This course aims to develop the knowledge of the theoretical foundation of Stochastic Calculus and Derivative Pricing and Hedging. This course corresponds to the Quantitative Finance and Investment (QFI) Core and Advanced examinations by the Society of Actuaries (SOA).
Chapter 1: Introduction
Chapter 2: The Binomial Model
Chapter 3: A More General One Period Model
Chapter 4: Stochastic Integrals
Chapter 5: Differential Equations
Chapter 6: Portfolio Dynamics
Chapter 7: Arbitrage Pricing
Chapter 8: Completeness and Hedging
Chapter 9: Parity Relations and Delta Hedging
Chapter 15: Incomplete Markets
1. Bjork, T. (2009), Arbitrage Theory in Continuous Time, 3rd edition, Oxford University Press.
2. Hand-Written Notes.
1. Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives}, 2nd edition, Springer.
2. Shreve, S. E. (2004), Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer.
3. Shreve, S. E. (2004), Stochastic Calculus for Finance II: Continuous-Time Models, Springer.
4. Cochrane, J. H. (2005), Asset Pricing, revised edition, Princeton University Press.
5. Derman, E. (2004), My Life as a Quant: Reflections on Physics and Finance, Wiley.
6. Follmer, H. and Schied, A. (2016), Stochastic Finance: An Introduction in Discrete Time, 4th edition, de Gruyter.
7. Hull, J. C. (2018), Options, Futures, and Other Derivatives, 10th edition, Pearson.
8. Karatzas, I. and Shreve, S. E. (1998), Methods of Mathematical Finance, Springer.
9. Merton, R. C. (1990), Continuous-Time Finance, Wiley-Blackwell.
10. Oksendal, B. (2003), Stochastic Differential Equations: An Introduction with Applications, 6th edition, Springer.
11. Revuz, D. and Yor, M. (2005), Continuous Martingales and Brownian Motion, 3rd edition, Springer.
12. Schoutens, W. (2003), Levy Processes in Finance: Pricing Financial Derivatives, Wiley.
13. Williams, D. (1991), Probability with Martingales, Cambridge University Press.
14. Wilmott, P. (2007), Paul Wilmott Introduces Quantitative Finance, 2nd edition, Wiley.