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Derivatives Pricing, Artificial Intelligence and Quantum Algorithms





Advanced course on valuation of derivative products using traditional models, AI, and quantum computing for variable income, fixed income, exchange rate, and credit.


The course covers various topics related to options trading, including hedging strategies and advanced pricing models for interest rate options. It also covers implicit, local and stochastic volatility models, as well as the Jump Diffusion Model. 

To properly value interest rate options, a module is dedicated to the construction of the Yield Curve, which is crucial for the valuation of interest rate derivative models. The course also covers the recent Libor transition and the creation of the SOFR yield curve, which will impact the pricing of derivatives and XVA. 

Moreover, the course introduces the application of machine learning tools such as neural networks and deep learning to value derivatives, calibrate stochastic differential equations, estimate implicit volatility and create the yield curve.

The course explains how to value exotic options of the first and second generation using machine learning models.


Numerical methods are exposed, such as partial differential equations, PDEs, trinomial trees and traditional Monte Carlo simulation, in addition to increasing calculation speed, pricing of options is explained through Fourier transformations and improvements in Monte Carlo Simulation. To significantly speed up the estimation of the Greeks, the Adjoint of Automatic Differentiation algorithm has been included.


The course has a significant number of exercises in Julia, Python and R as well as case studies that enhance learning. The advantages and disadvantages of each language for the valuation of derivatives are addressed. We have introduced a new language, called Julia, which is powerful, simple and very fast. All exercises in the JupyterLab environment.

Monte Carlo simulation is the most widely used technique to value derivatives. However, banks are turning to machine learning in an attempt to give their pricing models a boost. The technique consists of training deep neural networks to approximate the results to Monte Carlo models without having to run millions of simulations. The neural network approximates the price of your portfolio when you run a gigantic and complicated XVA.

XVA valuation adjustment methodologies are exposed, among other models: estimation of credit exposure, Credit Value Adjustment CVA, debit value adjustment DVA, Funding Value Adjustment, CoLVA, MVA and KVA, exposing traditional methodologies and deep learning models.

Pricing is a computationally demanding task that is traditionally solved using Monte Carlo simulation techniques. However, Quantum Accelerated Monte Carlo (QAMC) quantum computing techniques promise quadratic acceleration over Monte Carlo (MC) simulation, this quantum advantage of increasing computational speed would bring substantial benefits, particularly for the huge volume of derivative products what is on the market.

The quantum advantage of QAMC over MC simulation and the advantage of quantum machine learning over the traditional one will be exposed.

Didactic course, clearly presented, with the experience and quality of Fermac Risk, seeking to make the participant's learning the most important thing. The course is practical to apply what is learned immediately at work.



People who work in the following departments: Investment Management, Treasury, Credit Risk Analysis, Portfolio Modeling, Model Validation, Quantitative Research, Structuring, Pricing, Market Risk, methodologies, financial management, financial controllers and Portfolios managers. From banks, brokerage firms, corporations, insurance, stockbrokers, brokerage firms and stockbrokers.


The course does not address abstract mathematics or complex theory. Nevertheless, the mathematical models are seriously explained. The student will know not only the theory but also practical exercises. It is advisable to master some programming language.





Price: 6.900 €



  • Europe: Mon-Fri, CEST 16-19h


  • America: Mon-Fri, CDT 18-21 h

  • Asia: Mon-Fri, IST 18-21 h






Level: Advanced


Duration: 33 h




  • Presentations PDF

  • Exercises in: Excel, R, Python and Jupyterlab 



Derivatives Pricing, Artificial Intelligence and Quantum Algorithms


Anchor 10

Artificial Intelligence in Finance

​Module -2: AI in Finance (optional)

  • AI artificial intelligence in finance

  • Definition of Machine Learning

  • Machine Learning Methodology

    • Data Storage

    • Abstraction

    • Generalization

    • Assessment

  • Supervised Learning

  • Unsupervised Learning

  • Reinforcement Learning

  • deep learning

  • Typology of Machine Learning algorithms

  • Steps to Implement an Algorithm

    • Information collection

    • Exploratory Analysis

    • Model Training

    • Model Evaluation

    • Model improvements

  • Machine Learning in Finance

  • Applications in the valuation of options, projections, asset management and trading


Module -1: Deep Learning (optional)

  • Definition and concept of deep learning

  • Why now the use of deep learning?

  • Neural network architectures

  • Activation function

    • Sigmoidal

    • Rectified linear unit

    • Hypertangent

    • Softmax

  • Feedforward network

  • Multilayer Perceptron

  • Using Tensorflow

  • Using Tensorboard

  • R deep learning

  • Python deep learning

  • Convolutional Neural Networks

  • Use of deep learning in image classification

  • cost function

  • Gradient descending optimization

  • Using deep learning for credit scoring

    • How many hidden layers?

    • How many neurons, 100, 1000?

    • How many times and size of the batch size?

    • What is the best activation function?

  • Deep Learning Software: Caffe, H20, Keras, Microsoft, Matlab, etc.

  • Deployment software: Nvidia and Cuda

  • Hardware, CPU, GPU and cloud environments

  • Advantages and disadvantages of deep learning

  • Feedforward neural network

  • Multilayer Perceptron

  • Convolutional Neural Networks

  • Use of deep learning in image classification

  • recurrent neural networks

  • Temporal series

  • Long Short Term Memory

  • Exercise 1: Deep Learning feedforward perceptron neural network

Module 0: Quantum computing and algorithms (Optional)

  • Future of quantum computing in banking

  • Is it necessary to know quantum mechanics?

  • QIS Hardware and Apps

  • Quantum operations

  • Qubit representation

  • Complex numbers

  • Measurement

  • Overlap

  • Matrix multiplication

  • Qubit operations

  • Multiple Quantum Circuits

  • Entanglement

  • Deutsch Algorithm

  • Quantum Fourier transform and search algorithms

  • Hybrid quantum-classical algorithms

  • Quantum annealing, simulation and optimization of algorithms

  • Quantum machine learning algorithms

  • Quantum limitation

  • Quantum computers

  • Exercise 2: Quantum computing operations

Unsupervised Learning


Module 1: Unsupervised models

  • Hierarchical Clusters

  • K Means

  • standard algorithm

  • Euclidean distance

  • Principal Component Analysis (PCA)

  • Advanced PCA Visualization

  • Eigenvectors and Eigenvalues

  • Exercise 3: Principal components for yield curve

  • Exercise 4: Segmentation of financial data with K-Means

Supervised Learning​​​


Module 2: Support Vector Machine SVM

  • SVM with dummy variables

  • SVM

  • Optimal hyperplane

  • Support Vectors

  • Add costs

  • Advantages and disadvantages

  • SVM visualization

  • Tuning SVM

  • Kernel trick

  • Exercise 5: Support Vector Machine in Python financial data

Module 3: Neural Networks (Neural Networks NN)

  • Artificial neuron

  • Perceptron Training

  • perceptron

  • Backpropagation algorithm

  • Training procedures

  • Tuning NN

  • NN display

  • Advantages and disadvantages

  • Exercise 6: Neural Networks in Python financial data

Module 4: Ensemble Learning

  • Set models

  • Bagging

  • Bagging trees

  • Random Forest

  • Boosting

  • Adaboost

  • Gradient Boosting Trees

  • Advantages and disadvantages

  • Exercise 7: Random Forest, R and Python, data 1 and 2

  • Exercise 8: Gradient Boosting Trees​

Futures and Options


Module 5: Futures and Options


  • Derivatives market in Spain

  • Derivatives Market in Latin America

  • Futures

  • Forwards

    • Fx Forwards

    • FRAs

  • Swaps

    • Interest Rate Swaps IRS

    • Equity Swaps

    • Forex Swaps

    • Credit Default Swap CDS

  • ​Features Options

  • Type of options

  • European and American Call and Put

  • Valuation Models

    • Black-Scholes

    • HestonModel

    • Binomial tree

  • Stock and Currency Indices Options

  • Exercise 9: Heston Model

  • Exercise 11: Call Option Valuation in Python

  • Exercise 12: American Option Binomial Valuation in Python

  • Exercise 14: Option valuation by Monte Carlo Simulation in R and Python

  • Exercise 15: Black and Scholes titration in R

Module 6: Strategies with Options


  • Bullish, Bearish, movement and stability strategy

  • Bull and Bear Spread

  • Call-Put Back Spread Ratio

  • Purchase and Sale of Tunnel

  • Straddle and Strangle

  • Butterfly Strategies

    • Butterfly spread with calls

    • Butterfly spread with puts

  • Condor Strategies

    • Put

    • Calls

  • How do traders use the price of options?

Module 7: Treatment of volatility

  • Garch model

  • Implied Volatility

  • Local Volatility

  • volatility surfaces

  • volatility smiles

  • Stochastic volatility models

  • Jump Diffusion model

  • Volatility treatment using neural networks

  • Exercise 16: Local and Implied Volatility in R, volatility surface plots in R

  • Exercise 17: GARCH volatility modeling in Python

  • Exercise 18: Jump diffusion model simulation in R

  • Exercise 19: Neural Networks for implied volatility

Module 8: Option Portfolio Management

  • Coverage parameters

  • Greek: Delta, Gamma, Vega, Theta, Rho

  • Track and adjust option positions in real time

  • Simulations and analysis of option price sensitivities

  • Barone-Adesi and Whaley model

  • Monitoring and real management of:

    • Delta

    • Gamma

    • Theta

    • Vega

    • Elasticity

  • Adjustments before changes in volatility

  • Relationship between coverage parameters

  • Greek estimation approaches:

    • Differentiation

    • Binomial tree

    • Finite difference estimation

    • Maximum Likelihood Estimation (MLE)

  • Exercise 20: Estimation of Greek delta, gamma, theta and vega in Julia and Python

  • Exercise 21: Estimation of Greeks using R

Module 9: Derivatives used in Banking

  • Variable Income Derivatives

    • Variable Income Options

    • Equity Swaps

    • Organized Market Options

  • Fixed Income Derivatives

    • Fixed income forwards

  • Exchange rate derivatives

    • Cross Currency Swap

    • Exchange rate options

  • Credit Derivatives

    • Credit Default Swap CDS

  • Exercise 22: Pricing Cross Currency Swap

  • Exercise 23: Equity Option Pricing in Python

Interest Rate Options


Module 10: Term structure of interest rates (Yield Curve)

  • ETTI construction

  • Available instruments

    • Bonuses and Deposits

    • FRAs

    • Interest Rate Swap

    • Basis Swap

    • Cross Currency Swap

  • Using multiple instruments

  • ETTI in practice and main Issues

  • Collateralized curve

    • Overnight Index Swaps (OIS)/EONIA

  • Bootstrap approach

    • PCA Main Components

    • Euribor curve

    • Eonia curve

  • Focus Interpolation

    • Cubic Splines

    • Basis Splines

  • Approach Extrapolation

    • Smith wilson

  • Nelson Siegel Model Approach

    • Calibration

  • Stochastic modeling

    • Vasicek's model

    • Cox–Ingersoll–Ross model

    • Ornstein–Uhlenbeck model

    • Hull-White model

  • Neural networks to calibrate stochastic models

    • Vasicek's model

    • Hull–White model

  • Libor Market Model

  • Martingales and Numerary

  • Calibration of caps and swaptions

  • Multicurve Models

  • SABR models for negative rates

  • Exercise 24: Construction of Euribor and Eonia Interest Rate Term Structure Curve in Python

  • Exercise 25: Construction of the interest rate Term Structure Curve. Case study with deposits, FRAs and Interest Rates Swaps and PCA main components

  • Exercise 26: Real Case Bank of Spain Nelson Siegel exercise in R and Excel

  • Exercise 27: Temporary structure of cubic splines and basis splines in Excel

Module 11: Term interest rate structure for SOFR (Yield Curve)

  • Dual Bootsrapping

  • Multi yield curve

  • Calibration and optimization

  • New instruments for SOFR USD

  • Libor vs. ARR Rates

  • New risks to manage

  • Singular calibration curve

  • Global Calibration Interpolation

  • Optimization Model

  • Multi-dimensional Newton-Raphson solver

  • Using Jacobians for recalibration

  • Selection of instruments for calibration ARR Instruments

  • Yield Curve Calibration Steps

  • Requirements to achieve a proper calibration

  • Exercise 28: Multicurve estimation and optimization with Jacobian matrices in Python

  • Exercise 29: Multicurve estimation with Jacobian matrices

  • Exercise 30: SOFR curve estimation

Module 12: Calibration of stochastic interest rate models


  • Yield curve analysis

  • One-factor models

    • Vacicek's model

    • Cox–Ingersoll–Ross model

    • Hull-White model

  • Traditional calibration

  • Calibration with machine learning

  • Neural networks to calibrate stochastic models

    • Vasicek's model

    • Hull–White model

  • Exercise 31: Calibration of the Hull-Whit, CIR and Vacisek models

Module 14: Futures, Swaps and Interest Rate Options


  • Futures and Swaps

  • Forward Rate Agreements (FRAs)

  • Hedging Strategies with Interest Rate Futures

  • Interest Rate Swaps (IRS)

  • Overnight Index Swaps (OIS)

    • Risk-free rate vs OIS

    • OIS zero curve

    • OIS vs Libor

    • Funding risk

    • CVA and DVA

  • Interest rate options

    • Bond Options

    • Caplets/Caps

    • Floorlets/Floors

    • Swaptions

    • Necklace

    • Reverse necklace

  • Options and Futures on interest rate on SOFR

    • SOFR Options

    • SOFR Swaps

    • SOFR Futures

    • SOFR Trading Resources

  • Valuation models

    • Pricing caps and floors using Black`s Model

    • Pricing with trinomial trees

    • Pricing of Caps and Floors using the Libor Market Model

  • Exercise 32: Pricing of caps and floors Black`s model in Excel

  • Exercise 33: Pricing of Swaption encPython

  • Exercise 34: Caplet and Swaption Libor Market Model in Excel and VBA


Exotic options

Module 15: Exotic Options 1st and 2nd generation

  • First generation

  • Asian Options

  • Click Options

  • Gap Options

  • Perpetual American call/put option

  • Choose Options

  • Lookback Options

  • Barrier Options

  • Digital/Binary Options

  • Multi-Asset/Rainbow Options

  • Second generation

  • PowerOptions

  • Corridors

  • Faders Fx Option

  • Digital Barrier Options

  • Pay Later Options

  • Step Up and Step Down Options

  • Forward Volatility Agreements (FVAs)

  • Spread and Exchange Options

  • Baskets

  • Outside Barrier Options

  • Best-of and Worst-of Options

  • Exercise 35: Pricing option Lookback in Excel with VB

  • Exercise 36: Asian Option Pricing in Python

  • Exercise 37: Barrier option pricing in Python

Module 16: Options Speed Up Pricing Techniques

  • Numerical methods

    • Optimal stopping time for American options

    • Partial Differential Equations (PDEs) for European Options

    • Monte Carlo simulation

    • PDEs: Finite Differences

    • SDE simulation

  • ​Trinomial Trees

  • Speed improvements

  • Pricing Monte Carlo Simulation

    • European Option Pricing

    • American Option Pricing

    • Pricing Option Bermuda

    • Variance reduction

    • Antithetic Variable

    • Stratified Sampling

    • Sobol sequence

  • Fast Fourier (FFT) based option pricing

    • Carr–Madan approach

    • lewis approach

    • Convolution approach

    • Greek estimate

  • Adjoint of Automatic Differentiation​​​

    • Greek sensibilities

    • speed increase

    • Disadvantage and advantages

  • Exercise 38: Pricing using Monte Carlo simulation European and American option in Python

  • Exercise 39: Call estimation with FFT approach Carr-Madan, Lewis and Convolution with Python

  • Exercise 40: option valuation using with trinomial tree

  • Exercise 41: Adjoint of Automatic Differentiation to estimate Greeks in Python

AI for derivatives valuation

Module 17: Deep Learning for valuation of derivatives

  • Deep Learning in Finance

  • Speed and precision

  • Advantages and disadvantages of deep learning over traditional techniques

  • Partial Differential Equations PDE

  • PDE deep learning

  • Stochastic Differential Equations

  • Optimization models

  • Differential Stochastic Equation Models

  • Brownian movement

  • Black-Sholes Model

  • Libor Market Model

  • Pricing of a Swaption

  • Pricing on exotic options

  • Advantages and disadvantages of deep learning

  • Exercise 42: Deep Learning to assess the Black-Sholes model

  • Exercise 43: Deep Learning for Swaption Bermuda Pricing pricing

Module 18: Machine Learning for IV and Greek

  • Gaussian process

  • Gaussian multithreading

  • Linear and nonlinear regression

  • Covariance matrix

  • Kernel functions

  • Implied volatility

  • Volatility surfaces

  • Greek estimation with machine learning

  • Deep learning

  • Exercise 44: Machine Learning for Implied Volatility

  • Exercise 45: Greek using machine learning models

Module 19: Advanced Machine Learning for measuring volatility and exotic options

  • Deep Learning in volatility

  • Pricing and calibration

  • Local Volatility

  • Implied volatility surfaces

  • Valuation of exotic options

  • Derivatives pricing

  • Greek estimate

  • Exercise 46: Deep Learning Volatility

Quantum AI for derivatives valuation


Module 20: Quantum Machine Learning

  • What is quantum machine learning?

  • Qubit and Quantum States

  • Quantum Automatic Machine Algorithms

  • quantum circuits

  • Support Vector Machine

  • Support Vector Quantum Machine

  • Variational quantum classifier

  • Training quantum machine learning models

  • Quantum Neural Networks

  • Quantum GAN

  • Quantum Boltzmann machines

  • Exercise 47: Traditional machine learning and quantum machine learning of generative adversarial neural networks to value a derivative

Module 21: Tensor Networks for Machine Learning

  • What are tensor networks?

  • Quantum Entanglement

  • Tensor networks in machine learning

  • Tensor networks in unsupervised models

  • Tensor networks in SVM

  • Tensor networks in NN

  • NN tensioning

  • Application of tensor networks in credit scoring models

  • Exercise 48: Derivatives pricing model using Neural Networks versus neural network tensorization


​Module 22: Accelerated Quantum Monte Carlo Simulation

  • Derivatives Valuation

  • Classic Monte Carlo simulation

  • Quantum Accelerated Monte Carlo (QAMC)

  • Quadratic speed

  • Coding Monte Carlo problem

  • Breadth Estimation

  • Acceleration applying the amplitude estimation algorithm

  • Quantum circuit for amplification and amplitude estimation

  • Derivatives pricing

  • Quantum PDEs

  • Exercise 49: Quantum Monte Carlo Simulation vs. Classical Monte Carlo Simulation

Module 23: Pricing of Derivatives using Quantum Algorithms

  • Derivatives pricing

  • Monte Carlo to value derivatives

  • American Options Pricing by Simulation Longstaff and Schwartz

  • Quantum algorithms for derivatives

  • Pricing call European option using quantum algorithms

  • Pricing put European option using quantum algorithms

  • Pricing Bull-Spread

  • Pricing Asian Barrier Spread

  • Basket Options Pricing Using Quantum Algorithms

  • Quantum generative antagonistic networks

  • Exercise 50: European put and call option pricing using quantum algorithm

  • Exercise 51: American option pricing using a quantum algorithm

  • Exercise 52: Pricing of derivatives using Monte Carlo versus quantum algorithms

  • Exercise 53: Basket Options Pricing using Quantum Algorithm

  • Exercise 54: Bull Spread Pricing Using Quantum Algorithm

  • Exercise 55: Pricing of the Asian Barrier Spread using a quantum algorithm

XVA Valuation Adjustments


​Module 24: What is XVA?

  • Concept of XVAs


  • Return on derivatives

  • Regulatory perspective

  • XVA Trading

  • New XVA Trader Features

  • CSA Base Price

  • Collaterals and OIS as discount rate

  • Pricing and Negative Multicurve in the XVA Framework

Module 25: Expected Exposure and Potential Future Exposure

  • Counterparty risk exposure modeling

    • MtM+Add on

    • Monte Carlo simulation

  • Potential Future Exposure (PFE)

  • Expected Exposure (EE)

  • Maximum PFE

  • Expected positive exposure

  • Negative exposure

  • Effective expected positive exposure

  • Factors: maturity, payment frequencies, optionalities and default

  • PFE of Interest Rate Swaps, Swaptions and CDS

  • Netting impact on exposure

  • Collateralized exposure modeling

  • Collateral modeling

  • Unilateral Margin Agreement

  • Bilateral Margin Agreement

  • Collateralized Exposure Profiles

  • Collateralized PFE

  • Collateralized EE

  • Exercise 56: MtM Simulation of IRS Securities

  • Exercise 57: Simulation of the interest rate using the CIR and Vacicek model to determine IRS MtM. Estimation of PFE and EE

Module 26: Credit Value Adjustment (CVA) Modeling

  • Definition and CVA concept

  • Formula and parameters

  • Factors Affecting CVA

  • Risk management by CVA

    • Collateralized Counterparties

    • Hedge on market factors

    • Spread hedge

  • CVA seen as Spread

  • Adverse Correlation Risk

  • CVA mitigation mechanisms

  • Marginal CVA and Incremental CVA

  • CVA modeling with reduced form model

    • CVA in IRS

    • CVA in IRSs portfolio

    • Risk-neutral probability

    • Simulation

  • Exercise 58: CVA, EE, PFE estimation

  • Exercise 59: CVA estimation of IRS portfolios using Monte Carlo simulation

  • Exercise 60: CVA estimation of IRS portfolios using Machine Learning

​Module 27: Debt Value Adjustment (DVA)

  • Definition of Debt Value Adjustment (DVA)

  • IFRS accounting standard

  • Bilateral CVA

  • VAD properties

  • Risk Adjusted Value

  • DVA Monetization

  • DVA Coverage or Transfer to the Treasury

  • LVA concept

  • Exercise 61: DVA Estimation

Module 28: Funding Value Adjustment (FVA) and Deep Learning for XVA

  • Concept of value adjustments for financing costs

  • Overnight Indexed Swaps (OIS) vs. Bank Interest Rates

  • Discussion about FVA

  • FVA Formula: Negative and Positive

  • CVA, DVA and FVA interaction

  • Financing cost

  • Impact of the Net Stable Funding Ratio

  • Liquidity Premium

  • Risk Adjusted Value

  • Alternative FVA estimate

    • CollCA and MVA collateral cost adjustment formula

    • HVA Coverage Cost Adjustment Formula

    • FVA estimate

  • Estimation of the cost of capital KVA

  • XVA calculation

  • XVA risk management

  • Deep Learning for XVA

  • Exercise 62: Calculation of XVA in Python

  • Exercise 63: Estimation of CVA, DVA, FVA, CollVA, HVA, KVA, LVA and XVA in Excel

  • Exercise 64: Deep Learning for FVA and XVA

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