Proposal For New Mathematical Technology For Derivatives

I am writing this proposal for a robust new mathematical technology for derivatives project. Most of the technology for this project already exists, is proven and requires only minor modifications. I am looking for a paid commercial project with a derivatives technology company, investment bank or possibly sponsorship by some academic institution for a collaborative open source project. Many friends would have played with my matlab program that I uploaded on this thread post 105 https://forum.wilmott.com/viewtopic.php?f=4&t=99702&start=100 demonstrating how we can simulate the density of CEV noise using calculus of standard deviations. Friends would have noticed that this is a very fast way of simulating an SDE. There were problems at zero but these problems can now be seamlessly resolved. I truly believe that this new simulation paradigm can be easily developed as a robust and much faster alternative to simulation of stochastic differential equations by monte carlo and partial differential equations(both Fokker planck and backward PDEs). This new method has several advantages some of which I would like to state here. 1. The new technique is totally explicit and is much faster than both monte carlo and partial differential equations. Several high dimensional low factor (for example three factor) stochastic differential equations where the solution was earlier found using GPUs and special other techniques can now be solved in real time effortlessly. 2. The density of SDE obtained after simulation is smooth and we can take any number of derivatives which can be extremely helpful in many situations. In finance, this would be very helpful for calibration of the derivatives models one example of that can be pricing models where dupire local volatility is added on top of a stochastic volatility model. As an aside, Such calibrations can be done instantaneously by our new technique. Many high dimensional low factor models that were calibrated approximately could now be calibrated to perfect accuracy. 3. The transition density underlying our expanding/shifting/contracting grid is a standard normal density and this would help us easily do analytics that require complex conditional expectations. 4. We could very simply do backward dynamic programming on this grid so complex American options could be solved quite simply on this new grid. Path dependent Bermudan/American type high dimensional low factor(=3 factor) models can be easily solved with this new technique. 5. We could easily find the conditional value of all first and second order greeks almost instantaneously. My proposal is to write a fast and robust C++ code that would simulate two dimensional correlated stochastic volatility models of various types. We would also write robust code for high dimensional low factor models where perfectly accurate calibration would be done by this new method. We would write code for path dependent backward type American high dimensional but low factor models. We would also write code for simulation of totally arbitrary stochastic differential equations with perfect accuracy that could also be used in professions other than mathematical finance. This would be a paid commercial project with some derivatives technology company/investment bank where written code will be used only by that company. If there is a sponsor institution for open source effort, I would prefer to make the code open source. If some research department at a good university wants to partner in this new line of research, I would truly love to collaborate with other researchers but it would have to be a paid effort. If you are interested, please email me at anan2999(at)yahoo.com

4 comments on article "Proposal For New Mathematical Technology For Derivatives"

 Stephane Hardy, Computational Finance Quant and Options Trader

 Sunday, August 28, 2016

I point you to Quantlib.org

I have been involved with complex math, mostly in the derivatives, and contributed or commented on the techniques used to price dozens of derivative instruments, knock-ins, lookbacks, and many other instruments that cannot be replicated by simple puts and calls.

However, to get there, one is currently forced to re-invent the wheel every time. Even standard decade-old models, such as Black-Scholes, before Quantlib, still lacked a public robust implementation. As a consequences many good quants are wasting their time writing C++ classes which have been already written thousands of times.

QuantLib offers tools that are useful both for practical implementation and for advanced modeling, with features such as market conventions, yield curve models, solvers, PDEs, Monte Carlo (low-discrepancy included), exotic options, VAR, and so on.

So build on the shoulder of giants, leave your mark .

 Ahsan Amin, CEO at Infiniti Derivatives Technologies

 Monday, August 29, 2016

Stephane, thank you very much for your comment. I am very aware of Quantlib and I would be very willing to code the new technology in Quantlib, but it has to be a paid effort. Any thoughts if it could be possible to find a sponsor who would be willing to pay for the Quantlib coding effort for this new and better technology as compred to PDEs and monte carlo?

 John MERCEDES AC,PCLSCPAU, Fast Claim Consultants,Inc Owner Sr. Public Adjuster ACA PCLA

 Thursday, September 1, 2016

i think i got who is willing to take a shot Anand Sanghvi this is down your alley.

 Stephane Hardy, Computational Finance Quant and Options Trader

 Thursday, September 1, 2016

Being "aware" of quantlib does not make you a qualified coder for that platform. Quantlib coders, like me, are very expensive. In my humble opinion, if you have a cash generating algorithm, that is partly coded, and can function with live quotes and realistic execution objects, you should do your "minor modifications" with a programming friend and reap the proceeds. You see Ashan, just announcing you have a quality algorithm and offering it on LinkedIn, which is full of pro's, in exchange for money to make it happen, may not work. You are stuck in a conundrum. If it is true, you don't need help, if it is unproven but you have a hunch, investors will want more. You don't want to say what your unknown lottery ticket number is, lest they all buy one, but you need cash because it is an expensive ticket. What to do ?.... (I know what you should do)

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