Derivative products and their price

6 Topics | 1 Quiz
Pricing options with the Black-Scholes-Merton model

11 Topics | 1 Quiz
Computational methods for pricing options

10 Topics | 1 Quiz
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Lesson

Materials

Welcome to the course "Introduction to quantitative and computational finance".

“Introduction to Quantitative and Computational Finance” is a foundational course in the emerging multidisciplinary field of Quantum computing for finance. This course is designed for all those learners or quantum enthusiasts who wish to develop their skills in quantitative finance and start a career in the finance industry. You will learn the basics of derivative products and their pricing, the Black-Scholes-Merton model for pricing vanilla derivatives, hedging, volatility modelling, and computational techniques of pricing the exotic options using the famous Monte-Carlo method and the finite difference method. The computational and modelling techniques detailed in the course through the concepts of linear algebra, multiple statistical tools, and python programming language will help you develop the fundamental concepts required for an understanding of quantum algorithms and more advanced concepts in computational finance. This course will help you build a strong foundation for modeling and developing algorithms to solve complex financial problems by applying emerging cutting–edge computational technologies. Although the field of computational finance has been expanded in every area of financial services but are limited by the classical computers’ ability to solve computationally expansive problems. Quantum Computing is proving to be a game changer in the financial services for addressing the problems involving simulation, optimisation, and machine learning. Through this course, you will be able to step into this new computation era and join the world of Quantum Computing for Finance.

**Module 1:**Derivative Products and their price- Introduction to derivative products
- Exercise: Random behavior of a google stock value
- The price of a derivative product
- Risk-neutral pricing
- Fundamental theorem of asset pricing
- Pricing options with the Binomial model

**Module 2:**Pricing options with the Black-Scholes-Merton model- Introduction to stochastic calculus
- Exercise: Sample trajectories of a Brownian motion
- Introduction to the Black-Scholes-Merton model
- Exercise: A geometric Brownian motion
- The Black-Scholes formula for a European call
- The Black-Scholes partial differential equation
- Exercise: The Black-Scholes formula for a European call
- The Greeks
- Introduction to hedging
- Volatility modeling
- Implied volatility modeling

**Module 3:**Computational methods for pricing options- Monte-Carlo method - I
- Pricing a European call under the BSM model
- Pricing an Asian call option under the BSM model
- Monte-Carlo method -II
- Exercise: The constant Elasticity volatility
- The finite difference method
- The Euler scheme
- Exercise: The explicit Euler scheme
- Exercise: The implicit Euler scheme
- Summary - Computational method for pricing options