ERM-104-12: Study Note on Parameter Risk


#1

A Fellowship Forums Wiki Community Post

Online Link to this Reading: https://www.casact.org/pubs/forum/12sumforum/Venter_Sahasrabuddhe.pdf

Topics Covered in this Reading:

  • What is Economic Capital?

  • What are the Benefits of Economic Capital Analysis?

  • How Can Economic Capital Analysis be Applies?

  • What Type of Risks Should be Considered?

  • How should Each of These Risks be Measures?

    • VaR vs Tail-VaR
    • Stochastic Analysis vs Stress Test
    • Real Wold vs Risk Neutral
    • Diversification Effect
    • Time Horizon to Consider
    • Whether to allow Negative Cumulative Surplus in the Middle of Time Horizon
    • Whether to Account for Future New Business
  • What Modelling Decisions Should Inform the Analysis?

  • Illustrative Examples


This is a wiki post, editable by anyone. Feel free to edit and add key points/extra detail above!


#2

Hi,

This chapter states the parameter risk is a form of systemic risk that does not diversify with volume, although it may diversified across portfolios to some degree.

My questions are:

  • what is the systemic risk? Why parameter risk is a form of systemic risk?
  • I am confused about whether parameter can be diversified or not?

Any help will be appreciated!


#4

Systematic risk is a type of risk that is inherent in the very system you are working with.

Parameter risk is the risk that you have wrongly specified a parameter in your model. This is a systematic risk because it is inherent in the very environment you are working with -> the model. It won’t diversify with volume because if you have an incorrect parameter, it will be wrong for all projections. For example, if we have a model that is pricing insurance products, and we have a wrong mortality rate… this rate will be wrong for all policies whether we have 1000 policies or 1 million. We can’t “diversify away the risk” by adding more policies.


#5

Thanks for your replying,

I am still quite confused about the difference between systematic risk and systemic risk. Could you please explain the difference?:grimacing:


#6

I am still quite confused about the difference between systematic risk and systemic risk. Could you please explain the difference?:grimacing:

Where have you seen the term systemic risk? I think systematic risk is the correct term. I’m not an English major, but I googled the difference, and it looks like maybe systemic is a common misuse of the term systematic. I doubt you’d lose marks for it, but I don’t think there is a difference, and that when you say systemic risk, you should really use systematic risk instead.


#7

Perhaps this helps… they also indicate that systemic risk doesn’t really have a clear definition, but in certain, specific cases it could be used. I think the safe bet would be to just use the word systematic


#8

Funny, when I was studying I exclusively used the term systemic risk as the risk of failure of a financial system.

In the extension we learned about SIFIs (Systemically Important Financial Institutions), which are financial institutions so big that if they were to fail, they would cause an industry wide distribution.


#9

Thanks for your explanation, it helps a lot.:+1::+1::+1::+1:


#10

Funny, when I was studying I exclusively used the term systemic risk as the risk of failure of a financial system. In the extension we learned about SIFIs (Systemically Important Financial Institutions), which are financial institutions so big that if they were to fail, they would cause an industry wide distribution.

Thanks for adding this. I guess that interpretation fits in with the article from investopedia. The risk of the entire economic system failing would be systemic risk, and the risk of a “undiversifiable process error” within one organization’s processes would be systematic risk? What does everybody think of that distinction?


#11

I definitely agree with @David_Senensky re: systemic risk. ERM 127-17 defines systemic risk as “risk of disruption to financial services that is caused by an impairment of all or parts of the financial system and that has the potential to cause serious negative consequences for the real economy”; the 2008 financial crisis would be an example of systemic risk.

I agree with @XP-ERM re: systematic risk. I think his example with the wrong mortality assumption really highlights how parameter risk is a form of systematic risk.

@yywq90 - I think all the confusion comes from the fact that your original question asked how parameter risk was a form of systemic risk rather than systematic risk.

To answer your question about the difference between systemic risk and systematic risk:

Systemic risk is the risk that the entire market fails. It is non-diversifiable.
Systematic risk is something inherently wrong in a system that you cannot diversify away (such as parameter risk).

Do you guys agree?


#12

Simply put, I think systematic risk is one kind of market risk, such as the fluctuation of S&P500 or something else. Systemic risk seems like butterfly-effect that unexpected company level events that leads to disruption in entire financial system. Now I am getting more and more confused about the link between systematic risk and parametric risk!:rofl::rofl:


#13

Simply put, I think systematic risk is one kind of market risk, such as the fluctuation of S&P500 or something else

I don’t necessarily agree with you here. The article clearly points out that the parameter risk we have discussed is a systematic risk, and that is not a market risk. It is a risk that you encounter when working with systems -> something that arises when something is wrong with the very system you are working with (like a parameter in a model).

I think your definition of systemic risk is great though!


#14

OK, I going to forget the market risk. Just define systematic risk as some error that inherent within the system, and save this sentence in my head.

I hope question would not ask these items. :joy:


#15

Hi everyone,

About the 3 method of parameter estimation, can somebody explain the definition of “Model free model”? I tried to google this term, but there has not any explanation.


#17

I think you misread the notes. There are three ways to estimate parameters:

  1. Regression Analysis
  2. Maximum Likelihood Estimation
  3. Model free methods (not models)

The first two have formal, standardized ways to calculating the parameters. The third occurs when there is no distribution (thus, “model free”), so they suggest creating an empirical one from an available sample.


#18

My apologize for the typo.

Based on my understanding, we can use Regression analysis to estimate parameter if one variable is a function of others, such as y = ax + b. In this case, our intention is to calculated a and b. We also can use MLE if it specifies a distribution for the random variables, we then calculated the parameter of the given distribution, such as μ=?, σ=?.

My confusion is on Model free methods. If there does not specify a distribution or any function, then where are the parameters?