ADVANCED TOPICS IN FINANCIAL MATHEMATICS

Graduate

This course explores continuous-time models in financial mathematics. Topics include Brownian motion, geometric Brownian motion, quadratic variation, Riemann-Stieltjes and Ito integrals, Ito’s formula, replication and risk-neutral pricing under the Black-Scholes economy, Black-Scholes partial differential equation, delta-hedging for multi asset derivatives, and valuation of cross currency options. Graduate students will be required to learn and implement additional computational techniques such as Monte Carlo or numerical solutions of partial differential equations resulting from option pricing problems. Higher expectations for graduate students will be established for assessments, including a graduate level project involving computational techniques. This course is cross-level listed with AMS 4090. Credit cannot be received for both MCS 8090 and AMS 4090. PREREQUISITE: Admission to a graduate program in Science HOURS OF CREDIT: 3