Financial Mathematics
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King's College London Financial Mathematics |
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| Day 1. General theory of interest rate dynamics. | |
| 9.30-10.00 | Registration |
| 10.00-11.00 | Discount bonds and interest rates. Market conventions. Libor and swap rates. Short rates and forward short rates. Positive interest conditions. Interest rate derivative structures. |
| 11.00-11.30 | Coffee |
| 11.30-1.00 | Review of stochastic calculus and the theory of Brownian motion. Stochastic integrals and Itô processes. Martingales and related processes. Girsanov's theorem. Martingale representation theorem. |
| 1.00-2.00 | Buffet lunch |
| 2.00-3.00 | Stochastic dynamics for risky assets. No arbitrage and market completeness conditions. Derivatives hedging and replication. Existence and uniqueness of relative risk process. Change of measure, risk neutral valuation. Pricing kernel and natural numeraire. |
| 3.00-3.15 | Coffee |
| 3.15-4.45 | Price processes for discount bonds, no arbitrage and market completeness conditions. Interest rate volatility and correlation. Short rate and instantaneous forward rate processes. Heath-Jarrow-Morton (HJM) framework. General methodology for the valuation and hedging of interest rate derivatives. |
| 4.45-5.00 | Coffee |
| 5.00-6.00 | Review of the Flesaker-Hughston framework. Integral formulae for discount bonds. Supermartingale and potentials, Rogers' approach. |
| Day 2. Review of specific interest rate models. Extensions of the HJM theory. | |
| 9.30-10.00 | Registration |
| 10.00-11.00 | General theory of short rate models. Diffusion processes. The Feynman-Kac formula and its applications. Derivation of the bond pricing equation. Valuation of derivatives. |
| 11.00-11.30 | Coffee |
| 11.30-1.00 | Theory of affine term structure models. Gaussian interest rate models, including the Vasicek model and the Hull-White model. |
| 1.00-2.00 | Buffet lunch |
| 2.00-3.00 | The rational lognormal model and its extensions, with valuation formulae for derivatives. Caps, floors, and swaptions. Market models. |
| 3.00-3.15 | Coffee |
| 3.15-4.15 | Theory of affine term structure models, continued. Properties of square-root processes. The Cox-Ingersoll-Ross (CIR) model and its extensions. |
| 4.15-4.30 | Coffee |
| 4.30-6.00 | Multi-currency interest rate dynamics. Geometric analysis of foreign exchange volatility and correlation. Interest rate and foreign exchange derivatives. Real and nominal interest rates. Models for inflation. Valuation of index-linked bonds and other inflation related products. |