A preliminary full implementation of the Black-Scholes model for European options...

.paket/Paket.Restore.targets

@@ -71,7 +71,7 @@
       <PaketRestoreRequired Condition=" '$(PaketRestoreLockFileHash)' == '$(PaketRestoreCachedHash)' ">false</PaketRestoreRequired>
       <PaketRestoreRequired Condition=" '$(PaketRestoreLockFileHash)' == '' ">true</PaketRestoreRequired>
     </PropertyGroup>
-    
+
     <PropertyGroup Condition="'$(PaketPropsVersion)' != '5.174.2' ">
       <PaketRestoreRequired>true</PaketRestoreRequired>
     </PropertyGroup>
@@ -96,7 +96,7 @@
       <PaketOriginalReferencesFilePath Condition=" !Exists('$(PaketOriginalReferencesFilePath)')">$(MSBuildProjectDirectory)\$(MSBuildProjectName).paket.references</PaketOriginalReferencesFilePath>
       <!-- paket.references -->
       <PaketOriginalReferencesFilePath Condition=" !Exists('$(PaketOriginalReferencesFilePath)')">$(MSBuildProjectDirectory)\paket.references</PaketOriginalReferencesFilePath>
-      
+
       <DoAllResolvedFilesExist>false</DoAllResolvedFilesExist>
       <DoAllResolvedFilesExist Condition="Exists(%(PaketResolvedFilePaths.Identity))">true</DoAllResolvedFilesExist>
       <PaketRestoreRequired>true</PaketRestoreRequired>
@@ -144,11 +144,12 @@
         <PackageName>$([System.String]::Copy('%(PaketReferencesFileLines.Identity)').Split(',')[0])</PackageName>
         <PackageVersion>$([System.String]::Copy('%(PaketReferencesFileLines.Identity)').Split(',')[1])</PackageVersion>
         <AllPrivateAssets>$([System.String]::Copy('%(PaketReferencesFileLines.Identity)').Split(',')[4])</AllPrivateAssets>
+        <CopyLocal>$([System.String]::Copy('%(PaketReferencesFileLines.Identity)').Split(',')[5])</CopyLocal>
       </PaketReferencesFileLinesInfo>
       <PackageReference Include="%(PaketReferencesFileLinesInfo.PackageName)">
         <Version>%(PaketReferencesFileLinesInfo.PackageVersion)</Version>
         <PrivateAssets Condition=" ('%(PaketReferencesFileLinesInfo.AllPrivateAssets)' == 'true') Or ('$(PackAsTool)' == 'true') ">All</PrivateAssets>
-        <ExcludeAssets Condition="%(PaketReferencesFileLinesInfo.AllPrivateAssets) == 'exclude'">runtime</ExcludeAssets>
+        <ExcludeAssets Condition="%(PaketReferencesFileLinesInfo.CopyLocal) == 'false'">runtime</ExcludeAssets>
         <Publish Condition=" '$(PackAsTool)' == 'true' ">true</Publish>
       </PackageReference>
     </ItemGroup>

src/FSharp/BlackScholes.fs

@@ -0,0 +1,110 @@
+//Copyright (c) 2018 Giulio Occhionero
+
+//Permission is hereby granted, free of charge, to any person obtaining a copy
+//of this software and associated documentation files (the "Software"), to deal
+//in the Software without restriction, including without limitation the rights
+//to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+//copies of the Software, and to permit persons to whom the Software is
+//furnished to do so, subject to the following conditions:
+
+//The above copyright notice and this permission notice shall be included in all
+//copies or substantial portions of the Software.
+
+//THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+//IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+//FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+//AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+//LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+//OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+//SOFTWARE.
+
+namespace MathNet.Numerics.Equity.BlackScholes
+
+open MathNet.Numerics
+
+///Functions to compute the theoretical price and greek parameters of European call options on any time-frame
+///p = underlying price
+///k = strike price
+///v = logarithmic volatility of a single event (events may be days, months, years or whatever...)
+///n = number of events to expiration (events may be days, months, years or whatever...)
+///r = expected return per event, usually assumed equal to risk-free zero-coupon interest rate (events may be days, months, years or whatever...)
+module Call =
+
+    ///Computes the theoretical price of the option
+    let Price p k v n r =
+        (exp((n * v ** 2.0) / 2.0) * p * (1.0 + SpecialFunctions.Erf((n * (r + v ** 2.0) - log(k) + log(p)) / (sqrt(2.0 * n) * v))) + 
+            (k * (-2.0 + SpecialFunctions.Erfc((n * r - log(k) + log(p)) / (sqrt(2.0 * n) * v))))/ exp(n * r)) / 2.0
+
+    ///Computes the partial derivative of the theoretical price with respect to the underlying price
+    let Delta p k v n r =
+        (exp((n * v ** 2.0) / 2.0) * (1.0 + SpecialFunctions.Erf((n * (r + v ** 2.0) - log(k) + log(p)) / (sqrt(2.0 * n) * v))))/2.0
+
+    ///Computes the second partial derivative of the theoretical price with respect to the underlying price
+    let Gamma p k v n r =
+        exp((n * v ** 2.0) / 2.0 - (n * (r + v ** 2.0) - log(k) + log(p)) ** 2.0 / (2.0 * n * v ** 2.0)) / (sqrt(2.0 * n * Constants.Pi) * v * p)
+
+    ///Computes the partial derivative of the theoretical price with respect to the number of events remaining
+    let Theta p k v n r =
+        ((2.0 * k * r) / exp(n * r) + (k ** (1.0 + r / v ** 2.0 + log(p) / (n * v ** 2.0)) * sqrt(2.0 / Constants.Pi) * v) /
+            (exp((n ** 2.0 * r * (r + 2.0 * v ** 2.0) + log(k) ** 2.0 + log(p) ** 2.0) / (2.0 * n * v ** 2.0)) * sqrt(n) * p ** (r / v ** 2.0))
+            + exp((n * v ** 2.0) / 2.0) * p * v ** 2.0 + (2.0 * k * r * SpecialFunctions.Erf((n * r - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v))) / exp(n * r) + 
+            exp((n * v ** 2.0) / 2.0) * p * v ** 2.0 * SpecialFunctions.Erf((n * (r + v ** 2.0) - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v))) / 4.0
+
+    ///Computes the partial derivative of the theoretical price with respect to the expected return (interest rate)
+    let Rho p k v n r =
+        (k * n * (1.0 + SpecialFunctions.Erf((n * r - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v)))) / (2.0 * exp(n * r))
+
+    ///Computes the partial derivative of the theoretical price with respect to the volatility
+    let Vega p k v n r =
+        (k ** (1.0 + r / v ** 2.0 + log(p) / (n * v ** 2.0)) * sqrt(n)) /
+        (exp((n ** 2.0 * r * (r + 2.0 * v ** 2.0) + log(k) ** 2.0 + log(p) ** 2.0) / (2.0 * n * v ** 2.0)) * p ** (r / v ** 2.0) * sqrt(2.0 * Constants.Pi))
+        + (exp((n * v ** 2.0) / 2.0) * n * p * v) / 2.0 + (exp((n * v ** 2.0) / 2.0) * n * p * v * SpecialFunctions.Erf((n * (r + v ** 2.0) - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v))) / 2.0
+
+    ///Computes the leverage factor of the option with respect to the underlying
+    let Leverage p k v n r = p * (Delta p k v n r) / (Price p k v n r)
+
+
+///Functions to compute the theoretical price and greek parameters of European put options on any time-frame
+///p = underlying price
+///k = strike price
+///v = logarithmic volatility of a single event (events may be days, months, years or whatever...)
+///n = number of events to expiration (events may be days, months, years or whatever...)
+///r = expected return per event, usually assumed equal to risk-free zero-coupon interest rate (events may be days, months, years or whatever...)
+module Put =
+
+    ///Computes the theoretical price of the option
+    let Price p k v n r =
+        ((k * SpecialFunctions.Erfc((n * r - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v))) / exp(n * r) - 
+            exp((n * v ** 2.0) / 2.0) * p * SpecialFunctions.Erfc((n * (r + v ** 2.0) - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v))) / 2.0
+
+    ///Computes the partial derivative of the theoretical price with respect to the underlying price
+    let Delta p k v n r =
+        -(exp((n * v ** 2.0) / 2.0) * SpecialFunctions.Erfc((n * (r + v ** 2.0) - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v))) / 2.0
+
+    ///Computes the second partial derivative of the theoretical price with respect to the underlying price
+    let Gamma p k v n r =
+        exp((n * v ** 2.0) / 2.0 - (n * (r + v ** 2.0) - log(k) + log(p)) ** 2.0 / (2.0 * n * v ** 2.0)) / (sqrt(n) * p * sqrt(2.0 * Constants.Pi) * v)
+
+    ///Computes the partial derivative of the theoretical price with respect to the number of events remaining
+    let Theta p k v n r =
+        ((-2.0 * k * r * SpecialFunctions.Erfc((n * r - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v))) / 
+            exp(n * r) + v * ((k ** (1.0 + r / v ** 2.0 + log(p) / (n * v ** 2.0)) * sqrt(2.0 / Constants.Pi)) / 
+                (exp((n ** 2.0 * r * (r + 2.0 * v ** 2.0) + log(k) ** 2.0 + log(p) ** 2.0) /
+                    (2.0 * n * v ** 2.0)) * sqrt(n) * p ** (r / v ** 2.0)) - exp((n * v ** 2.0) / 2.0) * p * v *
+                        SpecialFunctions.Erfc((n * (r + v ** 2.0) - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v)))) / 4.0
+
+    ///Computes the partial derivative of the theoretical price with respect to the expected return (interest rate)
+    let Rho p k v n r =
+        -(k * n * SpecialFunctions.Erfc((n * r - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v))) / (2.0 * exp(n * r))
+
+    ///Computes the partial derivative of the theoretical price with respect to the volatility
+    let Vega p k v n r =
+        (sqrt(n) * ((k ** (1.0 + r / v ** 2.0 + log(p) / (n * v ** 2.0)) * sqrt(2.0 / Constants.Pi)) /
+          (exp((log(k) ** 2.0 + log(p) ** 2.0) / (2.0 * n * v ** 2.0)) * p ** (r / v ** 2.0)) - 
+            exp((n * (r + v ** 2.0) ** 2.0) / (2.0 * v ** 2.0)) * sqrt(n) * p * v *
+             SpecialFunctions.Erfc((n * (r + v ** 2.0) - log(k) + log(p)) / (Constants.Sqrt2 * sqrt(n) * v)))) /
+                (2.0 * exp((n * r * (r + 2.0 * v ** 2.0)) / (2.0 * v ** 2.0)))
+
+    ///Computes the leverage factor of the option with respect to the underlying
+    let Leverage p k v n r = p * (Delta p k v n r) / (Price p k v n r)
+

src/FSharp/FSharp.fsproj

@@ -39,6 +39,7 @@
     <Compile Include="BigIntegerExtensions.fs" />
     <Compile Include="BigRational.fsi" />
     <Compile Include="BigRational.fs" />
+    <Compile Include="BlackScholes.fs" />
     <Compile Include="Differentiate.fs" />
     <Compile Include="Fit.fs" />
     <Compile Include="FindRoots.fs" />