Financial Instruments Toolbox

Option Pricing Models

Financial Instruments Toolbox provides several approaches for option pricing.

Closed-Form Models

Models for closed-form option pricing include:

  • Black Scholes, for calculating price and sensitivity for equity options, futures, and foreign currencies
  • Black, for calculating implied volatility, price, and sensitivity for equity options and options on futures
  • Garman-Kohlhagen, for calculating price and sensitivity for foreign exchange options
  • Roll-Geske-Whaley and Bjerksund-Stensland, for calculating implied volatility, price, and sensitivity for American call options
  • Nengjiu Ju, for calculating price and sensitivity for European basket options using an approximation model
  • Stultz, for calculating price and sensitivity of rainbow options with the minimum and maximum of two risky assets

Binomial and Trinomial Trees

Models for binomial and trinomial trees include pricing and sensitivity calculations for interest-rate derivatives and equity derivatives.

  • Interest-rate derivatives help compute prices and sensitivities of interest-rate contingent claims based on different models: Heath-Jarrow-Morton (HJM), Black-Derman-Toy (BDT), Hull-White (HW), and Black-Karasinkski (BK).
  • Equity derivatives provide several types of recombining tree models to represent the evolution of stock prices: Cox-Ross-Rubinstein (CRR), equal probabilities (EQP), Leisen-Reimer (LR), and implied trinomial tree (ITT).

Monte Carlo Simulation

Option pricing with Monte Carlo simulation helps you calculate price and sensitivity for path-dependent or basket options that are difficult or not practical to price using trees. Financial Instruments Toolbox supports the Longstaff-Schwartz model for calculating price and sensitivity of basket equity options. Optionally, you can use the stochastic differential equation (SDE) solvers in Econometrics Toolbox to build custom Monte Carlo simulations for option pricing.

Next: Portfolio and Hedging Strategies

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