AnalyticApproach

Corresponds to the QuantLib AnalyticEuropean Engine.

It uses the Black-Scholes analytical formula for pricing european options. Web reference available here

Corresponds to the QuantLib AnalyticDividendEuropean Engine.

Arbitrage-free analytical formula developed by Lloyd Blenman and Steven Clark for pricing primarily European options with payoff Payoff::Payoff Type::RSO

Web reference available here

The call RSO price is given by

The put RSO price is given by

where

and

The greeks can be calculated by the following formulas, where

The following features are currently not supported:

American exercise, barriers, discrete dividends/storage costs.

Corresponds to the QuantLib AnalyticBSMHullWhite Engine.

2-factor model, with a closed-form solution, driven by stochastic underlying price and interest rates.

In particular, the underlying price is modelled to follow a Black-Scholes type, lognormal diffusion whereas the interest rate is modelled according to Hull White Model

The two processes are correlated with a given flat correlation number.

Corresponds to the QuantLib AnalyticHestonHullWhite Engine.

3-factor model, with a semi closed-form solution for call options, driven by stochastic underlying price, volatility and interest rates.

In particular, the underlying price is modelled to follow a Heston stochastic volatility process as in Heston Model, whereas the interest rate is modelled according to Hull White Model

References: Karel in't Hout, Joris Bierkens, Antoine von der Ploeg, Joe in't Panhuis.

Corresponds to the QuantLib AnalyticDigitalAmerican Engine.

Corresponds to the QuantLib AnalyticBarrier Engine.

Corresponds to the QuantLib AnalyticHeston Engine.

2-factor model, with a closed-form solution, driven by stochastic underlying price and volatility.

The underlying price process is modelled according to Heston Model

Allows the specification of:

Model[Vanilla Option]::Complex Log Formula

Model[Vanilla Option]::Integration

and also of the absolute/relative tolerance, maximum number of evaluations and the Andersen Piterbarg epsilon wrt the Fourier integration.

Corresponds to the QuantLib AnalyticPTDHeston Engine, which is the Piecewise Time Dependent version of the regular AnalyticHeston Engine.

2-factor model, with a semi closed-form solution, driven by stochastic underlying price and volatility.

The underlying price process is modelled according to PTD Heston Model

Corresponds to the QuantLib Bates Engine.

4-factor model, with a closed-form solution, driven by stochastic underlying price, volatility and jumps with random occurence and size.

The underlying price process is modelled according to Bates Model

Corresponds to the QuantLib Integral Engine.

It prices european options through numerical computation of the integral of the payoff function over all possible stock price states at expiry. Web reference available here

Corresponds to the QuantLib BaroneAdesiWhaleyApproximation Engine.

It uses an approximating semi-analytical formula for pricing american options. Web reference available here

Corresponds to the QuantLib BjerksundStenslandApproximation Engine.

It uses an approximating semi-analytical formula for pricing american options. Web reference available here

Corresponds to the QuantLib JuQuadraticApproximation Engine.

It uses an approximating semi-analytical formula for pricing american options. Web reference available here

Warning: Barone-Adesi-Whaley critical commodity price calculation is used.

It has not been modified to see whether the method of Ju is faster.

Ju does not say how he solves the equation for the critical stock price, e.g. Newton method.

He just gives the solution.

The method of BAW gives answers to the same accuracy as in Ju (1999).

Corresponds to the QuantLib AnalyticGJRGARCH Engine.

The underlying price is modelled according to GJRGARCH Model

Corresponds to the QuantLib JumpDiffusion Engine.

3-factor model, with a semi closed-form solution, driven by stochastic underlying price and jumps with random occurence and size.

The underlying price process is modelled according to Merton76 Model