Descriptif
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). Speakers from the industry will share their experience on the markets by giving a few presentations.
Diplôme(s) concerné(s)
Format des notes
Numérique sur 20Littérale/grade réduitPour les étudiants du diplôme M2 Probabilités et Finance
Programme détaillé
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
