def randTSGen(F0, Sigma, Kappa, StartDate, EndDate):
ts = curve.Curve()
factors = len(Sigma)
date = StartDate
ts[date] = F0
F = F0
while tenor.RDateAdd('1d', date, Holidays=[]) <= EndDate:
lastDate = date
date = tenor.RDateAdd('1d', date, Holidays=[])
dt = (date - lastDate).days / 365.0
tau = (EndDate - date).days / 365.0
x = 0.0
for sig, kap in zip(Sigma, Kappa):
x = x - 0.5 * sig**2 * math.exp(
-2 * kap * tau) * dt + sig * math.exp(
-kap * tau) * math.sqrt(dt) * random.gauss(0, 1)
F = F * math.exp(x)
ts[date] = F
return ts
def CF_DeltaHedge(IsCall,
ts,
strike,
vol,
expiryT,
rd=0.0,
rf=0.0,
rehedgingTenor="1d",
exceptionDateList=[]):
Dates = ts.Dates()
Prices = ts.Values()
# annualized days
startD = Dates[0]
endD = Dates[-1]
lastPrice = ts[startD]
lastTau = (expiryT - startD).days / YEARLY_DAYS
date = tenor.RDateAdd(rehedgingTenor, startD, exceptionDateList)
CF = 0.0
while date < endD:
if date in ts.Dates():
CF = CF + bsopt.BSDelta(IsCall, lastPrice, strike, vol, lastTau,
rd, rf) * (ts[date] - lastPrice)
lastPrice = ts[date]
lastTau = (expiryT - date).days / YEARLY_DAYS
date = tenor.RDateAdd(rehedgingTenor, date, exceptionDateList)
CF = CF + bsopt.BSDelta(IsCall, lastPrice, strike, vol, lastTau, rd,
rf) * (ts[endD] - lastPrice)
return CF
def BS_ConstDelta_VolSurf(tsFwd,
moneynessList,
expiryT,
rd=0.0,
rf=0.0,
exceptionDateList=[]):
ts = curve.Curve()
rptTenor = '-1m'
rehedgingTenor = '1d'
IsCall = 1
for d in tsFwd.Dates():
if d not in exceptionDateList:
ts[d] = tsFwd[d]
DateList = [x for x in ts.Dates() if x not in exceptionDateList]
TSstart = DateList[0]
TSend = DateList[-1]
date = copy.copy(TSend)
endDate = tenor.RDateAdd('1d', date)
startDate = tenor.RDateAdd(rptTenor, date, exceptionDateList)
volTS = curve.GRCurve()
while startDate >= TSstart:
subTS = ts.Slice(startDate, endDate)
vol = []
if len(subTS) < 2:
print 'No data in time series further than ', startDate
break
if 0.0 in subTS.Values():
print 'Price is zero at some date from ', startDate, ' to ', endDate
break
# for the moment, consider ATM vol
for m in moneynessList:
strike = subTS.Values()[0] * m
if IsCall:
finalValue = max((subTS.Values()[-1] - strike), 0)
else:
finalValue = max((strike - subTS.Values()[-1]), 0)
vol += [
BSrealizedVol(IsCall, subTS, strike, expiryT, rd, rf, finalValue,
rehedgingTenor, exceptionDateList)
]
if None in vol:
print 'no vol is found to match PnL- strike:' + str(
m) + ' expiry:' + expiryT
volTS[startDate] = vol
startDate = tenor.RDateAdd(rptTenor, startDate, exceptionDateList)
return volTS
def BSrealizedVol(IsCall,
ts,
strike,
expiryT,
rd=0.0,
rf=0.0,
optPayoff=0.0,
rehedgingTenor="1d",
exceptionDateList=[],
refVol=0.5):
startD = ts.Dates()[0]
endD = ts.Dates()[-1]
if tenor.RDateAdd(rehedgingTenor, startD, exceptionDateList) > endD:
raise ValueError, 'the difference between the start and the end is smaller than the hedging step'
if expiryT < endD:
raise ValueError, 'Expiry time must be later than the end of the time series'
F0 = ts.Values()[0]
numTries = 0
diff = 1000.0
tau = (expiryT - startD).days / YEARLY_DAYS
vol = refVol
def func(x):
return bsopt.BSOpt(IsCall, F0, strike, x, tau, rd, rf) + CF_DeltaHedge(
IsCall, ts, strike, x, expiryT, rd, rf, rehedgingTenor,
exceptionDateList) - optPayoff
while diff >= SOLVER_ERROR_EPSILON and numTries <= ITERATION_NUM:
current = func(vol)
high = func(vol + ITERATION_STEP)
low = func(vol - ITERATION_STEP)
if high == low:
volnext = max(vol - ITERATION_STEP, 1e-2)
else:
volnext = vol - 2 * ITERATION_STEP * current / (high - low)
if volnext < 1e-2:
volnext = vol / 2.0
diff = abs(volnext - vol)
vol = volnext
numTries += 1
if diff >= SOLVER_ERROR_EPSILON or numTries > ITERATION_NUM:
return None
else:
return vol
def rand2DTSGen(F0, Sigma, Kappa, rho, StartDate, EndDate):
ts1 = curve.Curve()
ts2 = curve.Curve()
date = StartDate
ts1[date] = F0[0]
ts2[date] = F0[1]
P = F0[0]
G = F0[1]
while tenor.RDateAdd('1d', date, Holidays=[]) <= EndDate:
lastDate = date
date = tenor.RDateAdd('1d', date, Holidays=[])
dt = (date - lastDate).days / 365.0
tau = (EndDate - date).days / 365.0
y1 = random.gauss(0, 1)
y2 = y1 * rho + math.sqrt(1 - rho**2) * random.gauss(0, 1)
x1 = -0.5 * Sigma[0]**2 * math.exp(
-2 * Kappa[0] * tau) * dt + Sigma[0] * math.exp(
-Kappa[0] * tau) * math.sqrt(dt) * y1
x2 = -0.5 * Sigma[1]**2 * math.exp(
-2 * Kappa[1] * tau) * dt + Sigma[1] * math.exp(
-Kappa[1] * tau) * math.sqrt(dt) * y2
P = P * math.exp(x1)
G = G * math.exp(x2)
ts1[date] = P
ts2[date] = G
return ts1, ts2
def BS_ATMVol_TermStr(IsCall,
tsFwd,
expiryT,
rd=0.0,
rf=0.0,
endVol=0.0,
termTenor="1m",
rehedgingTenor="1d",
exceptionDateList=[]):
ts = curve.Curve()
for d in tsFwd.Dates():
if d not in exceptionDateList and d <= expiryT:
ts[d] = tsFwd[d]
rptTenor = '-' + termTenor
DateList = [x for x in ts.Dates() if x not in exceptionDateList]
TSstart = DateList[0]
TSend = DateList[-1]
date = copy.copy(TSend)
endDate = tenor.RDateAdd('1d', date)
startDate = tenor.RDateAdd(rptTenor, date, exceptionDateList)
finalValue = 0.0
volTS = curve.Curve()
while startDate >= TSstart:
subTS = ts.Slice(startDate, endDate)
if len(subTS) < 2:
print 'No data in time series further than ', startDate
break
if 0.0 in subTS.Values():
print 'Price is zero at some date from ', startDate, ' to ', endDate
break
# for the moment, consider ATM vol
strike = subTS.Values()[0]
if endVol > 0:
tau = (expiryT - subTS.Dates()[-1]).days / YEARLY_DAYS
finalValue = bsopt.BSOpt(IsCall,
subTS.Values()[-1], strike, endVol, tau,
rd, rf)
refVol = endVol
elif endVol == 0:
if IsCall:
finalValue = max((subTS.Values()[-1] - strike), 0)
else:
finalValue = max((strike - subTS.Values()[-1]), 0)
refVol = 0.5
elif endVol == None:
raise ValueError, 'no vol is found to match PnL'
vol = BSrealizedVol(IsCall,
subTS,
strike,
expiryT,
rd,
rf,
finalValue,
rehedgingTenor,
exceptionDateList,
refVol=refVol)
volTS[startDate] = vol
endVol = vol
date = startDate
endDate = tenor.RDateAdd('1d', date)
startDate = tenor.RDateAdd(rptTenor, date, exceptionDateList)
return volTS