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

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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.

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

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