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# Advanced Financial Mathematics Workshop

Duration: 2 days
• Yield Curve Estimation
• Advanced Cash Flow Analysis
• Historical Simulations
• Scenario Analysis and Stress Testing
• Monte Carlo Simulation
• Pricing Complex Instruments
• Principal Components Analysis
At this advanced-level workshop, participants will learn how to develop and implement advanced financial models in MICROSOFT™ Excel™ and Visual Basic™ for Applications. We shall start with the estimation of yield curves and advanced cash flow analysis. Participants will learn how to “bootstrap”, smooth and interpolate the swap-curve (using the Cubic Spline technique), and they will use this curve to price selected instruments. We will then explain how Excel/VB can be used to perform historical simulations and scenario analysis. We will also show how “Stress Testing” can be performed using Extreme Value Theory analysis. After that, we will explain and work hands-on with the Monte Carlo Simulation. Participants will learn to generate random numbers and samples from uniform and normal distributions. We will define the stochastic differential equations (SDEs) for various processes for equities prices, interest rates etc., and use these SDEs in conjunction with Monte Carlo simulation routines to price and risk-assess various financial instruments, including path-dependent exotic options. We will show how to use “Cholesky Decomposition” when sampling from multivariate distributions, and we will discuss possible ways of achieving ”variance reduction”. The techniques are then used to price a range of complex financial products, such as exotic options. Finally, participants will learn how to implement “Principal Components Analysis” and how to combine PCA with Monte Carlo simulation in order to create efficient pricing and risk management applications that can be used in practice.

## Day One

### 09.15 - 12.00  Yield Curve Estimation and Cash Flow Analysis

• Yield Curves, Par Curves and Zero Coupon Curves
• Estimation Techniques
• Bootstrapping
• Cubic Spline
• Other Estimation Techniques
• Estimating and Valuing Complex Cash Flows
• Cash flows with pre-payment features

• Computer Workshop (Excel/VB)
Participants program yield curve estimation routines in Excel/VB and use the estimated yield curves to value complex cash flows

### 13.00 - 16.30  Monte Carlo Simulation

• Introduction to Monte Carlo Simulation
• Monte Carlo Toolkit
• Generating random numbers
• Sampling from normal/lognormal distributions
• Stochastic Differential Equations
• Cholesky Decomposition
• Variance reduction techniques
• Stratified sampling
• Control Variate
• Antithetic sampling

• Computer Workshop (Excel/VB)
Participants program and test sampling routines, SDE’ s and Cholesky factorisation routines

## 09.00 - 12.00  Pricing Complex Instruments

• Pricing Complex Interest Rate Products
• Defining and Calibrating Interest Rate Models
• Pricing Interest Rate Options and Structured Interest Rate Products
• Pricing Exotic Interest Rate Structures Using Monte Carlo Simulation
• Calculating VaR for complex instruments

• Computer Workshop (Excel/VB)
Participants price selected (exotic) structures using MC simulation

### 13.00 - 16.30  Principal Components Analysis

• Common Factors Affecting Bond Returns
• Overview of Multi-Factor Interest Rate Risk Models
• The Factor Model
• Eigenvalues, Eigenvectors and the Yield Curve  