public static object AmericanFutureOptionPV(
[ExcelArgument(Description = "Time-to-expiry")] double T,
[ExcelArgument(Description = "Strike")] double K,
[ExcelArgument(Description = "Forward")] double F,
[ExcelArgument(Description = "Discounting rate")] double R,
[ExcelArgument(Description = "Volatility")] double V,
[ExcelArgument(Description = "Call or Put")] string CP,
[ExcelArgument(Description = "Pricing method (Defult Trinomial)")] string Method)
{
return(ExcelHelper.Execute(_logger, () =>
{
if (!Enum.TryParse(CP, out OptionType optType))
{
return $"Could not parse call or put flag - {CP}";
}
if (!Enum.TryParse(Method, out AmericanPricingType method))
{
return $"Could not parse pricing type - {Method}";
}
if (method == AmericanPricingType.Binomial)
{
return BinomialTree.AmericanFutureOptionPV(F, K, R, T, V, optType);
}
else
{
return TrinomialTree.AmericanFutureOptionPV(F, K, R, T, V, optType);
}
}));
}
public void PVFacts()
{
var t = 1.0;
var k = 0;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
var df = System.Math.Exp(-rf * t);
//zero strike put is worthless
var PV = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(0, PV, 10);
PV = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(0, PV, 10);
//zero strike call is worth fwd with no discounting
cp = OptionType.C;
PV = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(f, PV, 10);
PV = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(f, PV, 10);
//and has delta = 1.0
var greeks = TrinomialTree.AmericanFutureOption(f, k, rf, t, vol, cp);
Assert.Equal(1.0, (double)greeks[1, 0], 10);
greeks = BinomialTree.AmericanFutureOption(f, k, rf, t, vol, cp);
Assert.Equal(1.0, (double)greeks[1, 0], 10);
//OTM option with zero vol is worthless
vol = 0.0;
k = f + 1;
PV = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(0, PV, 10);
PV = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.Equal(0, PV, 10);
//option worth >= black in all cases for same inputs
vol = 0.32;
k = f + 20;
var PVBlack = BlackFunctions.BlackPV(f, k, rf, t, vol, cp);
PV = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.True(PV >= PVBlack);
PV = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
Assert.True(PV >= PVBlack);
}
public void ImpliedVolFacts()
{
var t = 1.0;
var k = 120;
var f = 100;
var vol = 0.32;
var rf = 0.05;
var cp = OptionType.P;
var PVbi = BinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
var PVtri = TrinomialTree.AmericanFutureOptionPV(f, k, rf, t, vol, cp);
var impliedVolBi = BinomialTree.AmericanFuturesOptionImpliedVol(f, k, rf, t, PVbi, cp);
var impliedVolTri = TrinomialTree.AmericanFuturesOptionImpliedVol(f, k, rf, t, PVtri, cp);
Assert.Equal(vol, impliedVolBi, 10);
Assert.Equal(vol, impliedVolTri, 10);
}
