dxLibOptions Library

Class:com.devexperts.options.pricing.BinomialTreePricing

Directly provided results: price, delta, gamma.

Suitable for: log normal vanilla American and European options without dividend schedule.

Complexity: $O\left(n^2\right)$, where $n$ - number of steps.

Algorithm divides time until expiration into given number of equal segments. During each segment stock goes either up or down in price. There are two methods to calculate prices and probabilities: Cox-Ross-Rubinstein and Leisen-Reimer. Cox-Ross-Rubunstein tree example:

Further reading:

Class: com.devexperts.options.pricing.BjerksundStenslandPricing

Directly provided results: price

Suitable for: log normal vanilla American options without dividend schedule.

Algorithm uses Black-Scholes model with one or two early exercise strategies:

Further reading: "Numerical Methods versus Bjerksund and Stensland Approximations for American Options Pricing" by Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea Section IV. (Original document can be found here).

Class: com.devexperts.options.pricing.BlackScholesPricing

Directly provided results: price, delta, gamma, theta, vega, rho, phi, carry_rho, speed, vanna, vomma, ultima, zomma, charm, veta, color, totto, strike_delta, strike_gamma.

Suitable for: log normal vanilla and binary European options without dividend schedule.

Complexity: $O\left(1\right)$

Algorithm uses Black-Scholes model, namely it has following assumptions about market:

Further reading: Black-Scholes model.

Class: com.devexperts.options.pricing.BlackScholesUniversalPricing

Directly provided results: price, delta, gamma, theta, vega, rho, phi, vanna, vomma.

Suitable for: log normal vanilla, binary, single/double barrier (European payout for KO rebates) and single/double touch/no-touch European options without dividend schedule.

Complexity: $O\left(1\right)$

Algorithm uses Black-Scholes model with border condition to solve barrier and touch options.

Further reading: "Barrier options" (original document can be found here)

Class: com.devexperts.options.pricing.ExplicitFiniteDifferencePricing

Directly provided results: price, delta, gamma, speed, theta, charm, color.

Suitable for: log normal vanilla, binary, single/double barrier and single/double touch/no-touch European and American options without dividend schedule.

Complexity: $O\left(n\right)$, where $n$ - number of steps.

Algorithm uses finite difference method to solve Black-Scholes equation.

Further reading: "Numerical Approximation of Black-Scholes equation" by Dina Dura and Ana-Maria Moşneagu (original document can be found here)

Class: com.devexperts.options.pricing.MertonReinerRubinsteinBarrierPricing

Directly provided results: price, delta, gamma, speed, theta, charm, color.

Suitable for: log normal single barrier (American payout for KO rebates) European options without dividend schedule.

Complexity: $O\left(1\right)$

Algorithm uses Black-Scholes model modified to account for single barriers.

Further reading: E. G. Haug "The complete guide to options pricing formulas"

Class: com.devexperts.options.pricing.MonteCarloPricing

Directly provided results: price, delta, gamma, speed, theta, charm, color.

Suitable for: log normal vanilla European options.

Complexity: $O\left(n\right)$, where $n$ - number of steps.

Algorithm uses Euler method on geometrical Brownian motion.

Further reading: "Monte Carlo and Binomial Simulations for European Option Pricing" by Robert Hon Section 3.2.1 (original document can be found here).

Class: com.devexperts.options.pricing.FiniteDifferenceDerivativeImpl

For all the greeks not provided by pricing algorithms calculation is done using finite difference derivative approximation. There is no need to do anything as any pricing algorithm will use this method if it do not support corresponding greek internally.

Further reading: Finite difference

Class: com.devexperts.options.pricing.YieldCurve

Given prices of bonds with different expirations constructs interest rate curve for currency. Support bonds with and without coupons.

Further reading: "Methods for Constructing a Yield Curve" by Patrick S. Hagan and Graeme West (original document can be found here).

VanillaParams p = new VanillaParams();
p.setUnderlying(100);
p.setStrike(110);
p.setExpiration(0.5);
p.setVolatility(0.2);
p.setInterestRate(0.01);
p.setDividendYield(0.03);
p.setStyle(OptionStyle.EUROPEAN);
p.setPayoff(OptionPayoff.CALL);
BlackScholesPricing pr = new BlackScholesPricing();
double price = pr.computePrice(p);

BjerksundStenslandPricing pricing = new BjerksundStenslandPricing();
pricing.setVariant(BjerksundStenslandPricing.Variant.ONE_BOUNDARY);
VanillaParams params = new VanillaParams();
params.setExpiration(3);
params.setStyle(OptionStyle.AMERICAN);
params.setInterestRate(0.08);
params.setStrike(100);
params.setVolatility(0.2);
params.setDividendYield(0.12);
params.setUnderlying(80);
params.setPayoff(OptionPayoff.PUT);
pricing.computePrice(params);

VanillaParams p = new VanillaParams();
p.setStrike(100);
p.setUnderlying(90);
p.setExpiration(100d / 365);
p.setVolatility(0.22);
p.setInterestRate(0.0078);
p.setDividendYield(-0.004);
p.setPayoff(OptionPayoff.CALL);
VanillaBarrierOptionParams bp1 = new VanillaBarrierOptionParams();
bp1.setBase(p);
bp1.setBarrier(84);
bp1.setBarrierType(BarrierType.DOWN_OUT);
VanillaBarrierOptionParams bp2 = new VanillaBarrierOptionParams();
bp2.setBase(bp1);
bp2.setBarrierType(BarrierType.UP_IN);
bp2.setBarrier(104);
BlackScholesUniversalPricing pricing = new BlackScholesUniversalPricing();
UniversalParams up = new UniversalParams(p, bp2);
double price = pricing.computePrice(up);

double[] maturity = {1, 2, 3, 5, 7, 10, 20, 30};
double[] input = percentToFractions(0.60, 0.78, 0.91, 1.18, 1.44, 1.57, 1.90, 2.23);
YieldCurve constantResult = YieldCurve.bootstrap(maturity, input, 2, YieldCurve.BootstrappingMode.CONSTANT_RATE);
YieldCurve changingResult = YieldCurve.bootstrap(maturity, input, 2, YieldCurve.BootstrappingMode.CHANGING_RATE);