Marginal Default Probability for 1st year

[kc]

Hello,

I am confused with this way of calculating the marginal default probability for the 1st year.
The question is asking 1-year CVA, so my understanding is 1-year marginal default probability = cumulative default probability for the 1st year, so 1- e^(-0.06*1) = 0.058.
However, the number shown in below is calculated differently. Can someone please help ? Thanks.

 

[kc]

Second question is, the expected exposure is 20000000e^(-1*5%), what is this 5%? Thanks.

 

[Clay Carter]

Hello,

I am confused with this way of calculating the marginal default probability for the 1st year.
The question is asking 1-year CVA, so my understanding is 1-year marginal default probability = cumulative default probability for the 1st year, so 1- e^(-0.06*1) = 0.058.
However, the number shown in below is calculated differently. Can someone please help ? Thanks.
View attachment 4472

@kc Hi, I think the confusion is because the cumulative default probability and marginal default probability are related but distinct. Cumulative Default Probability: This gives the total probability of default occurring by time t1. It's an aggregated measure. Meanwhile, Marginal Default Probability isolates the likelihood of default occurring exactly within a specific time interval. In this case, for the first year.

 

[kc]

@kc Hi, I think the confusion is because the cumulative default probability and marginal default probability are related but distinct. Cumulative Default Probability: This gives the total probability of default occurring by time t1. It's an aggregated measure. Meanwhile, Marginal Default Probability isolates the likelihood of default occurring exactly within a specific time interval. In this case, for the first year.

Hi Clay, thanks for helping. In this case, if we are looking for a probability of the 1st year, isn't the cumulative probability = marginal probability? Thanks.

 

[Clay Carter]

Hi Clay, thanks for helping. In this case, if we are looking for a probability of the 1st year, isn't the cumulative probability = marginal probability? Thanks.

@kc Think of the hazard rate (λ) as a baseline rate of failure, while the marginal default probability adjusts this rate to reflect the survival of the entity up to the specific time period. Over time, the marginal probability decreases due to the compounding effect of survival probabilities. So to clarify the 6% is the average rate while 5.65% reflects the actual likelihood, accounting for survival during that year.

 

[kc]

@kc Think of the hazard rate (λ) as a baseline rate of failure, while the marginal default probability adjusts this rate to reflect the survival of the entity up to the specific time period. Over time, the marginal probability decreases due to the compounding effect of survival probabilities. So to clarify the 6% is the average rate while 5.65% reflects the actual likelihood, accounting for survival during that year.

Thanks, I will continue to have a look on that