The tag has no usage guidance.

learn more… | top users | synonyms

0
votes
0answers
45 views

The Merton's model

According to Merton's model we can calculate probability of default by this formula: $$P(V_T < B) = N \big[ \frac{\ln\frac{B}{V_0} - (\mu-\frac{1}{2}\cdot\sigma^2)T}{\sigma\sqrt{T}} \big]$$ I have ...
3
votes
1answer
57 views

How to find volatility of Asset given volatility of Stock in Merton model?

I encounter a problem in one of my project to find the 1 year, 2 year and 3 year Asset volatility. We are given 2015 Bell Canada's financial report and a software to do this. The financial report can ...
3
votes
1answer
108 views

Simple question on jump-diffusion

In the textbook by Shreve in sec. 11.7.2 a jump-diffusion process is introduced. More precisely $$ dS_t = \alpha\,S_t\,dt+\sigma\,S_t\,dW_t+S_{t-}\,d\left(Q_t-\beta\,\lambda\,t\right)\quad (1) $$ ...
1
vote
0answers
12 views

Why use Moody's KMV EDF for one year

If I were to use Moody's KMV proprietary database with expected default frequqncies(EDF) for sectors and countries, along with aggregations for financials and non-financials, significant banks etc: ...
9
votes
2answers
262 views

Solution of Merton's Jump-Diffusion SDE

In many textbooks and also in the original Merton's paper the solution of the SDE $$ dS_t = S_t\,\mu\,dt+S_t\,\sigma\,dW_t+S_{t^-}\,d\left(\sum_{j=1}^{N_t}V_j-1\right) $$ is written as $$ S_t = ...
2
votes
0answers
35 views

Future value of the debt under Merton model

The author Malz states the future value of the firm's debt under the Merton model can be found from: $$ D_{t} = D - \max(D - A_{t} , 0) $$ (where $D$ is the par value of the debt, $A_{t}$ is the ...
1
vote
2answers
218 views

Why is the value of debt modeled as a short put option in Merton's model?

Can someone give me an intuitive understanding of why the Merton model models the value of the debt from the lender's point of view as a short put with a risk free bond? I'm not well versed in this ...
0
votes
0answers
45 views

Merton Jump Diffusion Model: Influence of lambda

I use Monte Carlo to simulate sample paths of Merton's jump diffusin model. By plotting a histogram of the log returns and using kerneldensity to approximate the density function I try to look at the ...
1
vote
1answer
112 views

Question about the stochastic differential equation in the Merton model

in the following stochastic differential equation merton model we have $$\frac{ds}{s}=(\alpha-\lambda k)dt+\sigma dW+dq$$ where $\alpha$ is the instantaneous expected return on the stock; ...
3
votes
1answer
222 views

How to interpret negative asset volatility numerical results in Merton model?

I am currently working on my thesis where I discuss the Merton default probability model. I have a huge sample of US firms for the period 1990-2010. I use both numerical and complex iterative approach ...
1
vote
0answers
229 views

How to calculate modeled asset volatility by industry factor?

Currently I am working with huge data frame which consists of a lot firms. For each firm in my sample I calculated asset volatility ( I am using Merton default probability model, so I have used 2 ...
7
votes
2answers
3k views

How to use Merton model to calculate default probability with monthly stock prices?

I want to calculate the estimated default probability with only given data the monthly returns for the last 20 years, the risk-free rate ($R_f$), equity value (EV) and the face value of debt ($D$). My ...