280002 Econophysics (V) (WiSe 2017/2018)

1.Introduction
- brief historical outline;
- relations between physics and finance;

2.Basic concepts:
- arbitrage, efficient market hypothesis;
- financial leverage and financial risk;
- hedging strategy;
- portfolio;

3.Basic financial instruments:
- deposits;
- bonds;;
- stocks;
- derivatives (forward/futures, options, SWAPs);

4.Interest rates:
- interest compounding, (effective interest rate);
- continuos compounding;
- dynamics of interest rates;
- yield curve;
- FRA (forward rate agreements);

5.Random walk:
- Brownian motion, diffusion equation;
- central limit theorem;
- geometric Brownian motion;
- stochastic differential equations (Ito's lemma)

6.Stocks:
- Gaussian fluctuations;
- returns and logarithmic returns:
- expected price distribution in the ideal market;
- properties of the log-normal distribution;
- non-Gaussian fluctuations; Levy distribution;

7.Risk measures;
- volatility;
- VaR (value at risk);
- ESF (expected shortfall);
- Sharpe's ratio;
- loss distribution and extreme statistics;

8.Derivatives:
- basic ideas;
- symmetric derivatives:
- options;
- option types: (European, American, exotic options);
- estimation of option price;

9.Option pricing in the ideal market:
- binomial trees;
- neutral risk (martingales);
- application of stochastic equations to option pricing;
- arbitrage pricing (based on log-normal distribution)
- Black-Scholes-Merton formula;

10.Hedging strategies:
- naked and covered positions;
- stop-loss strategy;
- Black-Scholes strategy;
- Greek letters;

11.Portfolio theory;
- volatility and diversification;
- Markowitz theory;
- conditional extremum with
conditions given by equation/inequalities;
- covariance matrix (interpretation and estimation);
- model CAPM
- non-Gaussian portfolios;

Bibliography

1) John C. Hull
Options, Futures and Other Derivatives

2) Jean-Philippe Bouchaud, Marc Potters,
Theory of Financial Risk and Derivative Pricing:
From Statistical Physics to Risk Management

3) Rosario N. Mantegna, H. Eugene Stanley
An introduction to econophysics
Correlations and Complexity in Finance