#### DunderMifflin

##### New Member

I was reading the Stultz reading on Credit Derivatives and trying to replicate the same across excel.

One of the Stultz example has the following parameters:

Asset Value $ 120.00 S

Face Value of Debt $ 100.00 K

Time5 T

Risk Free Rate of Return10% r

Volatility20% Sigma

Return on Assets20% Mew

Although I was able to find the distance to default by the usual D2 formula of Black and Scholes,

Distance to default by this formula works out to be 2.42015

I just saw that an alternative formula works as well:

How i stumbled upon this formula,

1. I wanted to find out the value of Asset after 5 years.

Considering Return on Assets and Drift, The value of Asset after 5 years turns out to be $295.15

Value of V @ T=V*e^((Mew - Sigma Squared/2)*T))

2. I tried finding the log return of the Asset compared to the Face Value of Debt => ln(Value of S @ T/F) = 1.082322

3. I happened to multiply the log return is 2 with the square root of time {ln(Value of S @ T/F)*sqrt(T)}, this turned out to match the value of the distance to default which equals 2.42015

I tried the same exercise to find out the d2, by replacing the mew with the risk free rate and found that the same formula works and matches the d2. Hence, i hope that both these formula are matching.

However, I would like to ask you guys that is there any inference or meaning to the alternative formula that i stumbled upon.

//I have attached the excel for reference//

One of the Stultz example has the following parameters:

Asset Value $ 120.00 S

Face Value of Debt $ 100.00 K

Time5 T

Risk Free Rate of Return10% r

Volatility20% Sigma

Return on Assets20% Mew

Although I was able to find the distance to default by the usual D2 formula of Black and Scholes,

Distance to default by this formula works out to be 2.42015

I just saw that an alternative formula works as well:

**d2 = ln((S*e^((R asset returm-sigma squared/2)*T))/K)*sqrt(T)**How i stumbled upon this formula,

1. I wanted to find out the value of Asset after 5 years.

Considering Return on Assets and Drift, The value of Asset after 5 years turns out to be $295.15

Value of V @ T=V*e^((Mew - Sigma Squared/2)*T))

2. I tried finding the log return of the Asset compared to the Face Value of Debt => ln(Value of S @ T/F) = 1.082322

3. I happened to multiply the log return is 2 with the square root of time {ln(Value of S @ T/F)*sqrt(T)}, this turned out to match the value of the distance to default which equals 2.42015

I tried the same exercise to find out the d2, by replacing the mew with the risk free rate and found that the same formula works and matches the d2. Hence, i hope that both these formula are matching.

However, I would like to ask you guys that is there any inference or meaning to the alternative formula that i stumbled upon.

**/**/**d2 = ln((S*e^((R asset returm-sigma squared/2)*T))/K)*sqrt(T) //****Or is it just some mathematical transformation of the D2 Formula**//I have attached the excel for reference//