//-------------------------------------------------------------------------
public virtual void test_volatility()
{
for (int i = 0; i < NB_EXPIRY; i++)
{
double expiryTime = VOLS.relativeTime(TEST_EXPIRY[i]);
for (int j = 0; j < NB_STRIKE; ++j)
{
double volExpected = SMILE_TERM.volatility(expiryTime, TEST_STRIKE[j], FORWARD[i]);
double volComputed = VOLS.volatility(CURRENCY_PAIR, TEST_EXPIRY[i], TEST_STRIKE[j], FORWARD[i]);
assertEquals(volComputed, volExpected, TOLERANCE);
}
}
}
public virtual void test_recoverVolatility()
{
int nSteps = TREE_DATA.NumberOfSteps;
double spot = TREE_DATA.Spot;
double timeToExpiry = TREE_DATA.getTime(nSteps);
double dfDom = RATE_PROVIDER.discountFactors(USD).discountFactor(timeToExpiry);
double dfFor = RATE_PROVIDER.discountFactors(EUR).discountFactor(timeToExpiry);
double forward = spot * dfFor / dfDom;
for (int i = 0; i < 100; ++i)
{
double strike = spot * (0.8 + 0.004 * i);
OptionFunction func = EuropeanVanillaOptionFunction.of(strike, timeToExpiry, PutCall.CALL, nSteps);
double price = TREE.optionPrice(func, TREE_DATA);
double impliedVol = BlackFormulaRepository.impliedVolatility(price / dfDom, forward, strike, timeToExpiry, true);
double orgVol = VOLS.volatility(FX_PRODUCT.CurrencyPair, timeToExpiry, strike, forward);
assertEquals(impliedVol, orgVol, orgVol * 0.1); // large tol
double priceMrkt = TREE.optionPrice(func, TREE_DATA_MRKT);
double impliedVolMrkt = BlackFormulaRepository.impliedVolatility(priceMrkt / dfDom, forward, strike, timeToExpiry, true);
double orgVolMrkt = VOLS_MRKT.volatility(FX_PRODUCT.CurrencyPair, timeToExpiry, strike, forward);
assertEquals(impliedVolMrkt, orgVolMrkt, orgVolMrkt * 0.1); // large tol
}
}
//-------------------------------------------------------------------------
// bumping a node point at (nodeExpiry, nodeDelta)
private double nodeSensitivity(BlackFxOptionSmileVolatilities provider, CurrencyPair pair, ZonedDateTime expiry, double strike, double forward, double nodeExpiry, double nodeDelta)
{
double strikeMod = provider.CurrencyPair.Equals(pair) ? strike : 1.0 / strike;
double forwardMod = provider.CurrencyPair.Equals(pair) ? forward : 1.0 / forward;
InterpolatedStrikeSmileDeltaTermStructure smileTerm = (InterpolatedStrikeSmileDeltaTermStructure)provider.Smile;
double[] times = smileTerm.Expiries.toArray();
int nTimes = times.Length;
SmileDeltaParameters[] volTermUp = new SmileDeltaParameters[nTimes];
SmileDeltaParameters[] volTermDw = new SmileDeltaParameters[nTimes];
int deltaIndex = -1;
for (int i = 0; i < nTimes; ++i)
{
DoubleArray deltas = smileTerm.VolatilityTerm.get(i).Delta;
int nDeltas = deltas.size();
int nDeltasTotal = 2 * nDeltas + 1;
double[] deltasTotal = new double[nDeltasTotal];
deltasTotal[nDeltas] = 0.5d;
for (int j = 0; j < nDeltas; ++j)
{
deltasTotal[j] = 1d - deltas.get(j);
deltasTotal[2 * nDeltas - j] = deltas.get(j);
}
double[] volsUp = smileTerm.VolatilityTerm.get(i).Volatility.toArray();
double[] volsDw = smileTerm.VolatilityTerm.get(i).Volatility.toArray();
if (Math.Abs(times[i] - nodeExpiry) < TOLERANCE)
{
for (int j = 0; j < nDeltasTotal; ++j)
{
if (Math.Abs(deltasTotal[j] - nodeDelta) < TOLERANCE)
{
deltaIndex = j;
volsUp[j] += EPS;
volsDw[j] -= EPS;
}
}
}
volTermUp[i] = SmileDeltaParameters.of(times[i], deltas, DoubleArray.copyOf(volsUp));
volTermDw[i] = SmileDeltaParameters.of(times[i], deltas, DoubleArray.copyOf(volsDw));
}
InterpolatedStrikeSmileDeltaTermStructure smileTermUp = InterpolatedStrikeSmileDeltaTermStructure.of(ImmutableList.copyOf(volTermUp), ACT_365F);
InterpolatedStrikeSmileDeltaTermStructure smileTermDw = InterpolatedStrikeSmileDeltaTermStructure.of(ImmutableList.copyOf(volTermDw), ACT_365F);
BlackFxOptionSmileVolatilities provUp = BlackFxOptionSmileVolatilities.of(NAME, CURRENCY_PAIR, VAL_DATE_TIME, smileTermUp);
BlackFxOptionSmileVolatilities provDw = BlackFxOptionSmileVolatilities.of(NAME, CURRENCY_PAIR, VAL_DATE_TIME, smileTermDw);
double volUp = provUp.volatility(pair, expiry, strike, forward);
double volDw = provDw.volatility(pair, expiry, strike, forward);
double totalSensi = 0.5 * (volUp - volDw) / EPS;
double expiryTime = provider.relativeTime(expiry);
SmileDeltaParameters singleSmile = smileTerm.smileForExpiry(expiryTime);
double[] strikesUp = singleSmile.strike(forwardMod).toArray();
double[] strikesDw = strikesUp.Clone();
double[] vols = singleSmile.Volatility.toArray();
strikesUp[deltaIndex] += EPS;
strikesDw[deltaIndex] -= EPS;
double volStrikeUp = LINEAR.bind(DoubleArray.ofUnsafe(strikesUp), DoubleArray.ofUnsafe(vols), FLAT, FLAT).interpolate(strikeMod);
double volStrikeDw = LINEAR.bind(DoubleArray.ofUnsafe(strikesDw), DoubleArray.ofUnsafe(vols), FLAT, FLAT).interpolate(strikeMod);
double sensiStrike = 0.5 * (volStrikeUp - volStrikeDw) / EPS;
SmileDeltaParameters singleSmileUp = smileTermUp.smileForExpiry(expiryTime);
double strikeUp = singleSmileUp.strike(forwardMod).get(deltaIndex);
SmileDeltaParameters singleSmileDw = smileTermDw.smileForExpiry(expiryTime);
double strikeDw = singleSmileDw.strike(forwardMod).get(deltaIndex);
double sensiVol = 0.5 * (strikeUp - strikeDw) / EPS;
return(totalSensi - sensiStrike * sensiVol);
}
