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
- 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)
- 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)
- Valuing Equity-Linked Death Benefits in General Exponential Levy Models. J. Comput. and Appl. Math. (2019).
- Swing Option Pricing By Dynamic Programming with B-Spline Density Projection, IJTAF, Forthcoming (2020)
- Frame and Fourier Methods for Exotic Option Pricing and Hedging. Georgia Institute of Technology (2016).
II) Stochastic Volatility, Markov Chains, and Regime Switching
- 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)
- Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps. Insurance: Mathematics and Economics (2017)
- Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing. IMA Volumes on Mathematics (2019)
- Full-Fledged SABR Through Markov Chains, Wilmott (2019)
III) Stochastic Local Volatility (SABR, Quadratic SLV, etc)
IV) Time-Changed Processes
V) Multi-Dimensional Diffusions