Stochastic modelling and derivatives in traditional markets and in crypto-markets
E. Gobet
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
- Emmanuel GOBET, https://www.linkedin.com/in/emmanuel-gobet-0569b841/
Speakers from the industry will share their experience on the markets by giving a few presentations:
- Dorinel BASTIDE, https://www.linkedin.com/in/dorinelbastide/, traditional markets
- Clara MEDALIE, https://www.linkedin.com/in/clara-medalie-b31801124/, crypto-markets
- Anastasia MELACHRINOS, https://www.linkedin.com/in/anastasia-melachrinos-a0157a10a/, crypto-markets
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
- Traditional financial market
- Crypto-markets
II – Introduction to Pricing and Hedging
- Valuation without model, arbitrage
- Carr formula
- Binomial model
- Continuous-time market
- Black-Scholes formula, PDE, greeks
III – Some alternatives to lognormal modeling and pricing
- Implicit distribution
- Implied volatility
- Volatility skew and smile
- Merton and Heston models, Fourier-based pricing
IV – Market data and statistics
- Market data, order book
- Reference price vs Index
- Robust statistics
- Bid-ask spread on options
V – Pricing and hedging derivatives: general case
- Modelling the volatility
- Self-financing portfolio and no arbitrage
- Complete market
- Change of numéraire and applications
- Black formula with stochastic interest rates
- Future markets
- Forex
VI – Derivatives in crypto-markets
- Centralized Exchanges
- Lending-borrowing protocols in Decentralized Exchanges