From 5c767751754222462078605ebb20b56422fe542f Mon Sep 17 00:00:00 2001
From: Christoph Bunte <christophbunte@gmail.com>
Date: Tue, 5 Mar 2024 15:55:21 +0100
Subject: [PATCH] lv fit: add dynamic #knots selection

---
 .../scala/derifree/fd/LocalVolFitter.scala    | 38 ++++++++++++++++---
 .../src/test/scala/derifree/fd/lvfit.scala    |  4 +-
 .../src/test/scala/derifree/fd/lvfit2.scala   |  9 ++++-
 3 files changed, 41 insertions(+), 10 deletions(-)

diff --git a/derifree/src/main/scala/derifree/fd/LocalVolFitter.scala b/derifree/src/main/scala/derifree/fd/LocalVolFitter.scala
index 0a58b64..c81abd1 100644
--- a/derifree/src/main/scala/derifree/fd/LocalVolFitter.scala
+++ b/derifree/src/main/scala/derifree/fd/LocalVolFitter.scala
@@ -32,6 +32,7 @@ import scala.math.exp
 import scala.math.log
 import scala.math.max
 import scala.math.min
+import scala.math.round
 import scala.math.pow
 import scala.math.sqrt
 
@@ -104,9 +105,9 @@ sealed trait LocalVolFitter:
 object LocalVolFitter:
 
   case class Settings(
-      nKnots: Int,
-      minLv: Double,
-      maxLv: Double,
+      minLv: Double = 0.01,
+      maxLv: Double = 5.0,
+      nKnots: Settings.Knots = Settings.Knots.Fixed(5),
       spatialGrid: Settings.SpatialGrid = Settings.SpatialGrid(),
       timeGrid: Settings.TimeGrid = Settings.TimeGrid(),
       nRannacherSteps: Int = 2
@@ -132,6 +133,10 @@ object LocalVolFitter:
         expansionMaxIters: Int = 10
     )
 
+    enum Knots:
+      case Fixed(n: Int)
+      case Dynamic(min: Int, max: Int, alpha: Double, minStrikes: Int, minSpread: Double)
+
   case class Result(
       /** The fitted expiries in year fraction terms. By convention the first element is always
         * zero.
@@ -408,18 +413,39 @@ object LocalVolFitter:
 
     val timegrid = timeGridFactory(expiries.toSet)
 
+    val nKnotsByExpiry = settings.nKnots match
+      case Settings.Knots.Fixed(n) => obsByExpiry.map(_ => n)
+      case Settings.Knots.Dynamic(minKnots, maxKnots, alpha, minStrikes, minSpread) =>
+        obsByExpiry.map: (_, obs) =>
+          val nStrikes = obs.map(_.strike).toSet.size
+          val nObs = obs.length
+          val medianSpread = obs.map(_.spread).sorted.apply(nObs / 2)
+          round(
+            min(
+              maxKnots,
+              max(
+                minKnots,
+                alpha * log(1.0 + max(nStrikes - minStrikes, 0)) / max(
+                  medianSpread / minSpread,
+                  1.0
+                )
+              )
+            )
+          ).toInt
+
     val state = expiries
       .zip(obsByExpiry)
+      .zip(nKnotsByExpiry)
       .foldLeft(State()):
-        case (state, (t1, (t2, obs))) =>
+        case (state, ((t1, (t2, obs)), nKnots)) =>
           val timeGridSlice = timegrid.slice(t1, t2).get.yearFractions
 
           val minStrike = obs.map(_.strike).min
           val maxStrike = obs.map(_.strike).max
 
           val lvKnots = List
-            .tabulate(settings.nKnots)(i =>
-              minStrike * pow(maxStrike / minStrike, i.toDouble / (settings.nKnots - 1))
+            .tabulate(nKnots)(i =>
+              minStrike * pow(maxStrike / minStrike, i.toDouble / (nKnots - 1))
             )
             .toIndexedSeq
 
diff --git a/derifree/src/test/scala/derifree/fd/lvfit.scala b/derifree/src/test/scala/derifree/fd/lvfit.scala
index 8d54680..1963806 100644
--- a/derifree/src/test/scala/derifree/fd/lvfit.scala
+++ b/derifree/src/test/scala/derifree/fd/lvfit.scala
@@ -56,7 +56,7 @@ class LVFitSuite extends munit.FunSuite:
           PureObservation(1.10, t, vol, 0.01)
         )
       )
-    val settings = Settings(3, 0.01, 1.0)
+    val settings = Settings(0.01, 1.0, Settings.Knots.Fixed(3))
     val result = fitter.fitPureObservations(obs, settings).toTry.get
 
     val clue =
@@ -95,7 +95,7 @@ class LVFitSuite extends munit.FunSuite:
         )
       )
 
-    val settings = Settings(3, 0.01, 1.0)
+    val settings = Settings(0.01, 1.0, Settings.Knots.Fixed(3))
 
     val result = fitter.fitPureObservations(obs, settings).toTry.get
 
diff --git a/derifree/src/test/scala/derifree/fd/lvfit2.scala b/derifree/src/test/scala/derifree/fd/lvfit2.scala
index d913522..13e3d55 100644
--- a/derifree/src/test/scala/derifree/fd/lvfit2.scala
+++ b/derifree/src/test/scala/derifree/fd/lvfit2.scala
@@ -21,6 +21,7 @@ import cats.effect.IO
 import cats.syntax.all.*
 import derifree.dtos.etd.options.OptionQuote
 import derifree.dtos.etd.options.Snapshot
+import derifree.fd.LocalVolFitter.Settings
 import derifree.testutils.*
 
 import scala.concurrent.duration.*
@@ -51,7 +52,11 @@ class LVFitSuite2 extends munit.CatsEffectSuite:
         )
 
         val lvFitter = LocalVolFitter.apply
-        val lvSettings = LocalVolFitter.Settings(5, 0.01, 3.0)
+        val lvSettings = LocalVolFitter.Settings(
+          0.01,
+          3.0,
+          Settings.Knots.Dynamic(3, 12, 5.0, 3, 0.001)
+        )
 
         val initialBorrow = YieldCurve.zero[YearFraction]
         val divs = Nil
@@ -109,6 +114,6 @@ class LVFitSuite2 extends munit.CatsEffectSuite:
               YearFraction.oneDay * 7
             )
           )
-          _ <- IO.println(lv)
+          _ <- IO.println(s"#knots = ${lv.lvKnots.map(_.length).mkString(", ")}")
         yield ()
     )