def make_open_conic(P0, T0, P2, T2, P):
''' Construct an arbitrary open conic arc in three-dimensional
space. The resulting NURBS curve consists of either one, two, or
four segments connected with C1 continuity.
Source: The NURBS Book (2nd Ed.), Pg. 317.
'''
P0, T0 = [np.asfarray(V) for V in P0, T0]
P2, T2 = [np.asfarray(V) for V in P2, T2]
P = np.asfarray(P)
P1, w1 = make_one_arc(P0, T0, P2, T2, P)
if w1 <= -1.0:
raise ParabolaOrHyperbolaOutsideConvexHull(w1)
if w1 >= 1.0: # hyperbola or parabola
nsegs = 1
else: # ellipse
if w1 > 0.0 and util.angle(P0, P1, P2) > 60.0:
nsegs = 1
elif w1 < 0.0 and util.angle(P0, P1, P2) > 90.0:
nsegs = 4
else:
nsegs = 2
n = 2 * nsegs
Pw = np.zeros((n + 1, 4))
U = np.zeros(n + 4)
j = 2 * nsegs + 1
U[j:] = 1.0
Pw[0] = np.hstack((P0, 1.0))
Pw[n] = np.hstack((P2, 1.0))
if nsegs == 1:
Pw[1] = np.hstack((w1 * P1, w1))
cpol = curve.ControlPolygon(Pw=Pw)
return curve.Curve(cpol, (2, ), (U, ))
Q1, S, R1, wqr = split_arc(P0, P1, w1, P2)
if nsegs == 2:
Pw[2] = np.hstack((S, 1.0))
Pw[1] = np.hstack((wqr * Q1, wqr))
Pw[3] = np.hstack((wqr * R1, wqr))
U[3] = U[4] = 0.5
cpol = curve.ControlPolygon(Pw=Pw)
return curve.Curve(cpol, (2, ), (U, ))
Pw[4] = np.hstack((S, 1.0))
w1 = wqr
HQ1, HS, HR1, wqr = split_arc(P0, Q1, w1, S)
Pw[2] = np.hstack((HS, 1.0))
Pw[1] = np.hstack((wqr * HQ1, wqr))
Pw[3] = np.hstack((wqr * HR1, wqr))
HQ1, HS, HR1, wqr = split_arc(S, R1, w1, P2)
Pw[6] = np.hstack((HS, 1.0))
Pw[5] = np.hstack((wqr * HQ1, wqr))
Pw[7] = np.hstack((wqr * HR1, wqr))
for i in xrange(2):
U[i + 3] = 0.25
U[i + 5] = 0.5
U[i + 7] = 0.75
cpol = curve.ControlPolygon(Pw=Pw)
return curve.Curve(cpol, (2, ), (U, ))
def refit_curve(C, ncp, p=3, num=1000):
''' Refit an arbitrary Curve with another Curve of arbitrary degree
by sampling it at equally spaced intervals. If possible the
original end derivatives are kept intact.
Parameters
----------
C = the Curve to refit
ncp = the number of control points to use in the fit
p = the degree to use in the fit
num = the number of points to sample C with
Returns
-------
Curve = the refitted Curve
'''
U, = C.U
us, = util.construct_flat_grid((U, ), (num, ))
Q = C.eval_points(us).T
Ds, De = [], []
if ncp > 3:
Ds = C.eval_derivatives(U[0], 1)[1:]
De = C.eval_derivatives(U[-1], 1)[1:]
U, Pw = global_curve_approx_fixedn_ders(num - 1, Q, p, ncp - 1, len(Ds),
Ds, len(De), De, us)
return curve.Curve(curve.ControlPolygon(Pw=Pw), (p, ), (U, ))
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 Crack_ATMVol_TermStr(tsList,
weights,
expiryT,
termTenor="1m",
exceptionDateList=[]):
dates = []
if len(tsList) != len(weights):
raise ValueError, 'The number of elements of weights and time series should be equal'
for ts in tsList:
if dates == []:
dates = ts.Dates()
else:
dates = [d for d in ts.Dates() if d in dates]
Crk = curve.Curve()
undFwd = curve.Curve()
for d in dates:
Fwd = [ts[d] for ts in tsList]
Crk[d] = sum([f * w for (f, w) in zip(Fwd, weights)])
undFwd[d] = tsList[0][d]
IsCall = 1
CrkVol = BS_ATMVol_TermStr(IsCall,
Crk,
expiryT,
rd=0,
rf=0.0,
endVol=0.0,
termTenor=termTenor,
rehedge_period="1d",
exceptionDateList=exceptionDateList)
undVol = BS_ATMVol_TermStr(IsCall,
undFwd,
expiryT,
rd=0,
rf=0.0,
endVol=0.0,
termTenor=termTenor,
rehedge_period="1d",
exceptionDateList=exceptionDateList)
return CrkVol, undVol
def make_full_ellipse(P0, T0, P2, T2, P):
''' Construct a full ellipse in three-dimensional space based on
information given in the form of Group 2: start and end points,
together with their tangent directions and an additional point.
Source: The NURBS Book (2nd Ed.), Pg. 318-320.
'''
P0, T0 = [np.asfarray(V) for V in P0, T0]
P2, T2 = [np.asfarray(V) for V in P2, T2]
P = np.asfarray(P)
P1, w1 = make_one_arc(P0, T0, P2, T2, P)
S, T = P0 - P1, P2 - P1
k = 1.0 / w1**2
e = k / (k - 1.0) / 2
a = util.norm(S)**2
b = np.dot(S, T)
g = util.norm(T)**2
d = a * g - b**2
E = a + g - 2 * b
ls = np.roots((2 * d, -(k * E + 4 * b), 2 * (k - 1)))
l1, l2 = np.sort(ls)
r1, r2 = np.sqrt(e / l1), np.sqrt(e / l2)
if abs(k / 2 - g * l1) > abs(k / 2 - a * l1):
xb = k / 2 - g * l1
yb = b * l1 - k / 2 + 1
else:
xb = b * l1 - k / 2 + 1
yb = k / 2 - a * l1
r = a * xb**2 + 2 * b * xb * yb + g * yb**2
x0, y0 = xb / r, yb / r
Q1 = P1 + (e + r1 * x0) * S + (e + r1 * y0) * T
Q2 = P1 + (e - r1 * x0) * S + (e - r1 * y0) * T
U = util.normalize(Q2 - Q1)
V = np.cross(U, util.normalize(np.cross(S, T)))
Pw, Uq = np.zeros((8 + 1, 4)), np.zeros(8 + 4)
C = P1 + e * (S + T)
Pw[0] = Pw[8] = np.hstack((C + r1 * U, 1.0))
Pw[1] = np.hstack((w1 * (C + r1 * U + r2 * V), w1))
Pw[2] = np.hstack((C + r2 * V, 1.0))
Pw[3] = np.hstack((w1 * (C + r2 * V - r1 * U), w1))
Pw[4] = np.hstack((C - r1 * U, 1.0))
Pw[5] = np.hstack((w1 * (C - r1 * U - r2 * V), w1))
Pw[6] = np.hstack((C - r2 * V, 1.0))
Pw[7] = np.hstack((w1 * (C - r2 * V + r1 * U), w1))
for i in xrange(3):
Uq[i] = 0.0
Uq[i + 9] = 1.0
for i in xrange(2):
Uq[i + 3] = 0.25
Uq[i + 5] = 0.5
Uq[i + 7] = 0.75
cpol = curve.ControlPolygon(Pw=Pw)
return curve.Curve(cpol, (2, ), (Uq, ))
def BS_ConstDelta_VolSurf(tsFwd,
moneynessList,
expiryT,
rd=0.0,
rf=0.0,
exceptionDateList=[]):
ts = curve.Curve()
rptTenor = '-1m'
rehedge_period = '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,
rehedge_period, 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 BS_VolSurf_TermStr(tsFwd,
moneyness,
expiryT,
rd=0.0,
rf=0.0,
endVol=0.0,
termTenor="1m",
rehedge_period="1d",
exceptionDateList=[]):
ts = curve.Curve()
rptTenor = '-' + termTenor
def parse(self):
super(ParameterData126, self).parse()
n, p = [int(p) for p in self.params[1:3]]
U = self.params[7:9 + n + p]
w = self.params[9 + n + p:10 + 2 * n + p]
P = self.params[10 + 2 * n + p:13 + 5 * n + p]
w = np.resize(w, (n + 1, 1))
P = np.resize(P, (n + 1, 3))
P *= w
Pw = np.concatenate((P, w), axis=1)
c = curve.Curve(curve.ControlPolygon(Pw=Pw), (p, ), (U, ))
objs.append(c)
def _test_():
import curve
grids = [1, 2, 3, 4]
dfs = [0.99, 0.98, 0.97, 0.96]
c = curve.Curve(grids, dfs, interpolation_method='monotone_convex')
start = 0
end = 3
simple = SimpleRate(start, end)
print('Simple rate :', simple.par_rate(c))
roll = 0.5
swap = SingleCurrencySwap(start, end, roll)
print('Swap rate :', swap.par_rate(c))
def test_SingleTermStrComp():
IsCall = 1
startD = datetime.date(2006, 1, 1)
endD = datetime.date(2008, 12, 31)
trueVol = curve.Curve()
avgVol = curve.Curve()
varVol = curve.Curve()
expiryT = endD
Sigma = [0.4, 0.2]
Kappa = [2.0, 0.001]
numPath = 100
for i in range(numPath):
ts = randTSGen(1, Sigma, Kappa, StartDate=startD, EndDate=endD)
volTS = BSHistVol.BS_ATMVol_TermStr(IsCall,
ts,
expiryT,
rd=0.0,
rf=0.0,
endVol=0.0,
termTenor="22d",
rehedgingTenor="1d",
exceptionDateList=[])
if i == 0:
for d in volTS.Dates():
tau = (expiryT - d).days / 365.0
x = 0.0
for sig, kap in zip(Sigma, Kappa):
x = x + sig**2 * ((1 - math.exp(-2 * kap * tau)) /
(2 * kap * tau))
x = math.sqrt(x)
trueVol[d] = x
avgVol[d] = 0.0
varVol[d] = 0.0
for d in volTS.Dates():
avgVol[d] += volTS[d] / (numPath * 1.0)
varVol[d] += (volTS[d] - trueVol[d])**2 / (numPath * 1.0)
plotList = [avgVol, trueVol]
legendList = ['Vol', 'True Vol']
plotxy.PlotCurves(plotList, Legends=legendList)
diff = curve.Curve()
rvar = curve.Curve()
Texp = curve.Curve()
for d in trueVol.Dates():
diff[d] = avgVol[d] - trueVol[d]
varVol[d] = math.sqrt(varVol[d])
rvar[d] = varVol[d] / trueVol[d]
Texp[d] = (expiryT - d).days / 365.0 * 12.0
DiffRatio = [(Texp[d], diff[d], varVol[d], rvar[d])
for d in trueVol.Dates()]
print DiffRatio
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 testSearchEngine(cls, searchEngine, testQueries, measure):
x = range(0, 101)
meanCurve = Curve.Curve(x, [0. for i in x])
numberOfCurves = 0
for testQuery in testQueries.testQueries:
query = testQuery.query
if len(testQuery.expectedResult) > 0:
curve = cls.getCurve(searchEngine, testQuery, measure)
if len(curve) > 0:
numberOfCurves += 1
curve.removeWrongPoints()
curve.extrapolate(x)
meanCurve += curve
meanCurve = (1. / numberOfCurves) * meanCurve
return meanCurve
def Ed(seam, C):
value = 0
for c in C:
new_c = curve.Curve()
for point in c.points:
new_point = point
if point[1] < seam[point[0]]:
new_point[1] = new_point[1] - 1
new_c.addPoint(new_point)
c.transformBookstein()
new_c.transformBookstein()
value = value + curve.deformation(c.bookstein, new_c.bookstein)
return value
def getCurve(cls, searchEngine, testQuery, measure):
results = searchEngine.search(testQuery.query)
relevant = len(testQuery.expectedResult)
tp = [0 for i in range(0, len(results))]
for j in range(0, len(results)):
tp[j] = tp[max(0, j - 1)]
if results[j] in testQuery.expectedResult:
tp[j] += 1
curve = Curve.Curve([], [])
for j in range(0, len(results)):
if j == 0 or tp[j] > tp[j - 1]:
fp = j + 1 - tp[j]
fn = relevant - tp[j]
curve.append(measure.getRecall(tp[j], fp, fn),
measure.getMeasure(tp[j], fp, fn))
return curve
callabletypes = [
types.FunctionType, types.MethodType, types.ClassType,
types.BuiltinFunctionType, types.BuiltinMethodType
]
sequencetypes = [types.TupleType, types.ListType]
mappingtypes = [types.DictType]
try:
import ExtensionClass
callabletypes.append(ExtensionClass.ExtensionClassType)
except:
pass
try:
import curve
c = curve.Curve()
callabletypes.append(type(c.read))
except:
pass
def finisher(Object):
if type(Object) in callabletypes:
return "("
elif type(Object) in sequencetypes:
return "["
elif type(Object) in mappingtypes:
return "{"
elif members(Object):
return "."
return " "
N = 0xc0256a57b1434a4970e315e3e572ad7b6b6268ca27a1bc14a5ec8d6e8f46ab63
a = 138931309558156184106311716917677778941761847991286360325642242809534952018704195842136094062347931842162775765708572232752796610393601192925341167860358529602430304979627494497048448960083384310735203052588819895230906248500388348984991092188849520120483947949612966752973461165325952933739065855693165670941141036576698048539586409219548698834122183984266610530679658299939991747759033936995784464828547439035421618098378714023855965416127212175477937
alpha = 3
strategy = [256, 128, 110, 64, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 46, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 14, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 6, 4, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 64, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 128, 64, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 64, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 32, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 16, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1, 8, 4, 2, 1, 1, 2, 1, 1, 4, 2, 1, 1, 2, 1, 1]
# Choice of Delta depending on nbIterations and n
Delta = nbIterations
if protocol == 'fp' :
while Delta % (n-2) != 0 or (Delta // (n-2)) % 2 != 0:
Delta += 1
else :
while Delta % n != 0 or (Delta // n) % 2 != 0:
Delta += 1
print('Delta = %d' % Delta)
c = curve.Curve(f, n, N, a, alpha, Delta, strategy)
if protocol == 'fp' :
# for the Fp protocol, choose Delta = (n-2) * evenNumber
assert c.Delta % (c.n - 2) == 0
assert (c.Delta // (c.n - 2)) % 2 == 0
else :
# for the Fp2 protocol, choose Delta = n * number
assert c.Delta % c.n == 0
assert (c.Delta // c.n) % 2 == 0
file = open("timing_" + protocol + "_" + method + "_" + pSize + "_" + str(c.Delta) + "steps.txt", "a")
file.write("VDF over " + protocol + " with log_2(p) = " + str(ZZ(c.p).nbits()) + " and log_2(T) = " + str(ZZ(c.Delta).nbits()) + ".\n")
if method == 'kernel4' :
file.write('Points of [4]-torsion stored.\n\n')
def BS_ATMVol_TermStr(IsCall,
tsFwd,
expiryT,
rd=0.0,
rf=0.0,
endVol=0.0,
termTenor="1m",
rehedge_period="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,
rehedge_period,
exceptionDateList,
refVol=refVol)
volTS[startDate] = vol
endVol = vol
date = startDate
endDate = tenor.RDateAdd('1d', date)
startDate = tenor.RDateAdd(rptTenor, date, exceptionDateList)
return volTS
def make_circle_nrat(O, X, Y, r, ths, the, p=3, TOL=1e-5):
''' Construct a nonrational approximation to a circular arc in
three-dimensional space of arbitrary sweep angle theta (0 deg <
theta <= 360 deg).
In particular, the circular arc approximates
C(u) = O + r * cos(u) * X + r * sin(u) * Y ths <= u <= the
and is oriented counter-clockwise in the local coordinate system
defined by O, X and Y.
Parameters
----------
O = the center of the circular arc
X = a vector lying in the plane of definition of the circular arc
Y = a vector in the plane of definition of the circular arc, and
orthogonal to X
r = the radius
ths, the = the start and end angles (in degrees), measured with
respect to X
p = the degree of the circular arc
TOL = the maximum deviation from an exact circular arc
Returns
-------
Curve = the circular arc
Source
------
Piegl & Tiller, Circle Approximation Using Integral B-Spline Curves,
Computer-Aided Design, 2003.
'''
X, Y = [util.normalize(V) for V in (X, Y)]
if not np.allclose(np.dot(X, Y), 0.0):
raise NonOrthogonalAxes(X, Y)
if not r > 0 or not p > 1 or not ths < the:
raise ImproperInput(r, ths, the)
k = p - 1
n = k
if p == 2:
n += 1
ths, the = [np.deg2rad(th) for th in (ths, the)]
the0 = the
dth = the - ths
Q = np.zeros((n + 2, 3))
ns = 0
while True:
ns += 1
Ds, De = (util.eval_ders_trigo(ths, k), util.eval_ders_trigo(the, k))
for i in xrange(1, k + 1):
Ds[i] *= dth**i
De[i] *= dth**i
us = np.linspace(ths, the, n + 2)
for i, u in enumerate(us):
Q[i] = util.eval_ders_trigo(u, 0)
U, Pw = fit.global_curve_interp_ders(n + 1, Q, p, k, Ds[1:], k, De[1:])
nf = Pw.shape[0] - 1
mU = knot.midpoints_knot_vec(U)
errs = []
for m in mU:
um, = curve.curve_point_projection(nf, p, U, Pw, [0, 0, 0], ui=m)
P = curve.rat_curve_point(nf, p, U, Pw, um)
d = abs(1.0 - util.distance(P, [0, 0, 0]))
errs.append(d)
if max(errs) <= TOL:
break
dth = (the0 - ths) / (ns + 1)
the = ths + dth
dtheta = np.rad2deg(the0 - ths) / ns
cpol = curve.ControlPolygon(Pw=Pw)
arcs = []
for n in xrange(ns):
arc = curve.Curve(cpol, (p, ), (U, ))
arc.rotate(n * dtheta, L=[0, 0, 1], Q=[0, 0, 0])
arcs.append(arc)
arc = curve.make_composite_curve(arcs, remove=False)
arc.scale(r)
u = 1.0
for n in xrange(1, ns):
arc = arc.remove(u, k)[1]
u += 1.0
Z = np.cross(X, Y)
transform.custom(arc.cobj.Pw, R=np.column_stack((X, Y, Z)), T=O)
return arc
def Spread_ATMVolCorr_TermStr(ts1,
ts2,
op,
expiryT,
r1=0,
r2=0,
termTenor="1m",
exceptionDateList=[]):
if op != '*' and op != '/':
raise ValueError, 'Operator has to be either * or / for Spread_ATMVolCorr_TermStr'
dates = [d for d in ts1.Dates() if d in ts2.Dates() and d <= expiryT]
F1 = curve.Curve()
F2 = curve.Curve()
HR = curve.Curve()
for d in dates:
if ts1[d] > 0 and ts2[d] > 0:
F1[d] = ts1[d]
F2[d] = ts2[d]
if op == '/':
HR[d] = F1[d] / F2[d]
r = r1 - r2
else:
HR[d] = F1[d] * F2[d]
r = r1 + r2
IsCall = 1
HRVol = BS_ATMVol_TermStr(IsCall,
HR,
expiryT,
rd=r,
rf=0.0,
endVol=0.0,
termTenor=termTenor,
rehedge_period="1d",
exceptionDateList=exceptionDateList)
VolF1 = BS_ATMVol_TermStr(IsCall,
F1,
expiryT,
rd=r1,
rf=0.0,
endVol=0.0,
termTenor=termTenor,
rehedge_period="1d",
exceptionDateList=exceptionDateList)
VolF2 = BS_ATMVol_TermStr(IsCall,
F2,
expiryT,
rd=r2,
rf=0.0,
endVol=0.0,
termTenor=termTenor,
rehedge_period="1d",
exceptionDateList=exceptionDateList)
corr = curve.Curve()
for d in HRVol.Dates():
if op == '/':
corr[d] = (VolF1[d]**2 + VolF2[d]**2 -
HRVol[d]**2) / (2 * VolF1[d] * VolF2[d])
else:
corr[d] = (HRVol[d]**2 - VolF1[d]**2 -
VolF2[d]**2) / (2 * VolF1[d] * VolF2[d])
return HRVol, corr, VolF1, VolF2
def make_circle_rat(O, X, Y, r, ths, the):
''' Construct, using double knots, a rational quadratic circular arc
in three-dimensional space of arbitrary sweep angle theta (0 deg <
theta <= 360 deg).
In particular, the circular arc is represented exactly by
C(u) = O + r * cos(u) * X + r * sin(u) * Y ths <= u <= the
and is oriented counter-clockwise in the local coordinate system
defined by O, X and Y.
Parameters
----------
O = the center of the circular arc
X = a vector lying in the plane of definition of the circular arc
Y = a vector in the plane of definition of the circular arc, and
orthogonal to X
r = the radius
ths, the = the start and end angles (in degrees), measured with
respect to X
Returns
-------
Curve = the circular arc
Examples
--------
>>> O, X, Y = ([0, 1, 0], [1, 0, 0], [0, 0, 1])
>>> arc = nurbs.tb.make_circle_rat(O, X, Y, 3, 75, 340)
or
>>> full = nurbs.tb.make_circle_rat(O, X, Y, 3, 75, 75 + 360)
Source
------
The NURBS Book (2nd Ed.), Pg. 308.
'''
X, Y = [util.normalize(V) for V in (X, Y)]
if not np.allclose(np.dot(X, Y), 0.0):
raise NonOrthogonalAxes(X, Y)
if not r > 0:
raise ImproperInput(r)
if the < ths:
the += 360.0
theta = the - ths
if theta <= 90.0:
narcs = 1
elif theta <= 180.0:
narcs = 2
elif theta <= 270.0:
narcs = 3
else:
narcs = 4
n = 2 * narcs
Pw, U = np.zeros((n + 1, 4)), np.zeros(n + 4)
ths, the, theta = [np.deg2rad(th) for th in (ths, the, theta)]
dtheta = theta / narcs
w1 = np.cos(dtheta / 2.0)
P0 = O + r * np.cos(ths) * X + r * np.sin(ths) * Y
T0 = -np.sin(ths) * X + np.cos(ths) * Y
Pw[0] = np.hstack((P0, 1.0))
index = 0
angle = ths
for i in xrange(1, narcs + 1):
angle += dtheta
P2 = O + r * np.cos(angle) * X + r * np.sin(angle) * Y
Pw[index + 2] = np.hstack((P2, 1.0))
T2 = -np.sin(angle) * X + np.cos(angle) * Y
P1 = util.intersect_3D_lines(P0, T0, P2, T2)
Pw[index + 1] = np.hstack((w1 * P1, w1))
index += 2
if i < narcs:
P0, T0 = P2, T2
j = 2 * narcs + 1
U[j:] = 1.0
if narcs == 2:
U[3] = U[4] = 0.5
elif narcs == 3:
U[3] = U[4] = 1.0 / 3.0
U[5] = U[6] = 2.0 / 3.0
elif narcs == 4:
U[3] = U[4] = 0.25
U[5] = U[6] = 0.5
U[7] = U[8] = 0.75
return curve.Curve(curve.ControlPolygon(Pw=Pw), (2, ), (U, ))
def __test_curveman():
import curve
import curveman
import numpy as np
import scipy.optimize as so
import matplotlib.pyplot as plt
import time
# Define instruments which we calibrate curves to
grids_fixed_ois = [7 / 365, 1 / 12, 2 / 12, 3 / 12, 6 / 12, 9 / 12, 1]
fixed_ois = [ZeroRate(0, end, 'JPY-OIS') for end in grids_fixed_ois]
mid_fixed_ois = np.array(
[0.001, 0.001, 0.0015, 0.002, 0.0022, 0.003, 0.0035])
# Create CurveManager
cm = curveman.CurveManager()
# Define curves and register them to CurveManager
grids_ois = [7 / 365, 1 / 12, 0.4, 0.6, 1]
dfs_ois = np.ones((len(grids_ois), ))
ois_base = curve.Curve(grids_ois, dfs_ois, 'log_linear')
cm.append_curve('JPY-OIS-BASE', ois_base)
turn1_from = 0.2
turn1_to = 0.21
turn1_size = 0.0
turn1 = curve.TurnCurve(turn1_from, turn1_to, turn1_size)
cm.append_curve('JPY-Turn1', turn1)
turn2_from = 0.7
turn2_to = 0.71
turn2_size = 0.0
turn2 = curve.TurnCurve(turn2_from, turn2_to, turn2_size)
cm.append_curve('JPY-Turn2', turn2)
cm.register_basis_curve('JPY-OIS',
['JPY-OIS-BASE', 'JPY-Turn1', 'JPY-Turn2'])
print(cm.get_grids())
def loss(dfs):
cm.update_curves(dfs)
mids = np.array([ois.par_rate(cm) for ois in fixed_ois])
return np.sum((mid_fixed_ois - mids)**2)
#mids = [ois.par_rate(cm) for ois in fixed_ois]
initial = np.ones((len(grids_fixed_ois), ))
print('initial loss :', loss(initial))
t0 = time.time()
param = so.minimize(loss, initial, tol=1e-8, method='nelder-mead')
t1 = time.time()
print('time :', t1 - t0)
print('after calib :', loss(param.x))
print('params :', param.x)
mids = np.array([ois.par_rate(cm) for ois in fixed_ois])
print('calibrated ois :', mids)
cm.update_curves(param.x)
ts = np.arange(0, 1, 1 / 365)
df = cm.get_curve('JPY-OIS').get_df(ts)
fwd = -np.log(df[1:] / df[:-1]) / (ts[1:] - ts[:-1])
plt.plot(ts[:-1], fwd, label='turned')
plt.legend()
plt.show()
print(param.jac)
def handle_circle_menu():
window.bind('<Button-1>', drawAcircle)
def handle_curve_menu(numOfSegments):
window.bind('<Button-1>', drawAcurve)
print(numOfSegments)
global numOfSegments_g
numOfSegments_g = numOfSegments
line = line.Line()
circle = circle.Circle()
curve = curve.Curve()
window = Tk()
window.title("EX1")
w = Canvas(window, width=screen_width, height=screen_height)
img = PhotoImage(width=screen_width, height=screen_height)
w.create_image((screen_width / 2, screen_height / 2),
image=img,
state="normal")
menu = Menu(window)
window.config(menu=menu)
filemenu = Menu(menu, tearoff=0)
menu.add_cascade(label='File', menu=filemenu)
filemenu.add_command(label='Exit', command=window.quit)
def test_CorrTestComp():
IsCall = 1
exceptionDateList = []
op = '/'
startD = datetime.date(2005, 1, 1)
endD = datetime.date(2008, 12, 31)
trueCorr = curve.Curve()
avgCorr = curve.Curve()
varCorr = curve.Curve()
trueVol = curve.Curve()
avgVol = curve.Curve()
varVol = curve.Curve()
expiryT = endD
F = [1.0, 1.0]
Sig = [0.8, 0.5]
Kappa = [1.2, 0.8]
rho = 0.9
numPath = 200
HRPlotList = []
LegendList = []
CorrPlotList = []
for i in range(numPath):
ts1, ts2 = rand2DTSGen(F,
Sig,
Kappa,
rho,
StartDate=startD,
EndDate=endD)
HRVol, HRcorr, VolF1, VolF2 = BSHistVol.Spread_ATMVolCorr_TermStr(
ts1=ts1,
ts2=ts2,
op=op,
expiryT=expiryT,
r1=0.0,
r2=0.0,
termTenor="1m",
exceptionDateList=exceptionDateList)
ToM = [(expiryT - x).days / 365. * 12.0 for x in HRVol.Dates()]
cross_vol = [y * 100.0 for y in HRVol.Values()]
corr = [y * 100.0 for y in HRcorr.Values()]
HRPlotList.append(zip(ToM, cross_vol))
LegendList.append(str(i))
CorrPlotList.append(zip(ToM, corr))
if i == 0:
for d in HRVol.Dates():
tau = (expiryT - d).days / 365.0
s1 = Sig[0]**2 * (1 - math.exp(-2 * Kappa[0] * tau)) / (
2 * Kappa[0] * tau)
s2 = Sig[1]**2 * (1 - math.exp(-2 * Kappa[1] * tau)) / (
2 * Kappa[1] * tau)
s12 = Sig[0] * Sig[1] * rho * (
1 - math.exp(-(Kappa[0] + Kappa[1]) * tau)) / (
(Kappa[0] + Kappa[1]) * tau)
if op == '/':
s = math.sqrt(s1 + s2 - 2 * s12)
else:
s = math.sqrt(s1 + s2 + 2 * s12)
r = s12 / math.sqrt(s1 * s2)
trueVol[d] = s
trueCorr[d] = r
avgVol[d] = 0.0
varVol[d] = 0.0
avgCorr[d] = 0.0
varCorr[d] = 0.0
for d in HRVol.Dates():
avgVol[d] += HRVol[d] / (numPath * 1.0)
varVol[d] += (HRVol[d] - trueVol[d])**2 / (numPath * 1.0)
avgCorr[d] += HRcorr[d] / (numPath * 1.0)
varCorr[d] += (HRcorr[d] - trueCorr[d])**2 / (numPath * 1.0)
#gridfig, ax, axF = plotxy.createFigure(pylab.figure(), GridEnabled=True)
#plotxy.PlotXY(HRPlotList,Legends = LegendList, figure=gridfig)
#gridfig, ax, axF = plotxy.createFigure(pylab.figure(), GridEnabled=True)
#plotxy.PlotXY(CorrPlotList,Legends = LegendList, figure=gridfig)
plotList = [avgVol, trueVol]
legendList = ['Vol', 'True Vol']
gridfig, ax, axF = plotxy.createFigure(pylab.figure(), GridEnabled=True)
plotxy.PlotCurves(plotList, Legends=legendList, figure=gridfig)
plotList = [avgCorr, trueCorr]
legendList = ['Corr', 'True Corr']
gridfig, ax, axF = plotxy.createFigure(pylab.figure(), GridEnabled=True)
plotxy.PlotCurves(plotList, Legends=legendList, figure=gridfig)
diff = curve.Curve()
rcorr = curve.Curve()
Texp = curve.Curve()
for d in trueVol.Dates():
diff[d] = avgCorr[d] - trueCorr[d]
varCorr[d] = math.sqrt(varCorr[d])
rcorr[d] = varCorr[d] / trueCorr[d]
Texp[d] = (expiryT - d).days / 365.0 * 12.0
DiffRatio = [(Texp[d], diff[d], varCorr[d], rcorr[d])
for d in trueCorr.Dates()]
print DiffRatio
a = 10088
alpha = 1
if pSize == 'p89-toy':
f = 1
n = 64
N = 27212093
a = 6
alpha = 1
if pSize == 'p1506':
f = 63
n = 1244
N = 0xc0256a57b1434a4970e315e3e572ad7b6b6268ca27a1bc14a5ec8d6e8f46ab63
a = 138931309558156184106311716917677778941761847991286360325642242809534952018704195842136094062347931842162775765708572232752796610393601192925341167860358529602430304979627494497048448960083384310735203052588819895230906248500388348984991092188849520120483947949612966752973461165325952933739065855693165670941141036576698048539586409219548698834122183984266610530679658299939991747759033936995784464828547439035421618098378714023855965416127212175477937
alpha = 3
c = curve.Curve(f, n, N, a, alpha)
# The delay will depend on nbIterations *and n*
Delta = nbIterations
logging.info('Protocol: %s', protocol)
logging.info('Method: %s', method)
logging.info('Prime size: %s', pSize)
logging.info('Number of steps: %s', str(Delta))
if protocol == 'fp':
VDF = FpVerifiableDelayFunction(method, c, Delta)
else:
VDF = Fp2VerifiableDelayFunction(method, c, Delta)
time = cputime()
