your notes in the study manual
- Highlight all the key points there
(Will be used for memorization later)
- Label any calculations that you will go over again later
- Go over the related past exam questions once you finish that reading
Step 3: Read the SOA Past Papers
- Read them once you finish your first-round of readings (use the PAK Exam Aid)
- Understand how the topics were tested and how the questions were answered
Review Again
After completing the three steps above, you probably have a general idea about how the exam looks like. Now
you should review the source readings again but this time focus more on the key topics, clarify the confusing
concepts/calculations, think of what can be tested and read them carefully (use my mock exam questions)
Practice
The last month is the most critical month. Here are the steps:
- Practice the past exams and my mock questions to identify what you still do not know
- Go back to the readings and find your answers (or send me an email if you need help)
- Start memorizing the key points
(use the PAK Memorization Aid)
- Use the PAK Test Aid to test your knowledge
(Send me your answers and I will give you detailed
feedbacks on how to improve your score in the exams)
More Information
I will explain how to prepare for this exam in much more details in the PAK Study Manual.
Any Questions?
I know you probably have a lot of questions in your mind regarding the exam or choosing study aids. Please feel
free to contact me at eddy.chan@pakstudymanual.com
© 2014 PAK Study Manual
1
SOA CFE Exam (Study Manual)
F-107-13: A Market Cost of Capital Approach to Market Value Margins (by CFO Forum)
Key Points
SAMPLE
1.
Understand the economic balance sheet structure
2.
Understand how to use the market cost of capital approach to calculate the market value margin
1. Executive Summary
Two Common Approaches to Calculate the Market Value Margins (MVMs)
- Percentile approach
- Market cost of capital (MCoC) approach
Market Cost of Capital (MCoC) Appaoch
- The CRO Forum prefers the MCoC approach
- This approach works for both life and non-life business
Main Reasons for the CRO Forum’s Preference
1. Support appropriate risk management actions
2. Appropriate reflection of risk
3. Better response to a potential crisis
4. Easy to implement
5. Transparent, easily verifiable and understandable
6. Pass the “use test”
Figure 2: Economic Balance Sheet
Components of Market Consistent Value of Liabilities (MVL)
1. Expected PV of future LCFs
2. MVM for non-hedgeable risks (An explicit cost of risk for non-hedgeable risk)
MVL
-
It represents the market consistent value at which the liabilities could be transferred to a willing, rational,
diversified counterparty in an arms’ length transaction under normal business conditions
Note
“Arms’ Length Transaction” means the transaction made by two totally independent parties
2
MVM
-
It is the cost of risk (risk margin) in addition to the expected PV of future LCFs required to manage the
business on an ongoing basis
It is estimated by the PV of the cost of future capital requirements for non-hedgeable risks
Calculation of MVMs using a MCoC approach is straightforward given that the majority of the calculation
is prescribed under the standard SCR
2. Introduction
Purpose of This Paper
- The MCoC approach to MVMs is the CFO Forum’s preferred method
Calculate the Liability Value
- The assets and liabilities should be measured on a consistent basis for solvency purposes
o This basis should be market value
-
In order to determine the MVL, a MVM is added to the expected PV of future LCFs
o The CRO Forum does not agree with using the percentile method to calculate the MVM since it is
not consistent with the aim of introducing a risk based solvency assessment
o The MCoC approach to MVMs is the CFO Forum’s preferred method
3. Why Take a MCoC Approach to MVMs?
Two Common Approaches to Calculate the Market Value Margins (MVMs) for Non-Hedgeable Risks
1. Percentile approach
o Sufficient capital is needed to ensure that the liabilities can be met with a predefined confidence
level
2. Market cost of capital (MCoC) approach
o Sufficient capital is needed to be able to run-off the business
Main Reasons for the CRO Forum’s Preference
1. Support appropriate risk management actions
2. Appropriate reflection of risk
3. Better response to a potential crisis
4. Easy to implement
5. Transparent, easily verifiable and understandable
6. Pass the “use test”
Supports Appropriate Risk Management Actions
- MCoC approach
o It more appropriately differentiates between risks similar to the way in which capital markets
differentiate between risks (equity investment vs. equity option)
o
-
It ensures that the cost of risk is measured purely based on the economic cost of holding capital
to support non-hedgeable risks
 The cost of risk and any allowance for prudence are clearly separated
 The reserve reflects the best estimate of the cost of managing risk
 Margins for prudence should only be reflected in the capital held (SCR) and not in the
technical provision (MVL)
Percentile approach
o Prudence may be incorporated in both the reserves and capital which can lead to inefficient
management of risks and double counting of risks
3
Appropriate Reflection of Risk
- MCoC approach
o The MVMs will always reflect the risk inherent in the product
-
Percentile approach
o The MVMs will not always reflect the risk inherent in the product because there is no link
between the arbitrary percentile value chosen and the market price
o Also, the percentile approach does not refer to each risk type separately
Figure 1: Percentile vs. MCoC
Figure 1
- For the long tailed gamma distribution (“more-severity” risks: catastrophic risk, terrorist risk, etc)
o The percentile approach underestimates the price of non-hedgeable risk
-
For the normal distribution (regular insurance risks: mortality risk, etc)
o The percentile approach greatly overestimates the market price of risk
-
The MCoC approach ensures that insurers consider the tails of the distributions
o No consideration is given to the shape of the distribution using the percentile approach
Experiences of the Australian and the Swiss Regulators
- Australian regulators
o It is difficult to reasonably explain the spread of risk margins using the percentile approach
-
Swiss Regulators
o The MVMs under a MCoC approach appropriately reflect the risk inherent in the business
 The calculation is stable from period to period
 Life insurers writing mainly savings products have relatively small MVM since insurance
risk is small
 Life insurers writing risk products have relatively large MVM since they have a large
exposure to biometric risk and a long duration of the run-off portfolio
4
Response to a Potential Crisis
- MCoC approach
o It ensures that after a stressed event, the company will be able to appropriately remunerate either
a third party accepting the liability or new capital providers
o It achieves this through the SCR for non-hedgeable risks needed to support the liability in future
years and hence the MVM, which represents a provision for the cost of holding this capital
-
Percentile approach
o It implicitly forces the insurer to hold part of the capital needed to support the business in future
years in the form of a prudence margin
o This prudence margin will not suffice to run-off the liabilities with the level of confidence implied
by the SCR
o It does not ensure that there will be sufficient financial resources to cover future capital costs
needed to remunerate either a third party accepting this liability or new capital providers
Ease of Implementation
- Percentile approach
o It is complex (for small entities) to implement since it requires stochastic calculations over the
whole run-off period to determine the appropriate percentile on the distribution of liability values
-
MCoC approach
o It is easier to implement since there is only one unknown item (the SCR for non-hedgeable risks)
and this can be calculated with ease using the standard SCR
Transparent, Verifiable and Comprehensible
- MCoC approach
o Supervisors can easily replicate and verify the MVM calculation (using standard SCR and internal
model)
-
Percentile approach
o It is not so easily verified because it is not possible for the regulator to use the standard SCR to
benchmark the internal models used to determine the percentile value
o Australian regulators experienced a wide variation in the results from insurer to insurer , when
adopting a percentile approach
The “Use Test”
- The MCoC approach has been used for some 20 years
- It already passes the “use test” envisioned in the Solvency II framework
5
4. Theory Underpinning the MCoC Approach: The Economic (Solvency) Balance Sheet
Figure 2: Economic (Solvency) Balance Sheet
Note
In the general accounting framework, we know that assets = liabilities + equities.
Assume that assets = MVA and liabilities = MVL. Then equities = SCR + Excess capital
Economic (Solvency) Balance Sheet
- It distinguishes between the asset and liability values and the capital required for solvency purposes
- Capital requirements consider risks emanating from both sides of the balance sheet
- It does not explicitly identify the cost of capital
Market Value of Assets (MVA)
- The capital markets provide the MVA
Market Consistent Value of Liabilities (MVL)
- It is derived from the cost of managing the risks underlying the business on an ongoing basis
- It represents the market consistent value at which the liabilities could be transferred to a willing, rational,
diversified counterparty in an arms’ length transaction under normal business conditions
- Market values should be used where available to value the MVL
- Where market values are not available, the MVL must be explicitly calculated using market consistent
valuation techniques
6
Figure 3: Components Parts of the MVL Calculation
Expected Present Value of Future Liability Cash Flows
- It includes premiums, fees, policyholder claims, expenses and commissions
- The market consistent value of these future CFs may be determined as the cost of setting up a replicating
portfolio
Replicating (Hedge) Portfolio
- The portfolio of assets that most closely matches the corresponding liability CFs
- In the absence of arbitrage, and if the liability CFs could be matched exactly, the market consistent value
of the liabilities will exactly equal the market value of the replicating portfolio
Note
To the simplest form, the expected PV of future LCFs is the same as the reserve that we learnt in FAP. Remember the formula?
Reserve = PV(Expenses/Claims) – PV(Premiums)
Figure 4: Replicating Portfolio
7
MVM for Non-Hedgeable Risk
- The MVM is defined as the cost of risk (risk margin) in addition to the expected PV of future LCFs
required to manage the business on an ongoing basis
- It is only necessary to calculate an explicit MVM for non-hedgeable risks
Figure 5: Types of Risk Affecting the Liability Cash Flow
Hedgeable Risks
- A hedgeable risk is a risk which can be pooled or hedged using a replicating portfolio
o Hedging costs are implicit in the observed market price of those instruments
o Thus, it is not necessary to calculate an explicit MVM for hedgeable risks
Non-Hedgeable Risks
- Risks for which a deep and liquid market is not available are referred to as non-hedgeable
o They are risks for which a market price cannot be observed
-
To compensate an investor for the cost of taking non-hedgeable risks, an explicit MVM is demanded
o Under the MCoC approach, the MVM is the compensation required for the cost of holding capital
against non-hedgeable risks over the life of the policy
Figure 6: Flowchart for Determining the Appropriate Method for Calculating the MVL
8
Solvency Capital Requirement (SCR)
- It can be determined by the Standard Approach or the Internal Model Approach under Solvency II
- The projection of what the SCR is for non-hedgeable risk is needed to calculate the MVM
Cost of Capital (CoC)
- It refers to the capital charge on fully diversified capital held to cover non-hedgeable risks only
o This should not be seen as a total company CoC
Note
In the embedded value framework, the CoC means the cost of holding the capital needed to support the businesses of the whole company.
In the MVM calculation here, we just focus on the capital held to cover non-hedgeable risks only.
5. The MCoC Approach to MVMs
MCoC Approach to MVMs
- The MVM for non-hedgeable risk is calculated as the PV of the cost of future capital requirements for
non-hedgeable risks
Steps to Calculate the MVM for Non-Hedgeable Risks
1. Project the SCR for non-hedgeable risks
o Using the standard model or internal models, the projected SCR can be determined via an
underlying driver that is indicative of the risk level (e.g. PV of benefit) (See Appendix C)
o The required SCR at time 0 for non-hedgeable risk types would be set at 99.5% Value at Risk for
a holding period of one year and calculated net of full diversification effects (see Appendix B)
2. Calculate the capital charge
o The capital charge for non-hedgeable risks can be explicitly calculated by multiplying the future
SCR at each point in time by the CoC for non-hedgeable risk
o This cost of capital charge only applies to capital that is required for the non-hedgeable risk
3. Discount the projected capital charge
o The projected capital charge stream is then discounted at the risk free rate (swap rate) to get the
MVM
Figure 7: Calculating the MVM for Non-Hedgeable Risk
9
Illustrative Example
Data and Assumptions
- An insurer has sold 500 term policies and the premium on each policy is €50
- If the policyholder dies within a 5 year period, then a benefit of €1000 is paid
- The probability of dying within any one year is 1%
- The swap rate is 5% (yield curve is assumed to be flat)
- The CoC for non-hedgeable risks used to illustrate the approach in this example is 4%
Step 1: Project the SCR for Non-Hedgeable Risks
Time
No. of policies (start of year)
Premium (beginning of year)
Claims
PV Claims (Discounted at mid-year)
SCR
SCR as % of PV of benefits
0
500
25,000
5,000
21,764
2,176
1
495
2
490
3
485
4
480
4,950
17,729
1,773
4,901
13,543
1,354
4,851
9,199
920
4,803
4,687
469
5
0
= 10% x 21,764 = 10% x 17,729 = 10% x 13,543 = 10% x 9,199 = 10% x 4,687
10%
Step 2: Calculate the Capital Charge
Time
SCR
0
2,176
87
Capital Charge
Capital Charge / SCR
= 4% x 2,176
1
1,773
71
2
1,354
54
= 4% x 1,773 = 4% x 1,354
3
920
37
4
469
19
5
= 4% x 920
= 4% x 469
4%
Step 3: Discount the Capital Charge
Time
SCR
Capital Charge (mid-year)
0
2,176
87
85
Discounted Capital Charge
Total MVM
PV Liabilities
MVL
= 87/1.05^0.5
1
1,773
71
66
2
1,354
54
48
= 71/1.05^1.5 = 54/1.05^2.5
3
920
37
31
4
469
19
15
= 37/1.05^3.5
= 19/1.05^4.5
5
245
21,764
22,009
6. Frequently Asked Questions
Circularity
- The issue of circularity in the calculation arises because the MVM is calculated directly from the SCR
o But it also makes up part of the MVL and is assumed to be included in the SCR calculation
-
The relative size of the MVM in comparison to the total MVL is small so the impact of including the MVM
in the SCR calculation would be insignificant
o Thus, it is assumed that the MVM will have little or no effect on the SCR
Asset Liability Mismatching
- The acquiring insurer should not be compensated for any avoidable asset liability mismatch (ALM) taken
by the defaulting insurer
o ALM risk is a hedgeable risk so it is assumed that the acquiring insurer can swap back to the
replicating portfolio instantaneously and hedge any ALM taken by the defaulting insurer
10
Level of Risk Margin Relative to Overall Liability
- Some regulators and supervisors are concerned about the relatively low level of MVMs
- The explicit MVM only corresponds to the MVM charged for non-hedgeable risks
o Low margins are also observed using a percentile approach so this is not purely a MCoC issue
Tax
-
The liabilities and the MVM should be set on a pre-tax basis since this is analogous to how market values
are set for assets
Operational risk
- Since operational risk is a non-hedgeable risk, it should be included in the calculation of the MVM
Harmonization
- The MVM calculation is based on the projected capitals but various insurers have various internal models
o The CRO Forum has also formulated recommended approaches of benchmarking internal
models to address these concerns
o The proportion of the MVL that corresponds to the explicit MVM is relatively small so any
discrepancies will have a relatively small impact on the results
Total Portfolio vs. Different Business Line
- The MVM is calculated for each LoB for each risk type and then added to the best estimate liability value
o This will improve transparency and facilitate companies’ analysis of the risks they take
o The MVL is then aggregated to a company level
Non-Life Business
- The MCoC approach applies for non-life business
o For in-force business, a SCR for non-hedgeable risk will be set up for the current year to support
the insured risk
o In addition to this, SCR for the non-hedgeable reserve risks will be held after the expiration of the
contract
o This capital is held to cover the risk that reserves may not be sufficient to cover claims either
because ultimate claims or the pay out pattern had been incorrectly estimated
Small Entities
- The Swiss Solvency Field Test showed that this MCoC approach works well in smaller entities due to its
simplifying assumptions
- The standard SCR approach can be adopted to determine the SCR for non-hedgeable risks
Variation in CoC
- The CoC for non-hedgeable risks reflects the excess return over risk free rates that an acquiring company
would require to compensate them for the cost of holding capital to run-off the business
-
The CRO Forum suggests that the risk margin (MCoC) should not vary by risk type or business
o Since the SCR for non-hedgeable risk will differ between risk types, the MVM will automatically
differ under the MCoC approach thereby better reflecting risk
-
With regard to the reference market in which the products are sold, it is possible that the price of risk may
vary between countries due to uncertainty in the market
o Most of this uncertainty is due to the difficulties in hedging unwanted risk and will already be
factored into the SCR and MVM, as these risks are not hedgeable
11
Time Horizon
- One common misconception regarding the MCoC approach
o The MVM only considers one year worth of risk and everything after the first year is ignored
because the SCR is measured using a one-year shock approach
o This is incorrect
-
The SCR calculation does consider the expected LCFs over periods
o The SCR represents the change in liability value between expected future liability cash flows and
worst-case (99.5% percentile) cash flows
o These worst-case cash flows reflect not what we can observe in any one year but rather how far
off we can be in estimating our expected liability cash flows over their entire life
Appendix A. Expected Present Value of Future Cash Flows
Products without Optionality
- All cash flows that occur with certainty are totally risk free and can be replicated with risk-free assets of a
similar term
Diversifiable Risk
- The market consistent framework assumes that there is no reward for holding diversifiable risk
o This assumption implies that any cash flows that are not risk free but where risk is diversifiable
should be treated as risk free and hence discounted at the swap rate
o This assumption flows through to the treatment of the MVM for non-hedgeable risks
Non-Diversifiable Risk
- This assumption also implies that expected cash flows that are subject to non-diversifiable risk should be
discounted at a rate that reflects the risk inherent in the cash flow
o The risk-adjusted rate contains a risk premium that investors would demand for
o The greater the expected return driving such a risky cash flow, the greater the discount rate
applied to the cash flow
Certainty Equivalent Approach
- This is a form of risk-neutral valuation where the risky cash flows are adjusted and projected assuming
that all underlying assets earn the risk-free rate
Note
CFrisky ,t
1. Discount risky cash flows using risk-adjusted rate:
V0 = 
2. Discount risk-free cash flows using risk-free rate:
V0 = 
CFrisk free,t
3. Adjust risky cash flows and discount at risk-free rate:
V0 = 
CFrisky ,t − Z t
(1 + rf + rp )t
(1 + rf )t
(1 + rf )t
Products with Embedded Options or Guarantees
- For products with options/guarantees, using the certainty equivalent approach becomes a very complex
process due to the non-linear, asymmetric relationships with market returns that exist in these products
o It is necessary to determine the liability value using option pricing or Monte Carlo simulation
o In order to achieve market-consistency, both methods should be calibrated to reproduce the
prices of traded assets that best reflect the characteristics of the liabilities being valued
12
Appendix B. Diversification
Four Levels of Diversification
Diversification Levels
Level 1
(Within risk types)
Level 2
(Across risk types)
Level 3
(Across entities, within a given geography)
Example
Two or more insurance companies in the same geography within an
insurance Group
Level 4
(Across geographies or regulatory jurisdictions)
Two or more insurance companies in different geographies within an
insurance Group
Adding more unrelated risks to the portfolio
Combining two classes of insurance
Appendix C: Proxy Measures for Projecting Capital
Non-Hedgeable Risk Type
Mortality
Life
Morbidity
Insurance
Persistency
Products
Death Protection Survivorship Protection
Net amount at risk
N/A
Economic liability
PV of benefits
N/A
Economic liability
Savings
Accident & Health
Economic liability
N/A
Economic liability
Net amount at risk
Net amount at risk
Economic liability
Note
There is a long list in the reading. You should read it once. I personally think the life insurance line is more important so I put it here.
Practice Question
List the considerations of calculating the MVM
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Circularity
Asset Liability Mismatching
Level of Risk Margin Relative to Overall Liability
Tax
Operational risk
Harmonization
Total Portfolio vs. Different Business Line
Non-Life Business
Small Entities
Variation in CoC
Time Horizon
Past CFE/FETE SOA Questions Related To This Reading
SOA CFE Fall 2013 Q8 (Must Read)
13

PAK Study Manual Risk Neutral Dynamic Hedging

Transcription

Similar documents

Saturn Bioponics

value Pak Pricing

Pencak Silat Mande Muda Seminar

PAGE 4 - CycleBuy.com

biglo

Catering Menu

SAI KUNG DEPARTURE Jaspas Junks operate 3 party junks from

2F - G and G Supermarket

F SpeciaL ...................... $23. 99