/// <summary>
/// Calculates the theta of the bond future option product based on the price of the underlying future.
/// <para>
/// The theta of the product is minus of the option price sensitivity to the time to expiry.
/// The volatility is unchanged for a fixed strike in the sensitivity computation, hence the "StickyStrike" name.
///
/// </para>
/// </summary>
/// <param name="futureOption"> the option product </param>
/// <param name="discountingProvider"> the discounting provider </param>
/// <param name="volatilities"> the volatilities </param>
/// <param name="futurePrice"> the price of the underlying future </param>
/// <returns> the price curve sensitivity of the product </returns>
public double theta(ResolvedBondFutureOption futureOption, LegalEntityDiscountingProvider discountingProvider, BlackBondFutureVolatilities volatilities, double futurePrice)
{
ArgChecker.isTrue(futureOption.PremiumStyle.Equals(FutureOptionPremiumStyle.DAILY_MARGIN), "Premium style should be DAILY_MARGIN");
double strike = futureOption.StrikePrice;
ResolvedBondFuture future = futureOption.UnderlyingFuture;
double volatility = volatilities.volatility(futureOption.Expiry, future.LastTradeDate, strike, futurePrice);
double timeToExpiry = volatilities.relativeTime(futureOption.Expiry);
double theta = BlackFormulaRepository.driftlessTheta(futurePrice, strike, timeToExpiry, volatility);
return(theta);
}
//-------------------------------------------------------------------------
public virtual void test_theta_presentValueTheta()
{
double theta = PRICER.theta(CALL_OTM, RATES_PROVIDER, VOLS);
CurrencyAmount pvTheta = PRICER.presentValueTheta(CALL_OTM, RATES_PROVIDER, VOLS);
double timeToExpiry = VOLS.relativeTime(EXPIRY);
double dfDom = RATES_PROVIDER.discountFactor(USD, PAYMENT_DATE);
double forward = PRICER.DiscountingFxSingleProductPricer.forwardFxRate(FX_PRODUCT_HIGH, RATES_PROVIDER).fxRate(CURRENCY_PAIR);
double vol = SMILE_TERM.volatility(timeToExpiry, STRIKE_RATE_HIGH, forward);
double expectedTheta = dfDom * BlackFormulaRepository.driftlessTheta(forward, STRIKE_RATE_HIGH, timeToExpiry, vol);
assertEquals(theta, expectedTheta, TOL);
double expectedPvTheta = -NOTIONAL *dfDom *BlackFormulaRepository.driftlessTheta(forward, STRIKE_RATE_HIGH, timeToExpiry, vol);
assertEquals(pvTheta.Currency, USD);
assertEquals(pvTheta.Amount, expectedPvTheta, NOTIONAL * TOL);
}
public virtual void test_presentValueTheta_formula_shift()
{
CurrencyAmount computedCaplet = PRICER.presentValueTheta(CAPLET_LONG, RATES, SHIFTED_VOLS);
CurrencyAmount computedFloorlet = PRICER.presentValueTheta(FLOORLET_SHORT, RATES, SHIFTED_VOLS);
double forward = RATES.iborIndexRates(EUR_EURIBOR_3M).rate(RATE_COMP.Observation);
double expiry = SHIFTED_VOLS.relativeTime(CAPLET_LONG.FixingDateTime);
double volatility = SHIFTED_VOLS.volatility(expiry, STRIKE, forward);
double df = RATES.discountFactor(EUR, CAPLET_LONG.PaymentDate);
double shift = IborCapletFloorletDataSet.SHIFT;
double expectedCaplet = NOTIONAL * df * CAPLET_LONG.YearFraction * BlackFormulaRepository.driftlessTheta(forward + shift, STRIKE + shift, expiry, volatility);
double expectedFloorlet = -NOTIONAL *df *FLOORLET_SHORT.YearFraction *BlackFormulaRepository.driftlessTheta(forward + shift, STRIKE + shift, expiry, volatility);
assertEquals(computedCaplet.Currency, EUR);
assertEquals(computedCaplet.Amount, expectedCaplet, NOTIONAL * TOL);
assertEquals(computedFloorlet.Currency, EUR);
assertEquals(computedFloorlet.Amount, expectedFloorlet, NOTIONAL * TOL);
}
