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cetusfinance · Jul 31, 2018 · 43ca1d7 · 43ca1d7
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diff --git a/AsianFunctions.cs b/AsianFunctions.cs
@@ -0,0 +1,169 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Threading.Tasks;
+using ExcelDna.Integration;
+using Qwack.Options;
+using Qwack.Excel.Services;
+using Microsoft.Extensions.Logging;
+using Microsoft.Extensions.DependencyInjection;
+using Qwack.Options.VolSurfaces;
+using Qwack.Excel.Utils;
+using Qwack.Dates;
+using Qwack.Core.Basic;
+
+namespace Qwack.Excel.Options
+{
+    public class AsianFunctions
+    {
+        private static readonly ILogger _logger = ContainerStores.GlobalContainer.GetService<ILoggerFactory>()?.CreateLogger<BlackFunctions>();
+
+        [ExcelFunction(Description = "Returns asian option PV using the Turnbull-Wakeman formula", Category = CategoryNames.Options, Name = CategoryNames.Options + "_" + nameof(TurnbullWakemanPV))]
+        public static object TurnbullWakemanPV(
+            [ExcelArgument(Description = "Time-to-expiry")] double T,
+            [ExcelArgument(Description = "Time-to-average start")] double TavgStart,
+            [ExcelArgument(Description = "Average-to-date")] double KnownAverage,
+            [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)
+        {
+            return ExcelHelper.Execute(_logger, () =>
+             {
+                 if (!Enum.TryParse(CP, out OptionType optType))
+                 {
+                     return $"Could not parse call or put flag - {CP}";
+                 }
+                 return Qwack.Options.Asians.TurnbullWakeman.PV(F, KnownAverage, V, K, TavgStart, T, R, optType);
+             });
+        }
+
+        [ExcelFunction(Description = "Returns asian option PV using the Turnbull-Wakeman formula", Category = CategoryNames.Options, Name = CategoryNames.Options + "_" + nameof(TurnbullWakemanPV2))]
+        public static object TurnbullWakemanPV2(
+            [ExcelArgument(Description = "Evaluation Date")] DateTime EvalDate,
+            [ExcelArgument(Description = "Average Start Date")] DateTime AverageStartDate,
+            [ExcelArgument(Description = "Average End Date")] DateTime AverageEndDate,
+            [ExcelArgument(Description = "Average-to-date")] double KnownAverage,
+            [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)
+        {
+            return ExcelHelper.Execute(_logger, () =>
+            {
+                if (!Enum.TryParse(CP, out OptionType optType))
+                {
+                    return $"Could not parse call or put flag - {CP}";
+                }
+                return Qwack.Options.Asians.TurnbullWakeman.PV(F, KnownAverage, V, K, EvalDate, AverageStartDate, AverageEndDate, R, optType);
+            });
+        }
+
+        [ExcelFunction(Description = "Returns asian option delta using the Turnbull-Wakeman formula", Category = CategoryNames.Options, Name = CategoryNames.Options + "_" + nameof(TurnbullWakemanDelta))]
+        public static object TurnbullWakemanDelta(
+            [ExcelArgument(Description = "Evaluation Date")] DateTime EvalDate,
+            [ExcelArgument(Description = "Average Start Date")] DateTime AverageStartDate,
+            [ExcelArgument(Description = "Average End Date")] DateTime AverageEndDate,
+            [ExcelArgument(Description = "Average-to-date")] double KnownAverage,
+            [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)
+        {
+            return ExcelHelper.Execute(_logger, () =>
+            {
+                if (!Enum.TryParse(CP, out OptionType optType))
+                {
+                    return $"Could not parse call or put flag - {CP}";
+                }
+                return Qwack.Options.Asians.TurnbullWakeman.Delta(F, KnownAverage, V, K, EvalDate, AverageStartDate, AverageEndDate, R, optType);
+            });
+        }
+
+        [ExcelFunction(Description = "Returns strike for asian option with specified PV, using the Turnbull-Wakeman formula", Category = CategoryNames.Options, Name = CategoryNames.Options + "_" + nameof(TurnbullWakemanStrikeForPV))]
+        public static object TurnbullWakemanStrikeForPV(
+            [ExcelArgument(Description = "Evaluation Date")] DateTime EvalDate,
+            [ExcelArgument(Description = "Average Start Date")] DateTime AverageStartDate,
+            [ExcelArgument(Description = "Average End Date")] DateTime AverageEndDate,
+            [ExcelArgument(Description = "Average-to-date")] double KnownAverage,
+            [ExcelArgument(Description = "Target PV")] double PV,
+            [ExcelArgument(Description = "Forward")] double F,
+            [ExcelArgument(Description = "Discounting rate")] double R,
+            [ExcelArgument(Description = "Volatility Surface")] string VolSurface,
+            [ExcelArgument(Description = "Call or Put")] string CP)
+        {
+            return ExcelHelper.Execute(_logger, () =>
+            {
+                if (!ContainerStores.GetObjectCache<IVolSurface>().TryGetObject(VolSurface, out var surface))
+                {
+                    return $"Could not parse find vol surface {VolSurface} in the cache";
+                }
+
+                if (!Enum.TryParse(CP, out OptionType optType))
+                {
+                    return $"Could not parse call or put flag - {CP}";
+                }
+                return Qwack.Options.Asians.TurnbullWakeman.StrikeForPV(PV, F, KnownAverage, surface.Value, EvalDate, AverageStartDate, AverageEndDate, R, optType);
+            });
+        }
+
+        [ExcelFunction(Description = "Returns asian option PV using the Clewlow/LME formula", Category = CategoryNames.Options, Name = CategoryNames.Options + "_" + nameof(ClewlowPV))]
+        public static object ClewlowPV(
+            [ExcelArgument(Description = "Evaluation Date")] DateTime EvalDate,
+            [ExcelArgument(Description = "Average Start Date")] DateTime AverageStartDate,
+            [ExcelArgument(Description = "Average End Date")] DateTime AverageEndDate,
+            [ExcelArgument(Description = "Average-to-date")] double KnownAverage,
+            [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 = "Fixing Calendar")] object FixingCalendar)
+        {
+
+            return ExcelHelper.Execute(_logger, () =>
+            {
+                var fixCal = FixingCalendar.OptionalExcel<string>("Weekends");
+                if (!ContainerStores.SessionContainer.GetService<ICalendarProvider>().Collection.TryGetCalendar(fixCal, out var cal))
+                    return $"Calendar {FixingCalendar} not found in cache";
+
+                if (!Enum.TryParse(CP, out OptionType optType))
+                {
+                    return $"Could not parse call or put flag - {CP}";
+                }
+                return Qwack.Options.Asians.LME_Clewlow.PV(F, KnownAverage, V, K, EvalDate, AverageStartDate, AverageEndDate, R, optType, cal);
+            });
+        }
+
+        [ExcelFunction(Description = "Returns asian option delta using the Clewlow/LME formula", Category = CategoryNames.Options, Name = CategoryNames.Options + "_" + nameof(ClewlowDelta))]
+        public static object ClewlowDelta(
+            [ExcelArgument(Description = "Evaluation Date")] DateTime EvalDate,
+            [ExcelArgument(Description = "Average Start Date")] DateTime AverageStartDate,
+            [ExcelArgument(Description = "Average End Date")] DateTime AverageEndDate,
+            [ExcelArgument(Description = "Average-to-date")] double KnownAverage,
+            [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 = "Fixing Calendar")] object FixingCalendar)
+        {
+
+            return ExcelHelper.Execute(_logger, () =>
+            {
+                var fixCal = FixingCalendar.OptionalExcel<string>("Weekends");
+                if (!ContainerStores.SessionContainer.GetService<ICalendarProvider>().Collection.TryGetCalendar(fixCal, out var cal))
+                    return $"Calendar {FixingCalendar} not found in cache";
+
+                if (!Enum.TryParse(CP, out OptionType optType))
+                {
+                    return $"Could not parse call or put flag - {CP}";
+                }
+                return Qwack.Options.Asians.LME_Clewlow.Delta(F, KnownAverage, V, K, EvalDate, AverageStartDate, AverageEndDate, R, optType, cal);
+            });
+        }
+    }
+}
diff --git a/LME_Clewlow.cs b/LME_Clewlow.cs
@@ -0,0 +1,159 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+using Qwack.Dates;
+using Qwack.Core.Basic;
+using System.Linq;
+
+namespace Qwack.Options.Asians
+{
+    public static class LME_Clewlow
+    {
+        public static double PV(double forward, double knownAverage, double sigma, double K, DateTime evalDate, DateTime avgStartDate, DateTime avgEndDate, double riskFree, OptionType callPut, Calendar fixingCalendar)
+        {
+            if (avgEndDate == evalDate)
+                if (callPut == OptionType.C)
+                    return System.Math.Max(knownAverage - K, 0);
+                else
+                    return System.Math.Max(K - knownAverage, 0);
+
+            else if (avgEndDate < evalDate)
+                return 0;
+            else if (avgStartDate == avgEndDate)
+            {
+                var t = (avgEndDate - evalDate).TotalDays / 365.0;
+                return BlackFunctions.BlackPV(forward, K, riskFree, t, sigma, callPut);
+            }
+
+            //Build Vector of Observation Dates
+            var resetDates = avgStartDate.BusinessDaysInPeriod(avgEndDate, fixingCalendar);
+            var RT = resetDates.Count;
+
+            //Initialise Variables
+            double E1 = 0.0, E2 = 0.0, E3 = 0.0, E4 = 0.0, E5 = 0.0;
+            double DeltaTPrime = 0.0, DeltaT = 0.0;
+
+            var FBar = forward;
+            var tvs = resetDates.Count(x => x < evalDate);
+
+            if (tvs > 0)
+                DeltaTPrime = (resetDates[tvs + 1] - resetDates[tvs]).TotalDays / 365.0;
+            else
+                DeltaTPrime = ((resetDates[0] - evalDate).TotalDays) / 365.0;
+
+            if (tvs + 2 >= RT)
+                DeltaT = DeltaTPrime;
+            else
+                DeltaT = (avgEndDate - resetDates[tvs+1]).TotalDays / 365.0 / (RT - tvs);
+
+            var Ak = knownAverage * tvs  / RT;
+            E5 = 2 * Ak * FBar * (RT - tvs) / RT + (Ak * Ak);
+
+            if (tvs < RT)
+            {
+                E4 = (1 + System.Math.Exp(sigma * sigma * DeltaT)) * (System.Math.Exp((RT - tvs) * sigma * sigma * DeltaT) - 1);
+                E4 += 2 * (RT - tvs) * (1 - System.Math.Exp(sigma * sigma * DeltaT));
+                E4 /= (System.Math.Pow(System.Math.Exp(sigma * sigma * DeltaT) - 1, 2));
+            }
+            else
+                E4 = 1;
+
+
+            E3 = System.Math.Pow(FBar / RT, 2) * System.Math.Exp(sigma * sigma * DeltaTPrime);
+            E2 = E3 * E4 + E5;
+            E1 = FBar * (RT - tvs) / RT  + Ak;
+
+            var EA = Ak + FBar * (RT - tvs) / RT;
+
+            var b = System.Math.Log(E2) - 2 * System.Math.Log(E1);
+            var d1 = (System.Math.Log(EA / K) + 0.5 * b) / System.Math.Sqrt(b);
+            var d2 = d1 - System.Math.Sqrt(b);
+
+
+            var df = System.Math.Exp(-riskFree * (avgEndDate - evalDate).TotalDays / 365.0);
+
+            //Main Option valuation
+            if (callPut == OptionType.Call)
+            {
+                d1 = Math.Statistics.NormSDist(d1);
+                d2 = Math.Statistics.NormSDist(d2);
+                return (EA * d1 - K * d2) * df;
+            }
+            else
+            {
+                d1 = Math.Statistics.NormSDist(-d1);
+                d2 = Math.Statistics.NormSDist(-d2);
+                return (K * d2 - EA * d1) * df;
+            }
+
+        }
+
+        public static double Delta(double forward, double knownAverage, double sigma, double K, DateTime evalDate, DateTime avgStartDate, DateTime avgEndDate, double riskFree, OptionType callPut, Calendar fixingCalendar)
+        {
+            //Build Vector of Observation Dates
+            var resetDates = avgStartDate.BusinessDaysInPeriod(avgEndDate, fixingCalendar);
+            var RT = resetDates.Count;
+
+            if (avgEndDate == evalDate)
+                if (callPut == OptionType.C)
+                    return knownAverage > K ? 1.0 / RT : 0;
+                else
+                    return knownAverage < K ? -1.0 / RT : 0;
+            else if (avgEndDate < evalDate)
+                return 0;
+            else if (avgStartDate == avgEndDate)
+            {
+                var t = (avgEndDate - evalDate).TotalDays / 365.0;
+                return BlackFunctions.BlackDelta(forward, K, riskFree, t, sigma, callPut);
+            }
+
+
+            //Initialise Variables
+            double E1 = 0.0, E2 = 0.0, E3 = 0.0, E4 = 0.0, E5 = 0.0;
+            double DeltaTPrime = 0.0, DeltaT = 0.0;
+
+            var FBar = forward;
+            var tvs = resetDates.Count(x => x < evalDate);
+
+            if (tvs > 0)
+                DeltaTPrime = (resetDates[tvs + 1] - resetDates[tvs]).TotalDays / 365.0;
+            else
+                DeltaTPrime = ((resetDates[0] - evalDate).TotalDays) / 365.0;
+
+            if (tvs + 2 >= RT)
+                DeltaT = DeltaTPrime;
+            else
+                DeltaT = (avgEndDate - resetDates[tvs + 1]).TotalDays / 365.0 / (RT - tvs);
+
+            var Ak = knownAverage * tvs / RT;
+            E5 = 2 * Ak * FBar * (RT - tvs) / RT + (Ak * Ak);
+
+            if (tvs < RT)
+            {
+                E4 = (1 + System.Math.Exp(sigma * sigma * DeltaT)) * (System.Math.Exp((RT - tvs) * sigma * sigma * DeltaT) - 1);
+                E4 += 2 * (RT - tvs) * (1 - System.Math.Exp(sigma * sigma * DeltaT));
+                E4 /= (System.Math.Pow(System.Math.Exp(sigma * sigma * DeltaT) - 1, 2));
+            }
+            else
+                E4 = 1;
+
+
+            E3 = System.Math.Pow(FBar / RT, 2) * System.Math.Exp(sigma * sigma * DeltaTPrime);
+            E2 = E3 * E4 + E5;
+            E1 = FBar * (RT - tvs) / RT + Ak;
+
+            var EA = Ak + FBar * (RT - tvs) / RT;
+
+            var b = System.Math.Log(E2) - 2 * System.Math.Log(E1);
+            var d1 = (System.Math.Log(EA / K) + 0.5 * b) / System.Math.Sqrt(b);
+
+            var df = System.Math.Exp(-riskFree * (avgEndDate - evalDate).TotalDays / 365.0);
+
+            d1 = Math.Statistics.NormSDist(d1 *
+                (callPut == OptionType.Call ? 1.0 : -1.0));
+
+            var delta = d1 * df;
+            return delta;
+        }
+    }
+}