Derivatives Pricing, Artificial Intelligence and Quantum Algorithms
COURSE OBJECTIVE
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.
WHO SHOULD ATTEND?
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 €
Schedules:

Europe: MonFri, CEST 1619h

America: MonFri, CDT 1821 h

Asia: MonFri, IST 1821 h
Level: Advanced
Duration: 33 h
Material:

Presentations PDF

Exercises in: Excel, R, Python and Jupyterlab
AGENDA
Derivatives Pricing, Artificial Intelligence and Quantum Algorithms
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 quantumclassical 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 KMeans
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

BlackScholes

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

CallPut 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

BaroneAdesi 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

HullWhite 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

Multidimensional NewtonRaphson 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

Onefactor models

Vacicek's model

Cox–Ingersoll–Ross model

HullWhite model


Traditional calibration

Calibration with machine learning

Neural networks to calibrate stochastic models

Vasicek's model

Hull–White model


Exercise 31: Calibration of the HullWhit, 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)

Riskfree 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

MultiAsset/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

Bestof and Worstof 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 CarrMadan, 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

BlackSholes 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 BlackSholes 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
QUANTUM PRICING
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 BullSpread

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

CVA, DVA, LVA, FVA, CollVA, KVA

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

Riskneutral 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