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:
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//
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 2.42015I 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//
