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)
- Monte Carlo
- Analytical
- Fourier (Carr-Madan, PROJ)
- PDE/Finite Difference
- Lattice/Tree
Contract types supported:
- European Options
- Barrier Options (Single/Double barrier, with early excercise, 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)
- Forward Starting Options
- Step (Soft Barrier) Options
- Fader Options (To be added)
- Swing Options (To be added)
- Lookback/Hindsight Options (To be added)
- Credit default swaps (To be added)
Models supported:
- Diffusions (Black-Scholes-Merton)
- Jump Diffusions (Merton Jump, Kou double exponential, Mixed-Normal)
- General Levy processes (CGMY/KoBoL, Normal-Inverse-Gaussian (NIG), Variance Gamma, Meixner)
- SABR
- Stochastic Local Volatility
- 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)
Acknowledgement: These pricing libraries have been built in collaboration with:
Supporting Research Articles:
- Efficient Option Pricing by Frame Duality with the Fast Fourier Transform. SIAM J. Financial Math (2015)
- An Efficient Transform Method for Asian Option Pricing. SIAM J. Financial Math (2016)
- A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps. European J. Operational Research (2017)
- A unified approach to Bermudan and Barrier options under stochastic volatility models with jumps. J. Econ. Dynamics and Control (2017)
- Static Hedging and Pricing of Exotic Options With Payoff Frames. Mathematical Finance (2018)
- American and Exotic Option Pricing with Jump Diffusions and Other Levy Processes. J. Computational Finance (2018)
- Robust Barrier Option Pricing by Frame Projection Under Exponential Levy Dynamics. Applied Mathematical Finance (2018)
- Robust option pricing with characteristic functions and the B-spline order of density projection, J. Compuational Finance (2017)
- Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps. Insurance: Mathematics and Economics (2017)
- A General Framework for Time-Changed Markov Processes and Applications. European J. Operational Research (2018)
- A General Valuation Framework for SABR and Stochastic Local Volatility Models. SIAM J. Financial Mathematics (2018)
- Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing. IMA Volumes on Mathematics (2019)
- Frame and Fourier Methods for Exotic Option Pricing and Hedging. Georgia Institute of Technology (2016).