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Full-Text Articles in Physical Sciences and Mathematics
Applications Of Stochastic Calculus To Finance, Scott Stelljes
Applications Of Stochastic Calculus To Finance, Scott Stelljes
UNF Graduate Theses and Dissertations
Stochastic Calculus has been applied to the problem of pricing financial derivatives since 1973 when Black and Scholes published their famous paper "The Pricing of Options and Corporate Liabilities" in the Joumal of Political Economy. The purpose of this thesis is to show the mathematical principles underlying the methods applied to finance and to present a new model of the stock price process.
As part of this paper, we present proofs of Ito's Formula and Girsanov's Theorem which are frequently used in financial applications. We demonstrate the application of these theorems to calculating the fair price of a European call …
Monte Carlo Methods For Confidence Bands In Nonlinear Regression, Shantonu Mazumdar
Monte Carlo Methods For Confidence Bands In Nonlinear Regression, Shantonu Mazumdar
UNF Graduate Theses and Dissertations
Confidence Bands for Nonlinear Regression Functions can be found analytically for a very limited range of functions with a restrictive parameter space. A computer intensive technique, the Monte Carlo Method will be used to develop an algorithm to find confidence bands for any given nonlinear regression functions with a broader parameter space.
The logistic regression function with one independent variable and two parameters will be used to test the validity and efficiency of the algorithm. The confidence bands for this particular function have been solved for analytically by Khorasani and Milliken (1982). Their derivations will be used to test the …