In today’s video we learn all about the Monte Carlo Method in Finance.
About derivatives and quantitative finance. if this is the first video like this. by the end of this video you’ll know what the monte carlo method and when should you use it and when should you not. monte carlo methods are simulating the various sources of uncertainty affecting their value and or paths. okay so what does that mean? it means that rather than using a lot
Of computer simulation of the moving parts and see with enough runs of the model pricing method was developed by phelim boyle in 1977. it’s often considered a particularly useful in the valuation of options with multiple sources of impossible to value through a black scholes style partial differential technique is widely used in valuing path-dependent structures like look
Back above to my video explaining what real methods were considered to be too slow to be competitive, but with the faster so how does it work well let’s start with an idea taken from gambling and that you could get would be any number between 2 and 12. the lowest from rolling two sixes. now obviously with one dice you can get equal, it’s 1 over 6 which is a 16.7% chance,
However with the two dice one way to roll a 2 and one way to roll a 12 where in order to roll a 2 you have order to get a score of four for example with two dices can be achieved by separately, so even though the result is the second die is actually a different outcome from a 3 on the first die and a that we are able to achieve that. in this giving a 16.7% chance. you can
See a histogram on screen right now showing there’s two ways that we could work out these probabilities. one is the out numerically what the answer was, but the other simpler and maybe more times for example and note down the numbers that we’ve rolled each time. the it to price derivatives the monte carlo method involves simulate of the derivative that we are trying to
Price first you generate a price path and calculate the payoff from the derivative based on that path the image look like then you repeat these steps generating numerous sample values of the calculate the average of the sample payoffs giving an estimate of the payoff at the risk-free rate this result is the fair value of the option today depends on the required accuracy it
Is usual to calculate the standard uncertainty about the value of the derivative is inversely proportional to use the monte carlo method the monte carlo method can have great flexibility accommodated and different distributions including changing distributions can be more stochastic variables which make using a pde or a lattice based approach efficient than other approaches
As the time taken to run a monte carlo other methods the time taken increases exponentially with the number of pricing options it does not rely on a lot of financial theory it simply uses the monte carlo method is by no means free of assumptions though you always have to assume a distribution for the underlying asset as well as structure for black-scholes and lattice based
Approaches is that they not only give delta hedging which allows you to hedge your risk exposures if you have not those to understand how important that is to an options trader most of the to hedge or at least very difficult to hedge accurately and for this reason the the seller usually has to keep that option on their books for its entire that it can be used not only to
Price options where the payoff depends on the depends on the price path followed by the underlying the monte carlo method multiple underlying assets such as basket options or rainbow options take a in pricing those derivatives correlation between asset returns is also uncertainties such as where a joint probability distribution is used in the the concept generalizes to any
Number of random variables a stock in a foreign currency where the paths followed by the underlying stock two sources of risk must be incorporated. the monte carlo method cannot easily square monte carlo method with a backward induction approach is used. so the greeks using the monte carlo method is usually done by first pricing the small change in the input such as spot
Price to calculate delta or volatility the same number of iterations should be run in calculating the new price as were on my book – trading and pricing financial derivatives which is available on let me know if you found this video helpful and hit the subscribe button and
Transcribed from video
What is the Monte Carlo method? | Monte Carlo Simulation in Finance | Pricing Options By Patrick Boyle
