Financial Engineering in Interest Rates & FX

This is a high-level quantitative finance short course. Study quantitative finance and you’ll develop your knowledge of the most widely used models in the banking industry, particularly in relation to the interest rate and FX markets.

Learn from a highly experienced banking practitioner to prepare for the next steps in your finance career. You’ll also develop your knowledge of the C++ programming language.

Study quantitative finance online and you’ll learn the most important concepts in financial engineering from an expert with over 12 years of experience in the banking industry. A solid grounding in quantitative finance and the ability to use C++ will allow you to take the next steps in your banking career.

The course is taught once a week on weekday evenings, allowing you to fit your learning in around other commitments.

Who is it for?

You’ll need some knowledge of financial engineering to join this course. Strong mathematical skills are a must. It’s the ideal way into roles such as quantitative analyst, market risk manager or market risk model methodology manager.

Timetable

This course takes place for two hours every Wednesday evening for 10 weeks.

City Short Courses follow the academic year, delivering courses over three terms. These include:

• Autumn - October
• Spring - January
• Summer - April

Benefits

• Taught by an industry professional
• Access to online materials
• Awarded a City, University of London certificate

We will Price on Binomial Model, Trinomial Model, and  Monte Carlo models European Options, Digitals, Spread Options. Then extend our implementation to Barriers, Double-No-Touches. On the American Optionality, we will look at the switch Optionality for American Options on the trees and then on to the Monte-Carlo we will investigate the Longstaff-Schwartz methodology for exercise decision strategy on multi-call options. Then we will transition into pricing implementation for Swaptions and variance Reduction techniques on Sum of Libor Options.

More granularity of the course as follows:

1. Binomial Pricer
   • Cox-Ross-Rubinstein Procedure for Binomial Model Pricing
   • Functions, Pointers, Function Pointers
   • Classes, Inheritance, Virtual Functions
2. American Options
   • Multiple Inheritance
   • Virtual Inheritance
   • Class Templates
3. Monte-Carlo Methods
   • Path-dependent Options
   • Pricing Error
   • Greek Parameters
   • Variance Reduction
   • Path-dependent Basket Options
4. Non-linear solvers
   • Implied volatility
   • Bisection method
   • Newton-Raphson method
   • Function pointers
   • Virtual inheritance
   • Computing implied volatility
5. Introduction to interest rate concepts and Yield Curve Construction: Bootstrapping and interpolation:
   • Simply and Continuously compounded interest rates
   • Relationship between yield and inst forward rates
   • Zero-Coupon Bonds, Coupon Bearing Bonds, Swaps
   • Swaps as stochastic weighted sums of forward rates
   • 1. Linear in “yield*T)” (= R(0,T)*T)
   • 2. Linear in “yield” ( = R(0,T) )
   • 3. Linear in “log Rate” ( = log R(0,T) )
   • 4. Linear in “Discount Factors”
   • Tension Splines, Cubic Splines
   • C++ coding for all the above Yield Curve Construction methodologies
6. Short Rate Modeling
   • Merton, Vasicek, Hull-White (HW) one-factor.
   • Bond pricing/calibration
   • Caplet pricing as Option on Bond
   • Swaption Pricing – Jamshidian’s trick
   • Multi-factor HW
   • Shape of the yield curve
   • C++ coding of European option pricing on one and multi-factor HW.
7. Forward Rate modeling Heath-Jarrow-Merton model (HJM)
   • Libor volatility in terms of forward rate volatilities - Repricing of Caplets through Libor volatility and agreement with HW short-rate models.
   • Separability of volatility and Markovian representation of state variables.
   • Cheyette model
   • C++ pricing of Options
8. Libor Market Model
   • Numeraire – Spot, Terminal measures
   • Drift equations
   • Lognormal, CEV, and Displaced Diffusion Dynamics of Libors
   • Libor evolution
   • C++ Coding of Evolution of Libors. Calculation of Libors at reset times
   • PCA – Principal Component analysis and rank reduction of the model
   • Stochastic Volatility
9. Markov Functional Models
   • Explanation of the model details
   • Calculation of convexity adjustment at reset times
   • C++ code for convexity calculation
10. Option Pricing in Monte-Carlo Routine.
    • Extraction of the Implied Volatility Skew/Smile from SABR, CEV, and Normal models.
    • Option pricing C++ code for early exercise
    • Inflation, Stochastic spread yield curves, Local Volatility modeling etc if time allows.
11. SABR model / Option Hedging in Discrete and continuous time.

There’s no formal assessment for this course, but you will receive a certificate of completion.

This course is well-regarded across London, and employers here will understand that you’ve covered a wide range of material and developed extensive knowledge in the area of financial engineering in interest rates and FX.

Teaching

Your time in the virtual classroom will be split between lectures and completing exercises based on what is covered each week. Some of the projects you work on will be completed in C++.

The lectures are delivered by Dr Emiliano Papa, Director at Deutsche Bank. He has extensive experience in the field of quantitative finance and is still an active practitioner in the banking industry.

• You need some prior knowledge of financial engineering as well as strong mathematical skills, to succeed on this course.

• You should also be able to implement object-oriented concepts in C++ at a ‘schoolbook’ level such as taught in our course Object Oriented Programming using C++ Part 2

English requirements

You will need fluent spoken and written English to enrol on this course.

Books that cover the course well from the theory and coding perspective include:

• John Hull, Options, Futures and Other Derivatives, Prentice Hall 2006.
• Steve Shreve, Stochastic Calculus for Finance II, Springer 2004.
• Martin Baxter and Andrew Rennie, Financial Calculus: An Introduction to Derivative Pricing, Chapter 5, (CUP 1996).
• Mark Joshi, C++ Design Patterns and Derivative Pricing, (Cambridge University Press, 2004).