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Monte Carlo applications

GordonGekko

Joined
3/16/12
Messages
7
Points
13
Hi,

I'm working on a Monte Carlo project at school. I implemented simulations of Poisson process, compound Poisson, jump-diffusion, gamma and variance-gamma.

I am also asked to freely apply these simulations to finance. Could somebody indicate me some nice applications of these processes in finance (for example in pricing) ?

Thanks a lot
 
Operational Risk capital MC relies on frequency and severity estimates. VaR estimates can be built on gaussian copulae. Derivatives are prices using time series MC.

Often, when doing a VaR Monte Carlo one will superimpose "events" on the gaussian outcomes. These can be poisson.
 
GordonGekko said:
Hi,

I'm working on a Monte Carlo project at school. I implemented simulations of Poisson process, compound Poisson, jump-diffusion, gamma and variance-gamma.

I am also asked to freely apply these simulations to finance. Could somebody indicate me some nice applications of these processes in finance (for example in pricing) ?

Thanks a lot
Click to expand...

If you have Poisson, you can always use it for estimating frequncy regardless of what it's frequency if. It fits nicelly into the VaR frmework as Ken has pointed out. Jump diffusion certainly has pricing applications. Do you have any background in finance, or are you completely new to the field?
 
Hi Seniors,

Which tool is the most used in the industry for Monte Carlo in financial risk: MATLAB / R / SAS /Excel-VBA / SPSS / FinCAD other? If I were to try to implement some of the monte carlo simulations for FRM/VAR computations which one should I pick? Which one is most famous tool with investment banking trading risk management? Is SAS ever used on Monte Carlo as it seems toughest to impelment? Also, which tool is used to model intrest rate monte carlo simuations.

Is MS-Excel VBA capable of handling the complex data, symbolic computations, partial differntial equations, exotic distributions in Monte carlo?

Which tool would be the best if we were to do Beta computations, black scholes, merton model for PoD, forward bias on currency, volumes based strategy, pair trading, currency pairs, forward bais, SQL/SAS commands to pick data from Oracle SQL database, Short straddle, delta/gamma hedge, call writing, volatility trading, other implementation?

Shvigan Joshi
 
It's not about complexity - all the packages mentioned above can do it. It's about plumbing and throughput. Truth be told, the analytical part simply isn't that difficult - it usually takes much more time to write out the results than it does to do the calculations.

I think most big firms will use C++ and craft bespoke solutions, although I've seen all of those packages used in different places.
 
If you're doing something as embarrassingly parallel as Monte Carlo, the problem is almost begging for GPGPU -- see, for instance, Graphical Asian Options. As Ken mentioned, C++ is the obvious choice here.

I can just add that it will offer the most choices in terms of libraries for GPGPU (many, but not all, will also have C or Fortran versions) -- just off the top of my head: CUDA (with higher-level Thrust), OpenCL (with higher-level Bolt), C++ AMP, OpenACC -- and that doesn't even include a rich and growing ecosystem of GPU-Accelerated Libraries on top of that, like ViennaCL ("supports CUDA, OpenCL, and OpenMP"), or Algorithms/RNG/FFT/BLAS/LAPACK for C++ AMP.

So, yeah, C++ might be worth considering ;-)
 
Ken Abbott said:
Operational Risk capital MC relies on frequency and severity estimates. VaR estimates can be built on gaussian copulae. Derivatives are prices using time series MC.

Often, when doing a VaR Monte Carlo one will superimpose "events" on the gaussian outcomes. These can be poisson.
Click to expand...

Is Gaussian copula still used in the same way? What are the banks now focusing to improve models for Probability of default?
 
Hey I am learning Monte Carlo, any idea about who makes these two part of the simulation "copula vs cholesky decomposition", is it Financial Engg or hardcore Maths people.
I find it tough to get them completely, and tried to read them from internet. Any good source or book to get intro?
Can you share your experience on these two theories.
Thanks in advance!
 
copula and cholesky are simple concepts if you understand basic prob and math.
for copula: distribution functions >> all CDF are uniform >> inverses of CDF functions
for cholesky: Linear algebra I >> square root of positive definite matrices
 
Hi, I'll be doing a school project in Monte Carlo Methods class and I'm free to choose any topics I want. I would like to have some suggests on topics related to mathematical finance. Although I used MC to price different options using MatLab in my previous course, I am not familiar with advanced topics such as copula or cholesky as mentioned above, I'm also taking stochastic processes course at the moment, so something that brings both subjects together would be interesting. R software is what I need to use this time. Any topics (not too simple, but not too compliated) that covers basic, but important concepts would be appreciated. Thank you.
 
Some thoughts:

MC as a concept covers a very, very broad range of topics. To wit:
  • Outcomes simulation for one-step events (eg VaR)
  • Outcomes simulation for capital additions (eg Basel IRC)
  • Time series simulation for pricing
  • Time series simulation for risk (counterparty credit as in Canabarro and Duffie)
  • Portfolio selection (random selections of n assets, etc.)
What are the commonalities in terms of a) concepts b) coding preferences (R, Matlab, Stata, C++ bespoke, etc) and c) implementation challenges? What has been done in terms of variance reduction techniques?
 
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