Fix for TreeSwaptionEngine mispricing

[ralfkonrad]

This is a fix for #1143.

The idea is similar to the one for #1142. We use the dates from the fixed and floating swap schedule and adjust them to the exercise date if they are within a period of seven days. The adjusted dates are used to create a new snapped swap which than can be discretized. If the coupon is taken into account within preAdjustValuesImpl() or postAdjustValuesImpl() depends on the fact if the period start date of the coupon is before or after the exercise date.

However even if the jump is now at the coupon period dates the TreeSwaptionEngine still seems not to be stable compared to the FdHullWhiteSwaptionEngine.

#!/usr/bin/env python
# coding: utf-8

# In[1]:


from typing import Any, Dict

import QuantLib as ql
import matplotlib.pyplot as plt
import pandas as pd


# In[2]:


today = ql.Date(8, 7, 2021)
ql.Settings.instance().evaluation_date = today

termstructure = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.02, ql.Actual365Fixed()))
index = ql.Euribor3M(termstructure)


# In[3]:


def makeSwap(rate: float, effectiveDate: ql.Date) -> ql.VanillaSwap:
    swap = ql.MakeVanillaSwap(
        ql.Period(10, ql.Years),
        index,
        0.05,
        ql.Period(),
        effectiveDate=effectiveDate,
        Nominal=10000.00,
        swapType=ql.Swap.Payer)
    swap.setPricingEngine(ql.DiscountingSwapEngine(termstructure))
    return swap


# In[4]:


def makeBermudanSwaption(callDate: ql.Date) -> ql.Swaption:
    effectiveDate = ql.Date(15, 5, 2025)
    swap = makeSwap(0.00, effectiveDate)
    fairRate = swap.fairRate()
    swap = makeSwap(fairRate, effectiveDate)
    exerciseDates = [effectiveDate, callDate]
    bermudanExercise = ql.BermudanExercise(exerciseDates)
    bermudanSwaption = ql.Swaption(swap, bermudanExercise)
    return bermudanSwaption


# In[5]:


initialCallDate = ql.Date(15, 5, 2030)
calendar = index.fixingCalendar()

data = []

intervalOfDaysToTest = 60
for i in range(-intervalOfDaysToTest, intervalOfDaysToTest+1):
    callDate = initialCallDate + i

    bermudanSwaption = makeBermudanSwaption(callDate)
    model = ql.HullWhite(termstructure)

    bermudanSwaption.setPricingEngine(ql.FdHullWhiteSwaptionEngine(model))
    npvFD = bermudanSwaption.NPV()

    timesteps = 14 * 4 * 3
    bermudanSwaption.setPricingEngine(ql.TreeSwaptionEngine(model, timesteps))
    npvTree = bermudanSwaption.NPV()

    data.append(
        {
            'callDate': pd.Timestamp(callDate.ISO()),
            'FD':       npvFD,
            'Tree':     npvTree
        }
    )


# In[6]:


# Plot the results
df = pd.DataFrame(data)
df.set_index('callDate')

fig, ax = plt.subplots()
fig.set_size_inches(16, 9)
df.plot(ax=ax, style='-o', alpha=0.8, x = 'callDate')
ax.set_title('Compare FdHullWhiteSwaptionEngine with TreeSwaptionEngine', fontsize=20)
ax.set_ylabel('npv', fontsize=14)
ax.grid(True, lw=0.5, alpha=0.5)


# In[ ]:

[coveralls]

Coverage increased (+0.02%) to 71.044% when pulling e741173 on ralfkonrad:feature/treeswaptionengine2 into 1f70a67 on lballabio:master.

[lballabio]

Thanks!