Class AnalyticBarrierEngine

Namespace

NanoQL.PricingEngines

Assembly

NanoQL.dll

The analytic engine for European barrier options: Haug's closed forms ("Option pricing formulas", 1998, pp. 69-72) on a Black-Scholes process.

public static class AnalyticBarrierEngine

Inheritance

object

AnalyticBarrierEngine

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

QuantLib's formulas, with four changes, each a documented divergence that leaves QuantLib's bits where it doesn't apply. At a variance below machine epsilon the underlying follows its forward, as QuantLib's master prices it (e29c64126): a knock-out pays its rebate at the hit or the vanilla payoff, a knock-in the vanilla payoff or its rebate at expiry, a spot on the barrier a hit. A negative rebate is priced, where QuantLib's E and F test rebate > 0 and drop it. Each rate is read on the volatility's clock, the curve's zero rate times its own time over the volatility's, nothing accrued before a structure's reference date, so curves on other day counters or dates price as QuantLib's engine does on the same market restated on the volatility's (a factor of 1.0, and QuantLib's bits, where the clocks agree; 1.0 where the volatility's time is 0). A knock-out's rebate whose closed form has no real λ (λ² = μ² + 2r/σ² < 0, at negative rates), where QuantLib's is NaN, is the rebate's present value at the hit, integrated over the barrier's first-passage density.

The formulas are first-passage closed forms in one equivalent-constant carry and volatility, the variance and discounts to expiry: no exact closed form exists for a first passage under general deterministic term structures, and on shaped markets they miss QuantLib's finite-difference barrier engine by -1.6% to +0.6%; the term-structure-exact routes are FdBlackScholesBarrierEngine and the Monte Carlo engines.

QuantLib's references: Haug's formulas, and its testHaugValues table.

Methods

Calculate(BarrierOption, EvaluationContext, GeneralizedBlackScholesProcess)

Prices a barrier option.

public static OneAssetOptionResults Calculate(BarrierOption option, EvaluationContext context, GeneralizedBlackScholesProcess process)

Parameters

option BarrierOption

The option.

context EvaluationContext

The evaluation context.

process GeneralizedBlackScholesProcess

The Black-Scholes process.

Returns

OneAssetOptionResults

The option's results: the value; the expired results when the option has expired.

Exceptions

ArgumentNullException

An argument is null.

NanoQLException

The payoff isn't a plain vanilla one or its strike isn't positive, the exercise isn't European, the spot isn't positive, or it lies beyond the barrier ("barrier touched").