(Winter Semester 2025/26)
The seminar will cover topics in discrete-time and continuous-time financial mathematics, with a particular focus on computational methods. Among other topics, various options and their pricing, stochastic volatility models, and approximations of the Black-Scholes model will be discussed. Partial implementation of algorithms will be expected.
Prerequisites: Financial mathematics in discrete time or financial mathematics in continuous time. For some topics, Markov decision processes.
Date: Wednesday, 11:30-13:00 Uhr, SR -1.017
Appointment for the preliminary meeting: Wednesday 23.07.25 at 13:05 in SR 2.058.
Topics for Bachelor students (Prerequisite. Fima I)
1. Pricing of American Options in Incomplete Models. Cutland/Roux S. 250- 267
2. Pricing of Options with Transaction Cost. Cutland/Roux S. 281- 292
3. Perpetual American Options. Shreve S. 119-137
4. Interest Rate Dependent Assets. Shreve S. 143-168
5. A Flexible Binomial Option Pricing Model + code Tian
6. Black Scholes implied vola + code Oosterlee/Grzelak S. 81-89
Topics for Master students (Prerequisite Fima II)
1. Option Pricing and Densities Oosterlee/Grzelak S. 89-102
2. Deep Hedging of Derivatives Using Reinforcement Learning + MDP Kenntnisse Cao et al. 2021
3. On the Pricing of Forward Starting Options in Heston’s Model on Stochastic Volatility Kruse/Nögel 2005
4. Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes Broadie/Kaya 2006
5. Pricing of American Options. Glasserman S. 421-440
6. Pricing Bermudan Options Using Regression Trees/Random Forests El Filali Ech-Chafiq et al. 2023