Merge pull request #22 from jackgillett101/andraesen_huge_interpolation

Adding Andreasen-Huge volsurfaces
nhaga · Nov 4, 2020 · 5a40c6f · 5a40c6f
2 parents 19fe833 + 8a68dad
commit 5a40c6f
Showing 1 changed file with 97 additions and 25 deletions.
diff --git a/docs/termstructures/volatility.rst b/docs/termstructures/volatility.rst
@@ -74,6 +74,69 @@ BlackVarianceSurface
   )
   volatilitySurface.enableExtrapolation()
 
+
+HestonBlackVolSurface
+*********************
+
+.. function:: ql.HestonBlackVolSurface(hestonModelHandle)
+
+.. code-block:: python
+
+  flatTs = ql.YieldTermStructureHandle(
+    ql.FlatForward(ql.Date().todaysDate(), 0.05, ql.Actual365Fixed())
+  )
+  dividendTs = ql.YieldTermStructureHandle(
+    ql.FlatForward(ql.Date().todaysDate(), 0.02, ql.Actual365Fixed())
+  )
+
+  v0 = 0.01; kappa = 0.01; theta = 0.01; rho = 0.0; sigma = 0.01
+  spot = 100
+  process = ql.HestonProcess(flatTs, dividendTs,
+                              ql.QuoteHandle(ql.SimpleQuote(spot)),
+                              v0, kappa, theta, sigma, rho
+                              )
+
+  hestonModel = ql.HestonModel(process)
+  hestonHandle = ql.HestonModelHandle(hestonModel)
+  hestonVolSurface = ql.HestonBlackVolSurface(hestonHandle)
+
+
+AndreasenHugeVolatilityAdapter
+******************************
+
+An implementation of the arb-free Andreasen-Huge vol interpolation described in "Andreasen J., Huge B., 2010. Volatility Interpolation" (https://ssrn.com/abstract=1694972). An advantage of this method is that it can take a non-rectangular grid of option quotes.
+
+.. function:: ql.AndreasenHugeVolatilityAdapter(AndreasenHugeVolatilityInterpl)
+
+.. code-block:: python
+
+  today = ql.Date().todaysDate()
+  calendar = ql.NullCalendar()
+  dayCounter = ql.Actual365Fixed()
+  spot = 100
+  r, q = 0.02, 0.05
+
+  spotQuote = ql.QuoteHandle(ql.SimpleQuote(spot))
+  ratesTs = ql.YieldTermStructureHandle(ql.FlatForward(today, r, dayCounter))
+  dividendTs = ql.YieldTermStructureHandle(ql.FlatForward(today, q, dayCounter))
+
+  # Market options price quotes
+  optionStrikes = [95, 97.5, 100, 102.5, 105, 90, 95, 100, 105, 110, 80, 90, 100, 110, 120]
+  optionMaturities = ["3M", "3M", "3M", "3M", "3M", "6M", "6M", "6M", "6M", "6M", "1Y", "1Y", "1Y", "1Y", "1Y"]
+  optionQuotedVols = [0.11, 0.105, 0.1, 0.095, 0.095, 0.12, 0.11, 0.105, 0.1, 0.105, 0.12, 0.115, 0.11, 0.11, 0.115]
+
+  calibrationSet = ql.CalibrationSet()
+
+  for strike, expiry, impliedVol in zip(optionStrikes, optionMaturities, optionQuotedVols):
+    payoff = ql.PlainVanillaPayoff(ql.Option.Call, strike)
+    exercise = ql.EuropeanExercise(calendar.advance(today, ql.Period(expiry)))
+
+    calibrationSet.push_back((ql.VanillaOption(payoff, exercise), ql.SimpleQuote(impliedVol)))
+
+  ahInterpolation = ql.AndreasenHugeVolatilityInterpl(calibrationSet, spotQuote, ratesTs, dividendTs)
+  ahSurface = ql.AndreasenHugeVolatilityAdapter(ahInterpolation)
+
+
 BlackVolTermStructureHandle
 ***************************
 
@@ -100,31 +163,6 @@ RelinkableBlackVolTermStructureHandle
   blackTSHandle.linkTo(volatilitySurface)
 
 
-
-HestonBlackVolSurface
-*********************
-
-.. function:: ql.HestonBlackVolSurface(hestonModelHandle)
-
-.. code-block:: python
-
-  flat_ts = ql.YieldTermStructureHandle(
-    ql.FlatForward(ql.Date().todaysDate(), 0.05, ql.Actual365Fixed())
-  )
-  dividend_ts = ql.YieldTermStructureHandle(
-    ql.FlatForward(ql.Date().todaysDate(), 0.02, ql.Actual365Fixed())
-  )
-  v0 = 0.01; kappa = 0.01; theta = 0.01; rho = 0.0; sigma = 0.01
-  spot = 100
-  process = ql.HestonProcess(flat_ts, dividend_ts,
-                              ql.QuoteHandle(ql.SimpleQuote(spot)),
-                              v0, kappa, theta, sigma, rho
-                              )
-  heston_model = ql.HestonModel(process)
-  heston_handle = ql.HestonModelHandle(heston_model)
-  heston_vol_surface = ql.HestonBlackVolSurface(heston_handle)
-
-
 LocalConstantVol
 ****************
 
@@ -184,6 +222,40 @@ This powerful but dangerous surface will swallow any exceptions and return the s
   ql.NoExceptLocalVolSurface(blackVolTs, ratesTs, dividendTs, spot, illegalVolOverride)
 
 
+AndreasenHugeLocalVolAdapter
+****************************
+
+.. function:: ql.AndreasenHugeLocalVolAdapter(AndreasenHugeVolatilityInterpl)
+
+.. code-block:: python
+
+  today = ql.Date().todaysDate()
+  calendar = ql.NullCalendar()
+  dayCounter = ql.Actual365Fixed()
+  spot = 100
+  r, q = 0.02, 0.05
+
+  spotQuote = ql.QuoteHandle(ql.SimpleQuote(spot))
+  ratesTs = ql.YieldTermStructureHandle(ql.FlatForward(today, r, dayCounter))
+  dividendTs = ql.YieldTermStructureHandle(ql.FlatForward(today, q, dayCounter))
+
+  # Market options price quotes
+  optionStrikes = [95, 97.5, 100, 102.5, 105, 90, 95, 100, 105, 110, 80, 90, 100, 110, 120]
+  optionMaturities = ["3M", "3M", "3M", "3M", "3M", "6M", "6M", "6M", "6M", "6M", "1Y", "1Y", "1Y", "1Y", "1Y"]
+  optionQuotedVols = [0.11, 0.105, 0.1, 0.095, 0.095, 0.12, 0.11, 0.105, 0.1, 0.105, 0.12, 0.115, 0.11, 0.11, 0.115]
+
+  calibrationSet = ql.CalibrationSet()
+
+  for strike, expiry, impliedVol in zip(optionStrikes, optionMaturities, optionQuotedVols):
+    payoff = ql.PlainVanillaPayoff(ql.Option.Call, strike)
+    exercise = ql.EuropeanExercise(calendar.advance(today, ql.Period(expiry)))
+
+    calibrationSet.push_back((ql.VanillaOption(payoff, exercise), ql.SimpleQuote(impliedVol)))
+
+  ahInterpolation = ql.AndreasenHugeVolatilityInterpl(calibrationSet, spotQuote, ratesTs, dividendTs)
+  ahLocalSurface = ql.AndreasenHugeLocalVolAdapter(ahInterpolation)
+
+
 LocalVolTermStructureHandle
 ***************************