- Yield curve fitting with bootstrapping and parametric fitting models, and term-structure analysis with dual curve construction and pricing of swaps, caps, floors, and swaptions (using LIBOR-OIS and other curves)
- Black Scholes, Black, Garman-Kohlhagen, Roll-Geske-Whaley, Bjerksund-Stensland, Nengjiu Ju, Stulz, Levy jump diffusion, Longstaff-Schwartz, SABR, and tree models and Monte Carlo simulation
- Fixed-income and equity derivative calculations for price, yield, discount rate, cash-flow schedule, spread, implied volatility, option adjusted spread (OAS), and greeks
- Counterparty credit risk, CVA modeling, and credit instruments for mortgage pools, balloon mortgages, and credit default swaps
- Interest rate instruments: bonds, stepped-coupon bonds, futures, vanilla options, Bermudan options, bonds with embedded options, vanilla swaps, forward swaps, amortizing swaps, swaptions, caps, floors, range notes, floating-rate notes, and collared floating-rate notes
- Equity instruments: stocks, vanilla options, Bermudan options, Asian options, lookback options, barrier options, digital options, rainbow options, basket options, compound options, and chooser options
- Energy and commodity instruments: Asian options, Bermudan options, lookback options, swing options, spread options, and vanilla European/American options
Tree Viewer plots showing interactive querying of option pricing using trees. The left plot shows querying the highlighted path with each time step shown in a table. The right plot shows node prices for the two paths selected.
Yield Curve and Interest Rate Term Structure
Financial Instruments Toolbox provides customizable objects for fitting a yield curve to market data. The toolbox helps you analyze market data by deriving curve objects, including forward rate curve, discount rate curve, and par yield curve.
The interest rate curve objects help you fit yield curves to market data using several approaches:
- Bootstrap method
- Parametric models, including Nelson-Siegel, Svensson, and VRP
- Spline-based models
- Custom functions
Plot of yield curves fitted to market data using three parametric models.
Interest rate curve objects also help you analyze yield curves to derive discount rates, zero rates, forward rates, and par yields.
Plots of yield curve analysis using forward and zero rates with interpolation methods (left) and par yield curve (right).
Additionally, you can convert interest rate curve objects to model interest rate term structures and price fixed-income derivatives. For example, with dual curve construction functionality, you can price swaps, floors, caps, and swaptions with LIBOR-OIS curves.
Option Pricing Models
Financial Instruments Toolbox provides several approaches for option pricing.
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.
Portfolio and Hedging Strategies
Financial Instruments Toolbox enables you to price portfolios and apply hedging strategies. You can:
- Create and manage portfolios that include several types of financial instruments
- Calculate price and sensitivity for each instrument and the total portfolio
- View results either numerically or graphically
- Define a hedging strategy using selected instruments within a portfolio to achieve target sensitivity or cost
Sample hedging strategy developed using Financial Instruments Toolbox.
Interest Rate Instruments
Financial Instruments Toolbox includes functions for finding prices and sensitivities of several fixed-income instruments based on interest rate curves. You can price interest rate instruments using closed-form solutions, interest rate term structure, or trees. You can apply the functions to a portfolio of different types of instruments or to groups of instruments of the same type.
The toolbox provides tools to calculate price, par fixed-rate, and duration of interest rate swaps. The duration-hedging capabilities let you hedge a portfolio and address interest rate risk with a swap arrangement. Supported swaps include vanilla, forward, and amortizing. Dual curve construction tools enable you to price swaps, caps, floors, and swaptions using LIBOR-OIS curves or other combinations.
- For bond futures, you can calculate price, bond conversion factors, and implied repo rate. You can then use this information to manage interest rate risk for your portfolio.
- For convertible bonds, you can calculate price using binomial and trinomial trees. The value of the convertible bond is determined by the uncertainty of the relative stock.
Plots showing convertible bond floor when the share prices are low (left), and price as a function of share price and years to maturity (right).
You can also calculate prices using Black's model for forwards, futures, options on futures, swaptions, European call/put options, interest rate cap/caplets, and interest rate floor or floorlets. You can calibrate the SABR stochastic volatility model from market-implied Black volatilities.
Additional fixed-income instruments include:
- Zero-coupon bonds for calculating price and yield to extract the present value from any fixed coupon instrument for any time period
- Treasury bills for calculating price, yield, discount rate, and breakeven discount rate
- Corporate, treasury, and municipal bonds for calculating price, yield, and cash-flow schedules
- Stepped-coupon bonds for calculating price, yield, and cash-flow schedules
- Agency option-adjusted spread (OAS) for calculating price and spread for callable bonds
- Range, fixed-rate, floating-rate, and collared floating-rate notes for calculating price and accrued interest
- Vanilla and exotic options for calculating implied volatility, price, and sensitivity
Plot of an agency option adjusted spread for a noncallable bond issue, and a Z-spread for a callable bond issue for a range of bond prices.
Financial Instruments Toolbox provides functions for modeling the evolution of stock prices using these models:
- Cox-Ross-Rubinstein (CRR)
- Equal probabilities (EQP)
- Implied trinomial tree (ITT)
- Leisen-Reimer (LR)
With these discrete-time models, you can create binomial or trinomial trees and illustrate the expected stock price for each node in the tree with the corresponding volatility.
The toolbox also provides functions for calculating portfolio prices and sensitivities based on binomial and trinomial equity price trees.
Financial Instruments Toolbox supports the following equity options:
- Vanilla (American, European, and Bermuda)
Credit and Mortgage Instruments
Credit Default Swaps and Swaptions
Financial Instruments Toolbox includes functions to price credit derivatives such as new and existing credit default swap (CDS) agreements and credit default swaptions. You can value running spread CDS contracts that do not have upfront payments and standard spread contracts that require an upfront payment.
The toolbox simplifies common CDS valuation tasks so that you can:
- Estimate the default probability term structure by bootstrapping CDS market data
- Price new CDS contracts by calculating the breakeven spreads for multiple maturity dates and recovery rates
- Calculate the mark-to-market value of a CDS contract with either accrued or no accrued premium payment
- Convert between market quotes using running spreads and contracts valued using upfront payments and standard spreads
Counterparty Credit Risk
Financial Instruments Toolbox includes functions to compute credit exposures from mark-to-market OTC contract values and compute exposure profiles from credit exposures, along with an example that demonstrates how to compute the unilateral credit value adjustment (CVA) for a bank portfolio of vanilla swaps with several counterparties.
Mortgage-Backed Securities, Mortgage Pools, and Collateralized Mortgage Obligations
Financial Instruments Toolbox lets you model generic fixed-rate mortgage pools and balloon mortgages. The toolbox provides tools to calculate price and yield of mortgage-backed securities (MBS) using prepayment options derived from uniform practices of the Public Securities Association (PSA). You can calculate the mortgage-pool price or effective duration using the option adjusted spread method for your mortgage pool. Additionally, you can measure the risk for a mortgage-pool portfolio using convexity, duration, and average life calculations.
The toolbox provides functions to calculate price, yield, and spreads for collateralized mortgage obligations (CMO) and tools for scheduling cash flows between tranches. Supported schemes for prepayment tranches are:
- Sequential tranching, with or without Z-bond tranching
- Schedule bond tranching, both planned amortization class (PAC) bonds and target amortization class (TAC) bonds
Plots of mortgage pool monthly cash flows (left) and mortgage balance for two conditional payment rates (right).