INSTITUTE OF APPLIED MATHEMATICS
Last Updated:
21/07/2017 - 12:25

IAM615 - Advanced Stochastic Calculus for Finance

Credit: 3(3-0); ECTS: 8.0
Instructor(s): Azize Hayfavi
Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Financial modelling beyond Black-Scholes Model. Stochastic processes. Building Lévy processes. Option pricing with stochastic processes: Stochastic calculus for semimartingales, change of measure, exponential Lévy processes, stochastic volatility models, pricing with stochastic volatility models. Hedging in incomplete markets, risk-neutral modeling. Integro-partial differential equations. Further topics in numerical solutions, simulation and calibration of stochastic processes.

Course Objectives

The current market models using Brownian Motion have difficulty in accounting for the abrupt changes of financial markets, whereas models based on Lévy processes, themselves practically a combination of Brownian motions and Poisson processes, are more incline to respond to this need. This course reconsiders almost all the models used in Financial Mathematics beyond Black-Scholes model and completes the knowledge of students who have already been initiated to models in terms of the Brownian Motion.

Course Learning Outcomes

Tentative (Weekly) Outline

Financial modelling beyond Black-Scholes Model. Stochastic processes. Building Lévy processes. Option pricing with stochastic processes: Stochastic calculus for semimartingales, change of measure, exponential Lévy processes, stochastic volatility models, pricing with stochastic volatility models. Hedging in incomplete markets, risk-neutral modeling. Integro-partial differential equations. Further topics in numerical solutions, simulation and calibration of stochastic processes.

More Info on METU Catalogue

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