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Quant Option Pricing - Exotic/Vanilla: Barrier, Asian, European, American, Parisian, Lookback, Cliquet, Variance Swap, Swing, Forward Starting, Step, Fader

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jkirkby3/PROJ_Option_Pricing_Matlab

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Option Pricing PROJ Method (Exotic/Vanilla Options)

Option pricing (exotic/vanilla derivatives) based on an efficient and general Fourier transform pricing framework - the PROJ method (short for Frame Projection). The modules are organized by Pricing Method, then by Model, and then by Contract Type. Each contract has a run script, which starts with "Script_", e.g. "Script_BarrierOptions.m". Monte Carlo and other pricing libraries are also provided to support R&D.

Pricing methods supported:

  • PROJ (General Purpose Fourier Method)
  • CTMC Approximation
  • Monte Carlo
  • Analytical
  • Fourier (PROJ, Carr-Madan, CONV, Lewis, COS, Mellin Transform, Hilbert Transform)
  • PDE/Finite Difference
  • Lattice/Tree

Models supported:

  • Diffusions (Black-Scholes-Merton)
  • Multi-Dimensional Diffusions (Black-Scholes Multi-Asset)
  • Jump Diffusions (Merton Jump, Kou double exponential, Mixed-Normal)
  • General Levy processes (CGMY/KoBoL, Normal-Inverse-Gaussian (NIG), Variance Gamma, Meixner, FMLS, TS, Bilateral Gamma)
  • SABR
  • Stochastic Local Volatility (SLV)
  • Regime switching jump diffusions
  • Time-changed processes
  • Stochastic Volatility (Heston/Bates, Hull-White, 4/2, 3/2, alpha-hypergeometric, Jacobi, Schobel-Zhu, Stein-Stein, Scott, tau/2)

Contract types supported (single underlying):

  • European Options
  • Barrier Options (Single/Double barrier, and rebates)
  • Asian Options (Discrete/Continuous)
  • Discrete Variance Swaps, Variance/Volatility Options
  • Bermudan/American early-exercise Options
  • Parisian Options (Cumulative and resetting Parisian barrier options)
  • Cliquets/Equity Indexed Annuities (Additive/Multiplicative)
  • Equity Linked Death Benefits / Guaranteed Minimum Death Benefits (GMDB)
  • Forward Starting Options
  • Step (Soft Barrier) Options
  • Lookback/Hindsight Options
  • Credit default swaps / default probabilities
  • Swing Options (Fixed Rights, Linear Recovery & Constant Recovery)
  • Fader/Range-Accrual Options
  • Multi-Dimensional Payoffs, European/Bermudan/Barrier (Spread, Exchange, Best/Worst-of, Basket)
  • Risk Measures suchs as Expected Shortfall and VaR computations

Contract types supported (multi underlying):

  • European / Barrier / Bermudan Options
  • Spread, Exchange, Best-of, Worst-of, Basket (Geometric/Arthmetic)

Acknowledgement: These pricing libraries have been built in collaboration with:

Supporting Research Articles:

I) Levy Models, Jump Diffusions, Black Scholes

II) Stochastic Volatility, Markov Chains, and Regime Switching

III) Stochastic Local Volatility (SABR, Quadratic SLV, etc)

IV) Time-Changed Processes

V) Multi-Dimensional Diffusions