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Be English-friendly or any other language-friendly means that UC is taught in a language but can either of the
following conditions:
1. There are support materials in English / other language;
2. There are exercises, tests and exams in English / other language;
3. There is a possibility to present written or oral work in English / other language.
1- Being able to use the main tools of stochastic calculus. 2- Knowing how to build an arbitrage strategy with options. 3- Being able to use the Black & Scholes model in the valuation of options (including their related alternative formulations). 4- Knowing how to build a dynamic hedging strategy. 5- Being able to implement stochastic volatility models 6- Being able to price numerically and analytically American-style options
Program
1. Introduction to (financial) Options
2. Properties of the option price
3. Hedging and Speculation with Options
4. Valuation of financial derivatives in discrete time
5. Stochastic calculus Brownian Motion; Itô?s lemma and fundamental PDE; Feynman-Kac theorem.
6. Black-Scholes Model
7. Risk-Neutral Valuation Girsanov?s theorem; Change of numeraire.
8. Historical versus implied volatility
9. Merton?s model
10. Black?s model (options on futures) Stock versus futures style margining.
11. Greeks and Dynamic Hedging of option contracts
12. Beyond the Black-Scholes model Stochastic volatility
13. American-style options Binomial model: Cox, Ross, and Rubinstein (1979); Finite difference schemes: Brennan and Schwartz (1977); Quadratic approximation: Barone-Adesi and Whaley (1987); Integral representation method: Carr, Jarrow, and Myneni (1992), Ju (1998), Kim and Yu (1996) Optimal stopping approach: Nunes (2009)
Evaluation Method
The final grade will be based on two components:
a) Class participation and home works (50%); b) Final exam (open book exam) concerning the all syllabus (50%).
Teaching Method
Classes have mainly a practical content.
The classes with be focused on the application of stochastic calculus to Finance and, in special, to the valuation of American-style options.
Some Matlab programs and specific financial options software will also be used in the solutions of some problems.
Observations
Basic Bibliographic
Baxter, M., and A. Rennie, 1996, Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press.
Björk, T., 1988, Arbitrage Theory in Continuous Time, Oxford University Press.
Hull, J., 2008, Options, Futures and other Derivatives, Prentice Hall, 7th edition.
Cox, J., S. Ross, and M. Rubinstein. ?Option Pricing: A Simplified Approach.? Journal of Financial Economics, 7 (1979), 229-263.
Brennan, M., and E. Schwartz. ?The Valuation of American Put Options.? Journal of Finance, 32 (1977), 449-462.
Barone-Adesi, G., and R. Whaley. ?Efficient Analytic Approximation of American Option Values.? Journal of Finance, 42 (1987), 301-320.
Carr, P., R. Jarrow, and R. Myneni. ?Alternative Characterizations of American Put Options.? Mathematical Finance, 2 (1992), 87-106.
Ju, N. ?Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function.? Review of Financial Studies, 11 (1998), 627-646.
Kim, J., and G. G. Yu. ?An Alternative Approach to the Valuation of American Options and Applications.? Review of Derivatives Research, 1 (1996), 61-85.
Longstaff, F and E. Schwartz, 2001, Valuing American Options by Simulation: A Simple Least-Squares Approach, Review of Financial Studies 14, 113-147.
Nunes J (2009), ?Pricing American options under the constant elasticity of variance model and subject to bankruptcy?. Journal of Financial and Quantitative Analysis 44:1231-1263
