Stochastic modelling and derivatives in traditional markets and in crypto-markets

E. Gobet

Last updated on Aug 28, 2023

This course runs from September to October, 3 or 6 hours per week.

This course provides an overview of derivatives from a stochastic modeling and risk management perspective. The markets considered range from traditional markets (stocks/equity indices, foreign exchange) to the new crypto-markets (digital assets, blockchain, decentralized exchanges, automated market makers, etc). The main instructor for this course is

Speakers from the industry will share their experience on the markets by giving a few presentations:

The derivatives market is an important element in the transfer of market risk between investors (banks, hedge funds, financial institutions, etc). The objective of the course is to describe the financial products offered, and the theoretical and practical methods used in the market to value and hedge these financial products. The topics covered are the following.

I – Introduction to Financial markets

  1. Traditional financial market
  2. Crypto-markets

II – Introduction to Pricing and Hedging

  1. Valuation without model, arbitrage
  2. Carr formula
  3. Binomial model
  4. Continuous-time market
  5. Black-Scholes formula, PDE, greeks

III – Some alternatives to lognormal modeling and pricing

  1. Implicit distribution
  2. Implied volatility
  3. Volatility skew and smile
  4. Merton and Heston models, Fourier-based pricing

IV – Market data and statistics

  1. Market data, order book
  2. Reference price vs Index
  3. Robust statistics
  4. Bid-ask spread on options

V – Pricing and hedging derivatives: general case

  1. Modelling the volatility
  2. Self-financing portfolio and no arbitrage
  3. Complete market
  4. Change of numéraire and applications
  5. Black formula with stochastic interest rates
  6. Future markets
  7. Forex

VI – Derivatives in crypto-markets

  1. Centralized Exchanges
  2. Lending-borrowing protocols in Decentralized Exchanges