Applications of this project - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T00:15:03Z http://mathoverflow.net/feeds/question/87855 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/87855/applications-of-this-project Applications of this project Hardy 2012-02-07T23:35:49Z 2012-02-14T23:32:19Z <p>Hi Guys,</p> <p>Just wondering if you could suggest applications of distribution of the supremum of a fractional Brownian motion process with a drift ?</p> <p>Also if you could possibly recommend how to approach this problem, that would be much appreciated. </p> <p>Cheers</p> http://mathoverflow.net/questions/87855/applications-of-this-project/88469#88469 Answer by Samuel Vidal for Applications of this project Samuel Vidal 2012-02-14T23:32:19Z 2012-02-14T23:32:19Z <p>An application that springs to mind immediately is <em>option evaluation</em>. Suppose I offer you to buy a contract to me: after three months I pay you the maximum value of the price of an asset. How much are you willing to pay this contract ? If you model the price of the assert by a drifted brownian motion, then you'll probably want to estimate the distribution of this maximum and take the expected value as a first guess of this maximum price. This will also be my first guess at the minimum price at which I will be willing to sell the contract. This is a non arbitrage price.</p> <p>Note to purists : of course one will object that each of the parties can hedge himself, and that the distribution has to be corrected by a risk neutral argument (which will probably discard the initial drift and replace it by a zero risk rate drift instead).</p> <p>N.b. : this is a real world application, exotic option traders buy and sell like contracts everyday.</p>