MSc Financial Mathematics Taster Session (University of Aberdeen)

welcome my name is Eric and I am the program coordinator for financial mathematics this program is split 50-50 between the business school and mathematics so this means that there are four courses provided by the business school when they try to present more practical side of financial mathematics so four courses for the business school and also there are four courses provided by us the math department where we try to to tell you what's really inside the opponent of this financial mathematics program and how what kind of mathematics is used there and and why it fails so I would like to present an example with a question and give you a little bit of a taste of how our lectures look or more precisely how my lectures will look like in this in this program so the basic question we try to answer we try to build mathematical models for is the following suppose we have a share of stock now this share is not worth some money we know what it's worth but we'd like to know its future price at the future it's big unknown nobody knows it and we will try to build mathematical models which will not answer this question but we will which will try to provide a theory for answering different questions and I tell you what these questions are so imagine that this is axis of numbers there is zero and what I denote by s now is the price of our share and then in the future the future might be in one week in one month in one year we have a similar situation but we don't really know the price so what can happen between now and future well the prices can go down something very strange might happen and the price ended up here so if you see well in the future that price went up we got richer another scenario is that the price go up down down down something happens and the price ends up here we are poorer so we consider all possible scenarios which can happen this example show that the price of a share of stock is is random we don't really know what is happening in in the future so anything can happen so now if you look at this at this drawing well the price started here we don't really know what is happening in between it ended up there ok the price and here it decreased then we would like to consider all such possible scenarios and then what we will record is the the future price of our share of stock and sometimes for different scenarios the price can end up the same so we recalled all of those and we see it as a distribution ok so if I recall all the final prices some of them will happen more frequently some of them very early and let me try to draw another vision for you so keep in mind this and perhaps we should probably so in newspapers on TV but what is really interesting from the mathematical point of view is that of course this is 0 so the prices should never go below 0 and we record this distribution as a as a graph and it more or less will look like this so what is graph what this graph is telling us well it tells us that somewhere in this region if you look at that region then this looks like the price is falling into that region are the most probable okay so to check the probability we look so for first of all we ask the question what is the probability that the price will fall between these two values well from this graph it says the probability will be there in the area of this shaded region then you might be interested suppose you want to get very rich very quickly then you are interested about you sure stop growing very shortly that was the probability of your share of stock to have a price in this region well the area of this pink shaded region which is very small and then this of course creates a magical mathematical model so so this is a and the mathematical model is within the framework of probability theory so a big part of this course is about probability theory I assume that some of you or all of you already had basic probability course but in this program we'll go much further we'll present quite advanced probability techniques for for financial mathematics so the theory world building is within probability theory the most difficult part for making a very good model for finance is is the choice of that distribution so if you look at the past prices and if you analyze all past behavior of the market then you can of course approximate such a such distribution but essentially it's very hard to get it right so at this point when building a model we're making a choice we are guessing was the right distribution and so the most difficult part is to make a right choice then there are several topics within the course one of them is to present the standard theory which produces so-called black Scholes model so black Scholes model is a model for option pricing which is more or less the question is similar to what I presented so and this is a standard model which is taught in every financial mathematics course so we will also present it here although in my course I will try to go very deep so I will try to present all the mathematics needed for that model to a reasonable death so flag shows and the choice which is made in this model is so-called log normal distribution so it's a choice and one of the main flaws of this choice is that with within this model is very hard to predict and to deal with with rare events so some like a financial crash so this model is very bad if it comes to rare events like financial crashes in our course I will try to present examples where showing why this model fails although it's widely used and sometimes it's it is used as a benchmark but in principle it is incorrect so and it fails when it comes to rare events so nowadays people are trying to build models when the log normal distribution which is used for black Scholes is replaced by something which allows better predictions for battle better understanding of of rare events like southern market crushing or something so this is kind of a in a nutshell what this course is all about but a large part of the course is mathematics mostly probability theory we will also discuss the risk analysis for in finance for which is for which we use the linear algebra and more or less my lectures are only one of the many lectures in this program my lectures will look more or less like this I will draw things on the blackboard I will stop and explain whenever we confused I will do slowly when necessary I will try to be very detailed and very clear so I hope you liked it and I hope to see you very soon in Aberdeen thank you

Channel: University of Aberdeen

Views: 6,099

Rating: 5 out of 5

Keywords: university, aberdeen, Jarosław Kędra, MSc Financial Mathematics, MSc, mathematical models, stock markets, University of Aberdeen, aberdeen uni, scotland, study, uni, aberdeen university, study in scotland, higher education, studying, postgraduate, college

Id: 0MftOGl84IE

Length: 11min 11sec (671 seconds)

Published: Thu May 24 2018