Merton Model for PD

Dear friends,

I would like to solve for the market value of assets and volatility with the Black-Scholes model to use it to find the Firm value and consequently to use it in the Merton model to find the probability of default.

Could someone please help me how to approach this task?

many thanks

[the cyclist]

With the information you have given, this is approximately the only advice that can be given back:

-- Learn the Merton model

-- Learn MATLAB

-- Code the Merton model in MATLAB

Maybe if you give a lot more detail in your question, you could get a better answer.

[Nikolay]

I don't care much for your arrogance. Now everyone is borne with great optimisation and mathematical skills. I've never said I was professional in Matlab. I tried to be brief as I figured people who had done it before would know what I was asking. I know the model just not really certain how to do it in Matlab

in the future refrain from making such insinuations. If you don't want to help just keep your stupid comments to yourself

[Oleg Komarov]

@Nikolay: I really suggest you change the perception of how this forum works.

The cyclist is a very valid contributor and his suggestion reflects your question not his arrogance.

Read this tutorial to get an idea of what you can get from this forum: http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

I am not tagging you as doit4me, not yet, but many questions in your style get such a tag straight away without even a comment.

Answer 1

[Sap]

@Nikolay: I do agree with Oleg and cyclist, in the way the question is being asked. Having said that if you have no experience in MATLAB what so ever, i suggest you learn the basics for finance functions (it shouldn't take you more than 4-5 days)

As for your question to solve the Merton model, you need to simulate the firm value in a function .m file or directly, using the randn function for the brownian motion of S/current firm value. I am not sure about the probability default but this should start you off.

[Nikolay]

Thanks Sap. I've already solved it. I've managed to find the Asset value and volatility with fminsearch

[Oleg Komarov]

@Nikolay: you can post your solution and accept it as long as it's the only answer proposed that solves your question. This way, other people will be able to come and learn from your solution.

Answer 2

[Gabo]

Merton model is supported in Risk Management Toolbox. There are two implementations:

• The mertonmodel function: https://www.mathworks.com/help/risk/mertonmodel.html
• The mertonByTimeSeries function: https://www.mathworks.com/help/risk/mertonbytimeseries.html

Both functions solve for the asset value and asset volatility, and also find the distance to default and probability of default. The main difference is that mertonmodel works one time period at a time, whereas mertonByTimeSeries uses an entire time window for the model calibration. For additional information on these functions see https://www.mathworks.com/help/risk/default-probability-using-the-merton-model-for-structural-credit-risk.html.