I have to use "Merton Jump diffusion model" for estimating the price of options for my research work.
i am using VBA as a back-end program for MS-Excel.
I have calcualted all the variables required for the model except the two variables
1. Number of jumps per year and
2. % of the total volatility explained by the jumps.
how to estimate those two variables.
i read program manual, but no information is available about it.
can anybody help in in this regard
thanks in advance
Dear Srikanth,
We may have communicated on some other problem, but, if you take alook at my paper titled "Political environment and financial markets" on www.researchgate.net/profile/Soumitra_Mallick, you will get an idea of the technology to apply jump quantum conductance and the vector diffeotopy of embedding (Mallick, Hamburger & Mallick (2016, 2017, 2018)) in String Theoretically classified options market data (which defines the environment of stock markets using program trading) by using the Ito's Lemma kind of integration to price securities. That may give you some idea. But I can't tell you specifically about "Merton jump diffusion model". I hope I have partly answered your question.
Soumitra K. Mallick
for RHMHM School
VBA is a simple implementation of the model. I doubt there is some earth shaking financial facts missing in your model right away. However without inspecting your model and pointing out any implementation errors I can simply advise yourself to:
1. Add a user induced param for number of jumps. Thus for n=1,2,3 you will have different results
2. For the percent explained just compare the results of volatility after each n=1,2,3 etc and that will be the percent explained in each implementation . It will be different for the jump parameter.
You can otherwise share your source with me /pseudo code and I will be happy to guide you
Best regards
Dear Srikanth Potharla,
I recommend the paper "A Stochastic Processes Toolkit for Risk Management" from Damiano Brigo et al. since the authors explains the simulation paths of the GBM/Merton model with jump-diffusion and their calibration process using the Maximum Likelihood Estimation. On the other hand, they provide several matlab code. And it works!
Best regards,
Mário
Dear Srikanth
I have not done empirical research using the Merton jump diffusion model. Nonetheless, here are some relevant papers that may help:
Article A Jump-Diffusion Approach to Modeling Credit Risk and Valuin...
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=332400
Article A Jump-diffusion model for option pricing
https://epubs.siam.org/doi/abs/10.1137/S0036142903436186
Article Pricing Stock Options in a Jump-Diffusion Model with Stochas...
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=61998
Article Numerical Analysis of American Option Pricing in a Jump-Diff...
I teach Merton's model among others at Copenhagen University. My notes are freely available on slideshare:
www.slideshare.net/AntoineSavine/lecture-notes-from-volatility-modelling-lectures-at-copenhagen-university
Slide 139 to 149 are dedicated to Merton's jump model.
In addition, I explain the model and its implementation in C++ in my book:
www.researchgate.net/publication/328042479_Modern_Computational_Finance_AAD_and_Parallel_Simulations
Chapter 13, section 13.2.
Finally, I would advise to avoid VBA, instead, code models in C++ and export your code to Excel. I wrote a tutorial to show how to do this quickly and with minimal pain:
medium.com/@antoine_savine/exporting-c-code-to-excel-a-quick-and-painless-tutorial-ef43b07006a
You can also download my Merton code in:
github.com/asavine/CompFinance/blob/master/analytics.h
I hope it helps. Kind regards.
thank a lot Prof. Antoine Savine
i will read the sources suggested by you. It will definitely helpful to me.
once again thanks
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