Monte Carlo Methods and FX Derivatives Markets

Course Code :2000WETMCM
Study domain:Mathematics
Academic year:2019-2020
Semester:2nd semester
Contact hours:48
Credits:6
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction:English
Exam period:exam in the 2nd semester
Lecturer(s)Uwe Peter Wystup

3. Course contents *

We develop Monte Carlo simulation techniques from scratch and use these to calculate values and Greeks of financial products. In the course of this we get to know most frequently traded financial instruments including forwards, vanilla options, barrier options/touch products, Asian options, structured forwards, target forwards, variance and volatility swaps. Simulation methods are driven by the requirements of the products and will include random number generation, sampling from various distributions, confidence intervals, pathwise differentiation, likelihood ratio methods, finite differences, Brownian bridges, variance reduction techniques, efficient simulation. The models we cover include Black-Scholes, jump-diffusion models (Merton, Kou), stochastic volatility (Heston).

The second part of the course deals with Foreign Exchange (FX) derivatives markets: we construct the volatility smile surface from Brokers’ raw data, compare techniques for interpolation and extrapolation of the volatility smile including parabolic, polynomial, vanna-volga-based, stochastic-volatility-inspired (SVI), stochastic volatility based (SABR). We cover market conventions (at-the-money, risk reversals, butterflies, strangles) in detail, understand switching between the strike-space, moneyness space and the delta space and work on case studies how the FX product range can be applied to hedging FX risk for corporate treasurers and institutional investors. Simulation methods of the first part of the course can then be applied to structured forwards and target forwards.

In this course practical experience with the implementation of financial models will be obtained via Excel/VBA or matlab.