Examples of com.opengamma.analytics.financial.model.volatility.local.PureLocalVolatilitySurface

Package com.opengamma.analytics.financial.model.volatility.local

Examples of com.opengamma.analytics.financial.model.volatility.local.PureLocalVolatilitySurface

com.opengamma.analytics.financial.model.volatility.local.PureLocalVolatilitySurface
Under the assumption of cash and proportional discrete dividends, the stock price $S_t$ can be modelled as $S_t = (F_t-D_t)x_t + D_t$ where $F_t$ is the forward, $D_t$ is the growth-rate discounted value of future cash dividends, and $X_t$ is a positive martingale with $X_0 = 1$, known as the pure stock process. If the SDE for the pure stock process is $\frac{dX_t}{X_t} = \sigma^X(t,X_t)dW_t$ then $\sigma^X(t,X_t)$ is the pure local volatility, and can be found by applying the Dupire formula to call options on the the pure stock. See white (2012), Equity Variance Swap with Dividends, for details.

   */
  private void testNumerics(final AffineDividends dividends, final MultiHorizonMixedLogNormalModelData data, final double defaultTol) {


    final ForwardCurve fc = new ForwardCurve(1.0);
    final LocalVolatilitySurfaceStrike lv = MixedLogNormalVolatilitySurface.getLocalVolatilitySurface(fc, data);
    final PureLocalVolatilitySurface plv = new PureLocalVolatilitySurface(lv.getSurface());
    final BlackVolatilitySurfaceStrike iv = MixedLogNormalVolatilitySurface.getImpliedVolatilitySurface(fc, data);
    final PureImpliedVolatilitySurface piv = new PureImpliedVolatilitySurface(iv.getSurface());
    final double[] weights = data.getWeights();
    final double[] mus = data.getMus();
    final double[] sigmas = data.getVolatilities();

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      sum2 += w[i] * t * (mu[i] - sigma[i] * sigma[i] / 2);
    }
    double temp = Math.sqrt(2 * (Math.log(sum1) - sum2) / t);
    System.out.println("expected: " + temp);


    PureLocalVolatilitySurface plv = VolatilitySurfaceConverter.convertLocalVolSurface(lv2, new EquityDividendsCurvesBundle(spot, discountCurve, AffineDividends.noDividends()));
    EquityVarianceSwapBackwardsPurePDE backCal = new EquityVarianceSwapBackwardsPurePDE();
    res = backCal.expectedVariance(spot, discountCurve, AffineDividends.noDividends(), t, plv);
    System.out.println(Math.sqrt(res[0] / t));


    double vol = lvs.getVolatility(0.0, 25.0);

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    //test the new backwards local vol method for expected variance
    final YieldAndDiscountCurve yieldCurve = new YieldCurve("test", ConstantDoublesCurve.from(DRIFT));
    final AffineDividends ad = AffineDividends.noDividends();


    final EquityVarianceSwapBackwardsPurePDE backSolver = new EquityVarianceSwapBackwardsPurePDE();
    final PureLocalVolatilitySurface plv = new PureLocalVolatilitySurface(ConstantDoublesSurface.from(FLAT_VOL));


    final double[] res2 = backSolver.expectedVariance(SPOT, yieldCurve, ad, EXPIRY, plv);
    final double kVol2 = Math.sqrt(res2[0] / EXPIRY);
    assertEquals(FLAT_VOL, kVol2, 1e-6);
  }

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Related Classes of com.opengamma.analytics.financial.model.volatility.local.PureLocalVolatilitySurface

com.opengamma.analytics.financial.equity.variance.pricing.EquityVarianceSwapPricer

com.opengamma.analytics.financial.equity.variance.pricing.VolatilitySurfaceConverter

com.opengamma.analytics.financial.equity.variance.VarianceSwapWithDividendsTest

com.opengamma.analytics.financial.model.finitedifference.applications.LogPayoffTest

com.opengamma.analytics.financial.model.volatility.surface.MixedLogNormalVolatilitySurfaceTest

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