- Title
- A derivation of the the black-scholes equation using martingales
- Creator
- Nyarko , Ebenezer Narh
- Subject
- Mathematical models
- Date
- 2018
- Type
- Thesis
- Type
- Masters
- Type
- MSc
- Identifier
- http://hdl.handle.net/10353/14572
- Identifier
- vital:40016
- Description
- This work focuses on the application of stochastic differential equations, with martingales, in finance. The emphasis is on the derivation of the Black-Scholes model for the valuation of options. A theoretical framework in stochastic analysis, together with Itô calculus (Kiyoshi Itô), is explored. The Girsanov Theorem is applied in order to transform a modelled stochastic equation based, on predetermined stock and bond prices, into equivalent martingale measures. A replication strategy is then adopted to solve the two equations analytically, by finding the natural logarithm of the expectation of the solution to the stochastic models. We finally compute the resulting solution based on a standard, normal distribution to get the desired outcome of the Black-Scholes model.
- Format
- 57 leaves
- Format
- Publisher
- University of Fort Hare
- Publisher
- Faculty of Science and Agriculture
- Language
- English
- Rights
- University of Fort Hare
- Hits: 939
- Visitors: 961
- Downloads: 75
Collections
UFH Department of Mathematics
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | MSc Mini-Dissertation EN Nyarko 201012882.pdf | 962 KB | Adobe Acrobat PDF | View Details Download |