Option-Pricing

Pricing of options with various models (Black-Scholes, Heston, Merton jump diffusion, etc) and methods (Monte Carlo, finite difference, Fourier).

European Options

This folder contains notebooks with for the pricing of European options with the following models:

• Black-Scholes,
• Merton jump diffusion.

Black-Scholes

Pricing of European options according to the Black-Scholes model using the following methods:

• Analytical solution,
• Monte Carlo,
• Finite difference (explicit scheme),
• Fourier transform.

Merton Jump Diffusion

Pricing of European options according to the Merton jump diffusion model using the following methods:

• Analytical solution,
• Monte Carlo,
• Fourier transform.

Heston model

Pricing of European options according to the Heston stochastic volatility model using the following methods:

• Analytical solution
• Monte Carlo

Binomial model

Pricing of European options according to the binomial model (Cox, Ross, Rubinstein).

Exotics

Pricing of the following exotic options:

• Barrier (discrete and continuous monitoring, analytical and Monte Carlo).

Barrier options

Pricing of barrier options (discretely and continuously monitored) using the following methods:

• Analytical solution,
• Monte Carlo.

Implied Volatility

Computation of implied volatility for European options using the Newton-Raphson method and the Black-Scholes model. Plotting of the volatility smile.