Financial Engineering in Interest Rates and FX (C++ applications in Quantitative Finance)  Short Courses

Course Information

Start DateStart TimeDurationCostCourse CodeApply
Wednesday 17 January 2018 18:30 - 20:30 10 weekly classes (no class on 24/1/2018) £880.00 CS3509 Apply Now
Wednesday 2 May 2018 18:30 - 20:30 10 weekly classes £880.00 CS3509 Apply Now

Course Content

In this quantitative finance evening course students learn the most widely used models in the banking industry on the Interest Rates and FX markets. The course will start with Libor Market Model for single and Multi-Currency models, then move to Markov Functional Models, the ShortRate Models, and then volatility models like SABR models, inflation, etc.

Tutor Info

Emiliano Papa received his PhD in Theoretical Physics from Oxford University. After that he spent 7 years at various academic research and lecturing positions at the University of Texas at Austin, UVA. Visiting scholar at Caltech, Brokhaven National Lab,etc. Currently he is a Director at Deutsche Bank, Heading the Rates and FX teams, having previously worked at Bank of America Merrill Lynch.


Prior knowledge required:

  • ability to implement object-oriented concepts in C++ at a 'schoolbook' level (professional experience in C++  not required);
  • strong mathematical skills;
  • knowledge of financial engineering is expected.

English Requirements

Applicants must be proficient in written and spoken English.

What will I learn?

  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

Recommended Reading

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

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).

Application Deadline: