It’s All inside a Monte Carlo Simulation!
September 12, 2010
The other day, one of our CFE students did 50,000 iterations in a Monte Carlo simulation in the class using a very fast laptop within 10 minutes and generated some nice and fancy output while valuing an interest rate derivative using a three factor interest rate model. This was truly stunning as I myself have never gone beyond 10,000 iterations on my laptop and with a three factor model if you can complete 5,000 iterations in 15 to 20 minutes on your 2GB RAM, 2.16 GHz processor laptop you should consider yourself quite lucky.
Anyway, the feeling that we all had in the class that day was that no matter how complex the math, with Monte Carlo simulation it was all a walk in the park and with sufficiently large number of iterations you have a complete handle on reality.
Listening to the conversation in the class that day, I was reminded of another conversation I had many years ago with a friend on a similar subject.
In September 1998, as the Long Term Capital Management (LTCM) saga was unfolding and the world was stunned by the inadequacies of “Noble prize winning” mathematical models as applied to the real world of finance, a young physics Ph.D. who was then working as an associate in a top tier bank in London was engaged in a task that by his own reckoning was “impossible”.
In the thick of it all while everybody was asking questions like how could LTCM have happened, how can the theories of Myron Scholes and Fisher Black (the famous Black-Scholes duo of quantitative finance) be wrong, how could a hedge fund have advisors like Myron Scholes and Robert Merton and yet lose money, how can correlations between all assets move to one, how could the big banks and Federal Reserve not see this coming, so on and so forth, Andrew was working furiously to figure out what would happen to the entire interest rate derivatives book of his bank if all liquidity in the market dried up.
Eventually, after many nerve wracking days, he concluded that it is a question to which there are many answers, so many in fact, that any one seen on its own would be meaningless. Even though he had built a very fancy simulation model to analyze the problem he found out that it is the input parameters – and there were a large number of these parameters – that held the key. If he changed a certain parameter by a small amount and kept the others same or if he changed two parameters by a certain amount and made a correlated change in two others he would get very different results. The math was fine, the model was fine but it threw out different – and sometimes dramatically different – answers every time an input parameter was altered. The outliers were too many and too widely separated.
On hearing this, his boss was outraged. He thought Andrew was simply trying to skirt the problem. Under great pressure from the top, his boss asked him to go back to the drawing board again and come back with one definitive answer, a dollar figure for loss – a single quantifiable number – that would encapsulate the reality. After another week of extreme intellectual torture and skull drudgery he gave up and quit his post at that bank. Of course, the bank maintained that it had fired him. No one knows what happened, but Andrew quit the banking world for good.
Shortly thereafter, on a fine winter evening on one of the pristine beaches of Phuket as we – Andrew and I – watched the sun set and sat talking about the incident, amongst other things, he told me it was all just an illusion. "Nothing matters, nothing really changes……it is one big f***ing Monte Carlo simulation". His conclusion of the LTCM fiasco and everything else in the financial markets was that reality, with all its interpretation, lies hidden within the simulations that we do on our computers; there are these scenarios, infinite in number – or you could even call them alternate forms of reality – which are output of a Monte Carlo simulation and each of these scenarios are as important and as meaningless as the other because we simply do not know which one of them will happen when we look up from our screens.
And then Andrew dropped the bombshell. He said something that has come back to haunt me every now and then. "There is no one reality, for what is real is just another output of a simulation". And I had protested, "…but Andrew, we live in a world of profit and loss, that is real. Your loss in Dollars is as real as it gets."
He had simply shrugged off and replied, "It’s all inside the simulation, mate".
I thought this was plain nonsense. In any case, it was quite heavy duty stuff for me and sitting on that beach that evening with my half filled glass of pinacolada and watching the last rays of sun dancing on the water I thought Andrew might have had one too many.
Or did he?
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