KK04

02-06-2008, 08:40 PM

that's all I had to say

View Full Version : Crouhy is torturing me!

KK04

02-06-2008, 08:40 PM

that's all I had to say

TiderInsider

02-07-2008, 07:33 AM

Amen! I'm about to cowboy up on chapter 11...only a few more to go.

Laurelinda

02-07-2008, 01:59 PM

Crouhy has put me in a stagnant no-progress state for the last week, putting me 2.5 weeks behind my schedule.

Bell

02-07-2008, 08:42 PM

LaureLinda & all;

one of the things you shall remenber about Crouhy is that it is attempting to compare different schools of credit risk modeling.

Since modeling is a difficult activity, modelers need to make assumptions. While some credit risk modelers focus on default probabilities, other focus on credit migration.

To even define default probability, modelers will resort to their modeling paradigm/assumptions set. Some dont even venture there.

For instance:

(i) The CreditMetrics school of thought:

Default probability is a function of the firm's credit class. All firms within the same credit class have the same chances of defaulting, regardless of the capital structure (mix of debt and equity).

(ii) Merton school: the structural model of default risk:

These guys have made research that concluded that default shall be related to capital structure. They went on to define default as: A firm defaults at time T only if its value V(T) is less than the face value of its debt (F).

Think about the (positive) amount by which the firm defaults under Merton's paradigm: It is the Max(Debt-V(T);0). Isnt this the payoff of a put option of strike K?

Therefore, the cost of the default protection is simply the value of a put option p, of strike: Face value of the debt, and underlying asset V(T).

Now, in the risk neutral world, all investors earn the risk free rate, thus, in the SDE of the process V(t) uses r as the drift. This r goes in the BS equation.

In the real world, simply uses the estimated value of the drift (mu) instead of r.

Let me know if this make sense or not.

If you want, we can talk about other default models, in a user friendly way as this.

Thanks.

one of the things you shall remenber about Crouhy is that it is attempting to compare different schools of credit risk modeling.

Since modeling is a difficult activity, modelers need to make assumptions. While some credit risk modelers focus on default probabilities, other focus on credit migration.

To even define default probability, modelers will resort to their modeling paradigm/assumptions set. Some dont even venture there.

For instance:

(i) The CreditMetrics school of thought:

Default probability is a function of the firm's credit class. All firms within the same credit class have the same chances of defaulting, regardless of the capital structure (mix of debt and equity).

(ii) Merton school: the structural model of default risk:

These guys have made research that concluded that default shall be related to capital structure. They went on to define default as: A firm defaults at time T only if its value V(T) is less than the face value of its debt (F).

Think about the (positive) amount by which the firm defaults under Merton's paradigm: It is the Max(Debt-V(T);0). Isnt this the payoff of a put option of strike K?

Therefore, the cost of the default protection is simply the value of a put option p, of strike: Face value of the debt, and underlying asset V(T).

Now, in the risk neutral world, all investors earn the risk free rate, thus, in the SDE of the process V(t) uses r as the drift. This r goes in the BS equation.

In the real world, simply uses the estimated value of the drift (mu) instead of r.

Let me know if this make sense or not.

If you want, we can talk about other default models, in a user friendly way as this.

Thanks.

TiderInsider

02-07-2008, 09:27 PM

Crouhy is water-boarding me.

KK04

02-08-2008, 12:05 AM

Bell, Are you a manual-author or just an exam-taking actuarial guy??

LaureLinda & all;

one of the things you shall remenber about Crouhy is that it is attempting to compare different schools of credit risk modeling.

Since modeling is a difficult activity, modelers need to make assumptions. While some credit risk modelers focus on default probabilities, other focus on credit migration.

To even define default probability, modelers will resort to their modeling paradigm/assumptions set. Some dont even venture there.

For instance:

(i) The CreditMetrics school of thought:

Default probability is a function of the firm's credit class. All firms within the same credit class have the same chances of defaulting, regardless of the capital structure (mix of debt and equity).

(ii) Merton school: the structural model of default risk:

These guys have made research that concluded that default shall be related to capital structure. They went on to define default as: A firm defaults at time T only if its value V(T) is less than the face value of its debt (F).

Think about the (positive) amount by which the firm defaults under Merton's paradigm: It is the Max(Debt-V(T);0). Isnt this the payoff of a put option of strike K?

Therefore, the cost of the default protection is simply the value of a put option p, of strike: Face value of the debt, and underlying asset V(T).

Now, in the risk neutral world, all investors earn the risk free rate, thus, in the SDE of the process V(t) uses r as the drift. This r goes in the BS equation.

In the real world, simply uses the estimated value of the drift (mu) instead of r.

Let me know if this make sense or not.

If you want, we can talk about other default models, in a user friendly way as this.

Thanks.

LaureLinda & all;

one of the things you shall remenber about Crouhy is that it is attempting to compare different schools of credit risk modeling.

Since modeling is a difficult activity, modelers need to make assumptions. While some credit risk modelers focus on default probabilities, other focus on credit migration.

To even define default probability, modelers will resort to their modeling paradigm/assumptions set. Some dont even venture there.

For instance:

(i) The CreditMetrics school of thought:

Default probability is a function of the firm's credit class. All firms within the same credit class have the same chances of defaulting, regardless of the capital structure (mix of debt and equity).

(ii) Merton school: the structural model of default risk:

These guys have made research that concluded that default shall be related to capital structure. They went on to define default as: A firm defaults at time T only if its value V(T) is less than the face value of its debt (F).

Think about the (positive) amount by which the firm defaults under Merton's paradigm: It is the Max(Debt-V(T);0). Isnt this the payoff of a put option of strike K?

Therefore, the cost of the default protection is simply the value of a put option p, of strike: Face value of the debt, and underlying asset V(T).

Now, in the risk neutral world, all investors earn the risk free rate, thus, in the SDE of the process V(t) uses r as the drift. This r goes in the BS equation.

In the real world, simply uses the estimated value of the drift (mu) instead of r.

Let me know if this make sense or not.

If you want, we can talk about other default models, in a user friendly way as this.

Thanks.

Laurelinda

02-08-2008, 12:38 AM

Let me know if this make sense or not.

Yeah, thanks, that makes sense. I like comparing aspects of the different models right next to each other...would you do more of that for me, please? :tup:

Yeah, thanks, that makes sense. I like comparing aspects of the different models right next to each other...would you do more of that for me, please? :tup:

Laurelinda

02-08-2008, 12:39 AM

Crouhy is water-boarding me.

:lolup:

:lolup:

Bell

02-08-2008, 12:44 PM

:lolup:

So far:

two schools of credit risk modeling:

(i) CREDITMetrics, which used a CREDITMigration approach and

(ii) Merton. Assumes firm has a simple capital structure, and believes that the credit derivative is an implicit put option.

Per the previous discussion, the value of the put option that the firm shall hold to completely eliminate credit risk, according to the BS model is:

p = -V(0).N(-d1)+Fexp(-rT)N(-d2).

Where V(o) is the current value of the firm = Equity(0) + Debt(0). Debt(0) is noted B0 in the book.

N(-d2) is the default probability.

in the BS framework, d2 depends on a number of things:

the current stock (V(0);

the strike (F)

the risk free rate (r)

the volatility (the volatility of the returns of firm assets).

Merton's model therefore believes that N(-d2) is firm's specific. This is better than assuming that all firm within the same credit class have the same chance of defaulting, like CREDITMetrics.

Remenber that in the risk neutral world, all derivatives can be expressed as the expected value of the payoff.

Here, the payoff is the shortfall. Thus; you can p as:

p =(Expected Shortfall)*N(-d2)

If you were to take N(-d2) out from the BS equation of p, you will end up with the expected shortfall value of:

-V(0)*N(-d1)/N(-d2) + Fexp(-rT)

Since, Fexp(-rT) = B(0) is the bond price, V(0)*N(-d1)/N(-d2) has to be the recovery value.

Isn't it???

Note though: Since in only in the risk neutral world that the put can be written as the expected value of the derivative payoff, the d1 and d2 values here shall use the risk free rates. Do not use the real world probabilities values (that is mu instead of r).

Let me know how you're doing so far.

Next we look at:

(iii) KMV

(i) CREDITMetrics

(iv) and Other Aaproaches.

So far:

two schools of credit risk modeling:

(i) CREDITMetrics, which used a CREDITMigration approach and

(ii) Merton. Assumes firm has a simple capital structure, and believes that the credit derivative is an implicit put option.

Per the previous discussion, the value of the put option that the firm shall hold to completely eliminate credit risk, according to the BS model is:

p = -V(0).N(-d1)+Fexp(-rT)N(-d2).

Where V(o) is the current value of the firm = Equity(0) + Debt(0). Debt(0) is noted B0 in the book.

N(-d2) is the default probability.

in the BS framework, d2 depends on a number of things:

the current stock (V(0);

the strike (F)

the risk free rate (r)

the volatility (the volatility of the returns of firm assets).

Merton's model therefore believes that N(-d2) is firm's specific. This is better than assuming that all firm within the same credit class have the same chance of defaulting, like CREDITMetrics.

Remenber that in the risk neutral world, all derivatives can be expressed as the expected value of the payoff.

Here, the payoff is the shortfall. Thus; you can p as:

p =(Expected Shortfall)*N(-d2)

If you were to take N(-d2) out from the BS equation of p, you will end up with the expected shortfall value of:

-V(0)*N(-d1)/N(-d2) + Fexp(-rT)

Since, Fexp(-rT) = B(0) is the bond price, V(0)*N(-d1)/N(-d2) has to be the recovery value.

Isn't it???

Note though: Since in only in the risk neutral world that the put can be written as the expected value of the derivative payoff, the d1 and d2 values here shall use the risk free rates. Do not use the real world probabilities values (that is mu instead of r).

Let me know how you're doing so far.

Next we look at:

(iii) KMV

(i) CREDITMetrics

(iv) and Other Aaproaches.

beck

02-08-2008, 01:43 PM

Bell, Are you a manual-author or just an exam-taking actuarial guy??

i was wondering the same thing

i was wondering the same thing

Laurelinda

02-10-2008, 07:41 PM

Hooray, I finished reading Crouhy.

Bell, I follow you and am ready for more. :D

Meanwhile, can anyone give me a precise but general definition of leverage? I've always thought of it only in terms of the amount of debt in a company's capital structure (as in "leverage ratio"), but I've been reading things like ""The buyer leverage its position 10 times by putting aside 10 percent of the initial value of the underlying instrument as collateral" (p. 457) and "a way for banks to free regulatory capital, and thus leverage their intermediation business" (p. 461) and am now confused. What makes a TRS "leveraged"? Why have I heard someone say, "the value of a call changes more dramatically than that of the underlyer, because it's leveraged"? Can anyone give me a definition of leverage that I can apply to all these situations? Because they clearly have nothing to do (directly) with debt.

Bell, I follow you and am ready for more. :D

Meanwhile, can anyone give me a precise but general definition of leverage? I've always thought of it only in terms of the amount of debt in a company's capital structure (as in "leverage ratio"), but I've been reading things like ""The buyer leverage its position 10 times by putting aside 10 percent of the initial value of the underlying instrument as collateral" (p. 457) and "a way for banks to free regulatory capital, and thus leverage their intermediation business" (p. 461) and am now confused. What makes a TRS "leveraged"? Why have I heard someone say, "the value of a call changes more dramatically than that of the underlyer, because it's leveraged"? Can anyone give me a definition of leverage that I can apply to all these situations? Because they clearly have nothing to do (directly) with debt.

Bell

02-11-2008, 02:33 PM

Hooray, I finished reading Crouhy.

Bell, I follow you and am ready for more. :D

Meanwhile, can anyone give me a precise but general definition of leverage? I've always thought of it only in terms of the amount of debt in a company's capital structure (as in "leverage ratio"), but I've been reading things like ""The buyer leverage its position 10 times by putting aside 10 percent of the initial value of the underlying instrument as collateral" (p. 457) and "a way for banks to free regulatory capital, and thus leverage their intermediation business" (p. 461) and am now confused. What makes a TRS "leveraged"? Why have I heard someone say, "the value of a call changes more dramatically than that of the underlyer, because it's leveraged"? Can anyone give me a definition of leverage that I can apply to all these situations? Because they clearly have nothing to do (directly) with debt.

LaureLinda;

Good that you've finished with the Crouhy manual. You probably have a better understanding of it than before. Good luck on the exam!!!

Bell, I follow you and am ready for more. :D

Meanwhile, can anyone give me a precise but general definition of leverage? I've always thought of it only in terms of the amount of debt in a company's capital structure (as in "leverage ratio"), but I've been reading things like ""The buyer leverage its position 10 times by putting aside 10 percent of the initial value of the underlying instrument as collateral" (p. 457) and "a way for banks to free regulatory capital, and thus leverage their intermediation business" (p. 461) and am now confused. What makes a TRS "leveraged"? Why have I heard someone say, "the value of a call changes more dramatically than that of the underlyer, because it's leveraged"? Can anyone give me a definition of leverage that I can apply to all these situations? Because they clearly have nothing to do (directly) with debt.

LaureLinda;

Good that you've finished with the Crouhy manual. You probably have a better understanding of it than before. Good luck on the exam!!!

Car'a'carn

02-11-2008, 02:40 PM

Hooray, I finished reading Crouhy.

Bell, I follow you and am ready for more. :D

Meanwhile, can anyone give me a precise but general definition of leverage? I've always thought of it only in terms of the amount of debt in a company's capital structure (as in "leverage ratio"), but I've been reading things like ""The buyer leverage its position 10 times by putting aside 10 percent of the initial value of the underlying instrument as collateral" (p. 457) and "a way for banks to free regulatory capital, and thus leverage their intermediation business" (p. 461) and am now confused. What makes a TRS "leveraged"? Why have I heard someone say, "the value of a call changes more dramatically than that of the underlyer, because it's leveraged"? Can anyone give me a definition of leverage that I can apply to all these situations? Because they clearly have nothing to do (directly) with debt.

Leverage is using financial instruments to increase your potential payoff, whether it is positive or negative, borrowing money is one way to leverage your position. Using derivatives is another. Since the option has bigger risk than the underlaying asset its price will change more, percentage wise, that the price of the underlying asset.

More can be found here:

http://www.investopedia.com/terms/l/leverage.asp

Bell, I follow you and am ready for more. :D

Meanwhile, can anyone give me a precise but general definition of leverage? I've always thought of it only in terms of the amount of debt in a company's capital structure (as in "leverage ratio"), but I've been reading things like ""The buyer leverage its position 10 times by putting aside 10 percent of the initial value of the underlying instrument as collateral" (p. 457) and "a way for banks to free regulatory capital, and thus leverage their intermediation business" (p. 461) and am now confused. What makes a TRS "leveraged"? Why have I heard someone say, "the value of a call changes more dramatically than that of the underlyer, because it's leveraged"? Can anyone give me a definition of leverage that I can apply to all these situations? Because they clearly have nothing to do (directly) with debt.

Leverage is using financial instruments to increase your potential payoff, whether it is positive or negative, borrowing money is one way to leverage your position. Using derivatives is another. Since the option has bigger risk than the underlaying asset its price will change more, percentage wise, that the price of the underlying asset.

More can be found here:

http://www.investopedia.com/terms/l/leverage.asp

KK04

02-11-2008, 05:34 PM

I'm done too! Actually, its not that bad. I found it interesting by the time I got to Chapter 10,11...I think these are important topics too.

remilard

02-12-2008, 09:09 AM

Meanwhile, can anyone give me a precise but general definition of leverage? .

Precise? No

General? Yes

Anytime the returns from some strategy are correlated with but increase/decrease more than 1 to 1 with the returns from some basic investment leverage is being used.

Similarly any time you lift a heavy object with less force than it would take if you just bent over and picked it up you are using leverage (or pulleyage or enginage but pulleyaged and enginaged don't sound as cool as leveraged).

Precise? No

General? Yes

Anytime the returns from some strategy are correlated with but increase/decrease more than 1 to 1 with the returns from some basic investment leverage is being used.

Similarly any time you lift a heavy object with less force than it would take if you just bent over and picked it up you are using leverage (or pulleyage or enginage but pulleyaged and enginaged don't sound as cool as leveraged).

Laurelinda

02-14-2008, 07:50 PM

Thanks to Car'a'carn and remilard...that makes sense. So it really isn't as technical a term as I thought, after all.

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