Examples of cern.jet.random.engine.MersenneTwister

cern.jet.random.engine.MersenneTwister
fsu.edu/~geo/diehard.html">diehard test of G. Marsaglia and the load test of P. Hellekalek and S. Wegenkittl.
Performance: Its speed is comparable to other modern generators (in particular, as fast as java.util.Random.nextFloat()). 2.5 million calls to raw() per second (Pentium Pro 200 Mhz, JDK 1.2, NT). Be aware, however, that there is a non-negligible amount of overhead required to initialize the data structures used by a MersenneTwister. Code like
```
 double sum = 0.0; for (int i=0; i<100000; ++i) { RandomElement twister = new MersenneTwister(new java.util.Date()); sum += twister.raw(); } 
```
will be wildly inefficient. Consider using
```
 double sum = 0.0; RandomElement twister = new MersenneTwister(new java.util.Date()); for (int i=0; i<100000; ++i) { sum += twister.raw(); } 
```
instead. This allows the cost of constructing the MersenneTwister object to be borne only once, rather than once for each iteration in the loop.
Implementation: After M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3--30.
More info on Masumoto's homepage.
More info on Pseudo-random number generators is on the Web.
Yet some more info.
The correctness of this implementation has been verified against the published output sequence mt19937-2.out of the C-implementation mt19937-2.c. (Call test(1000) to print the sequence).
Note that this implementation is not synchronized.
Details: MersenneTwister is designed with consideration of the flaws of various existing generators in mind. It is an improved version of TT800, a very successful generator. MersenneTwister is based on linear recurrences modulo 2. Such generators are very fast, have extremely long periods, and appear quite robust. MersenneTwister produces 32-bit numbers, and every k-dimensional vector of such numbers appears the same number of times as k successive values over the period length, for each k <= 623 (except for the zero vector, which appears one time less). If one looks at only the first n <= 16 bits of each number, then the property holds for even larger k, as shown in the following table (taken from the publication cited above):

n

1

2

3

4

5

6

7

8

9

10

11

12 .. 16

17 .. 32

k

19937

9968

6240

4984

3738

3115

2493

2492

1869

1869

1248

1246

623

MersenneTwister generates random numbers in batches of 624 numbers at a time, so the caching and pipelining of modern systems is exploited. The generator is implemented to generate the output by using the fastest arithmetic operations only: 32-bit additions and bit operations (no division, no multiplication, no mod). These operations generate sequences of 32 random bits (int's). long's are formed by concatenating two 32 bit int's. float's are formed by dividing the interval [0.0,1.0] into 2³² sub intervals, then randomly choosing one subinterval. double's are formed by dividing the interval [0.0,1.0] into 2⁶⁴ sub intervals, then randomly choosing one subinterval.
@author wolfgang.hoschek@cern.ch @version 1.0, 09/24/99 @see java.util.Random

  public void longShortParity() {
    final MultipleCurrencyAmount pvLongExplicit = METHOD_LMM_CAP.presentValue(CAP_LAST, LMM_MULTICURVES);
    final MultipleCurrencyAmount pvShortExplicit = METHOD_LMM_CAP.presentValue(CAP_LAST_SHORT, LMM_MULTICURVES);
    assertEquals("Cap/floor - LMM - present value - long/short parity", pvLongExplicit.getAmount(EUR), -pvShortExplicit.getAmount(EUR), TOLERANCE_PV);
    LiborMarketModelMonteCarloMethod methodLmmMc;
    methodLmmMc = new LiborMarketModelMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
    final MultipleCurrencyAmount pvLongMC = methodLmmMc.presentValue(CAP_LAST, EUR, LMM_MULTICURVES);
    methodLmmMc = new LiborMarketModelMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
    final MultipleCurrencyAmount pvShortMC = methodLmmMc.presentValue(CAP_LAST_SHORT, EUR, LMM_MULTICURVES);
    assertEquals("Cap/floor - LMM - present value MC- long/short parity", pvLongMC.getAmount(EUR), -pvShortMC.getAmount(EUR), TOLERANCE_PV);
  }

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    final MultipleCurrencyAmount pvFixedExplicit = SWAP_PAYER.getFirstLeg().getNthPayment(NB_CPN_IBOR - 1).accept(PVDC, MULTICURVES);
    final MultipleCurrencyAmount pvIborExplicit = SWAP_PAYER.getSecondLeg().getNthPayment(NB_CPN_IBOR - 1).accept(PVDC, MULTICURVES);
    assertEquals("Cap/floor - LMM - present value Explcit- cap/floor/strike/Ibor parity", pvCapExplicit.getAmount(EUR) - pvFloorExplicit.getAmount(EUR) - pvFixedExplicit.getAmount(EUR),
        pvIborExplicit.getAmount(EUR), TOLERANCE_PV);
    LiborMarketModelMonteCarloMethod methodLmmMc;
    methodLmmMc = new LiborMarketModelMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
    final MultipleCurrencyAmount pvCapMC = methodLmmMc.presentValue(CAP_LAST, EUR, LMM_MULTICURVES);
    methodLmmMc = new LiborMarketModelMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
    final MultipleCurrencyAmount pvFloorMC = methodLmmMc.presentValue(FLOOR_LAST, EUR, LMM_MULTICURVES);
    assertEquals("Cap/floor - LMM - present value - cap/floor/strike/Ibor parity", pvCapMC.getAmount(EUR) - pvFloorMC.getAmount(EUR) - pvFixedExplicit.getAmount(EUR), pvIborExplicit.getAmount(EUR),
        1.0E+3);
  }

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  public void performance() {
    long startTime, endTime;
    final int nbTest = 10;


    LiborMarketModelMonteCarloMethod methodLmmMc;
    methodLmmMc = new LiborMarketModelMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
    final double[] pvMC = new double[nbTest];


    startTime = System.currentTimeMillis();
    for (int looptest = 0; looptest < nbTest; looptest++) {
      pvMC[looptest] = methodLmmMc.presentValue(CAP_LAST, EUR, LMM_MULTICURVES).getAmount(EUR);

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   * Compare explicit formula with Monte-Carlo and long/short and payer/receiver parities.
   */
  public void presentValueMonteCarlo() {
    final int nbPath = 12500;
    HullWhiteMonteCarloMethod methodMC;
    methodMC = new HullWhiteMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), nbPath);
    // Seed fixed to the DEFAULT_SEED for testing purposes.
    final CurrencyAmount pvPayerLongExplicit = METHOD_HW.presentValue(SWAPTION_PAYER_LONG, BUNDLE_HW);
    final CurrencyAmount pvPayerLongMC = methodMC.presentValue(SWAPTION_PAYER_LONG, CUR, FUNDING_CURVE_NAME, BUNDLE_HW);
    assertEquals("Swaption physical - Hull-White - Monte Carlo", pvPayerLongExplicit.getAmount(), pvPayerLongMC.getAmount(), 1.0E+4);
    final double pvMCPreviousRun = 5137844.655;
    assertEquals("Swaption physical - Hull-White - Monte Carlo", pvMCPreviousRun, pvPayerLongMC.getAmount(), 1.0E-2);
    methodMC = new HullWhiteMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), nbPath);
    final CurrencyAmount pvPayerShortMC = methodMC.presentValue(SWAPTION_PAYER_SHORT, CUR, FUNDING_CURVE_NAME, BUNDLE_HW);
    assertEquals("Swaption physical - Hull-White - Monte Carlo", -pvPayerLongMC.getAmount(), pvPayerShortMC.getAmount(), 1.0E-2);
    final CurrencyAmount pvReceiverLongMC = methodMC.presentValue(SWAPTION_RECEIVER_LONG, CUR, FUNDING_CURVE_NAME, BUNDLE_HW);
    final double pvSwap = SWAP_RECEIVER.accept(PVC, CURVES);
    assertEquals("Swaption physical - Hull-White - Monte Carlo - payer/receiver/swap parity", pvReceiverLongMC.getAmount() + pvPayerShortMC.getAmount(), pvSwap, 1.0E+5);

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   */
  public void presentValueCurveSensitivityMonteCarlo() {
    final double toleranceDelta = 1.0E+6; // 100 USD by bp
    final InterestRateCurveSensitivity pvcsExplicit = METHOD_HW.presentValueCurveSensitivity(SWAPTION_PAYER_LONG, BUNDLE_HW);
    final int nbPath = 30000; // 10000 path -> 200 USD by bp
    final HullWhiteMonteCarloMethod methodMC = new HullWhiteMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), nbPath);
    InterestRateCurveSensitivity pvcsMC = methodMC.presentValueCurveSensitivity(SWAPTION_PAYER_LONG, FUNDING_CURVE_NAME, BUNDLE_HW);
    pvcsMC = pvcsMC.cleaned();
    final InterestRateCurveSensitivity diff = pvcsExplicit.cleaned().plus(pvcsMC.multipliedBy(-1)).cleaned();
    final List<DoublesPair> sensiDsc = diff.getSensitivities().get(FUNDING_CURVE_NAME);
    final int nbDsc = sensiDsc.size();

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    final int nbTest = 25;
    CurrencyAmount pvMC = CurrencyAmount.of(CUR, 0.0);
    final InterestRateCurveSensitivity pvcsExplicit = METHOD_HW.presentValueCurveSensitivity(SWAPTION_PAYER_LONG, BUNDLE_HW);
    InterestRateCurveSensitivity pvcsMC = pvcsExplicit;
    final int nbPath = 12500;
    final HullWhiteMonteCarloMethod methodMC = new HullWhiteMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), nbPath);


    startTime = System.currentTimeMillis();
    for (int looptest = 0; looptest < nbTest; looptest++) {
      pvMC = METHOD_HW_MONTECARLO.presentValue(SWAPTION_PAYER_LONG, CUR, FUNDING_CURVE_NAME, BUNDLE_HW);
    }

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  /**
   * Test the Ratchet present value in the case where the first coupon is fixed. Tested against a previous run number.
   */
  public void presentValueFixed() {
    LiborMarketModelMonteCarloMethod methodMC;
    methodMC = new LiborMarketModelMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
    // Seed fixed to the DEFAULT_SEED for testing purposes.
    final CurrencyAmount pvMC = methodMC.presentValue(ANNUITY_RATCHET_FIXED, EUR, CURVES.getCurve(CURVES_NAMES[0]), BUNDLE_LMM);
    final double pvMCPreviousRun = 8525698.689;
    assertEquals("Annuity Ratchet Ibor - LMM - Monte Carlo", pvMCPreviousRun, pvMC.getAmount(), 1.0E-2);
  }

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  public void presentValueIbor() {
    final ZonedDateTime referenceDate = DateUtils.getUTCDate(2011, 8, 18);
    final AnnuityCouponIborRatchet annuityRatchetIbor = ANNUITY_RATCHET_IBOR_DEFINITION.toDerivative(referenceDate, FIXING_TS, CURVES_NAMES);
    final LiborMarketModelDisplacedDiffusionParameters parameterLMM = TestsDataSetLiborMarketModelDisplacedDiffusion.createLMMParameters(referenceDate, ANNUITY_RATCHET_FIXED_DEFINITION);
    final LiborMarketModelDisplacedDiffusionDataBundle bundleLMM = new LiborMarketModelDisplacedDiffusionDataBundle(parameterLMM, CURVES);
    final LiborMarketModelMonteCarloMethod methodMC = new LiborMarketModelMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), NB_PATH);
    // Seed fixed to the DEFAULT_SEED for testing purposes.
    final CurrencyAmount pvMC = methodMC.presentValue(annuityRatchetIbor, EUR, CURVES.getCurve(CURVES_NAMES[0]), bundleLMM);
    final double pvMCPreviousRun = 8259675.715;
    assertEquals("Annuity Ratchet Ibor - LMM - Monte Carlo", pvMCPreviousRun, pvMC.getAmount(), 1.0E-2);
  }

View Full Code Here

  /**
   * Test the Ratchet present value in the degenerate case where the coupon are fixed (floor=cap).
   */
  public void presentValueFixedLeg() {
    final int nbPath = 12500;
    final LiborMarketModelMonteCarloMethod methodMC = new LiborMarketModelMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), nbPath);
    final double[] mainFixed = new double[] {0.0, 0.0, 0.0};
    final double[] floorFixed = new double[] {0.0, 0.0, FIRST_CPN_RATE};
    final double[] capFixed = new double[] {0.0, 0.0, FIRST_CPN_RATE};
    final AnnuityCouponIborRatchetDefinition ratchetFixedDefinition = AnnuityCouponIborRatchetDefinition.withFirstCouponFixed(SETTLEMENT_DATE, ANNUITY_TENOR, NOTIONAL, INDEX_EURIBOR3M, IS_PAYER,
        FIRST_CPN_RATE, mainFixed, floorFixed, capFixed, TARGET);

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    for (int loopcpn = 1; loopcpn < ibor.getNumberOfPayments(); loopcpn++) {
      iborFirstFixed[loopcpn] = ibor.getNthPayment(loopcpn);
    }
    final LiborMarketModelDisplacedDiffusionParameters parameterLMM = TestsDataSetLiborMarketModelDisplacedDiffusion.createLMMParameters(REFERENCE_DATE, ratchetFixedDefinition);
    final LiborMarketModelDisplacedDiffusionDataBundle bundleLMM = new LiborMarketModelDisplacedDiffusionDataBundle(parameterLMM, CURVES);
    final LiborMarketModelMonteCarloMethod methodMC = new LiborMarketModelMonteCarloMethod(new NormalRandomNumberGenerator(0.0, 1.0, new MersenneTwister()), nbPath);
    final CurrencyAmount pvIborMC = methodMC.presentValue(ratchetFixed, EUR, CURVES.getCurve(CURVES_NAMES[0]), bundleLMM);
    final double pvIborExpected = new Annuity<Payment>(iborFirstFixed).accept(PVC, CURVES);
    assertEquals("Annuity Ratchet Ibor - Hull-White - Monte Carlo - Degenerate in Ibor leg", pvIborExpected, pvIborMC.getAmount(), 1.0E+4);
    // For 500,000 path the difference is 755.92
  }

View Full Code Here

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n	1	2	3	4	5	6	7	8	9	10	11	12 .. 16	17 .. 32
k	19937	9968	6240	4984	3738	3115	2493	2492	1869	1869	1248	1246	623