def gen_map2(a, b):
if len(a.shape) * len(b.shape) <= 1 or len(a.shape) != len(b.shape): return [a, b]
axis = random.randrange(len(a.shape))
for index, (dima, dimb) in enumerate(zip(a.shape, b.shape)):
if index != axis and dima != dimb: return [a, b]
return [expr.concatenate(a, b, axis)]
def gen_map2(a, b):
if len(a.shape) * len(b.shape) <= 1 or len(a.shape) != len(b.shape):
return [a, b]
axis = random.randrange(len(a.shape))
for index, (dima, dimb) in enumerate(zip(a.shape, b.shape)):
if index != axis and dima != dimb: return [a, b]
return [expr.concatenate(a, b, axis)]
def simulate(ts_all, te_all, lamb_all, num_paths):
'''Range over a number of independent products.
:param ts_all: DistArray
Start dates for a series of swaptions.
:param te_all: DistArray
End dates for a series of swaptions.
:param lamb_all: DistArray
Parameter values for a series of swaptions.
:param num_paths: Int
Number of paths used in random walk.
:rtype: DistArray
'''
swaptions = []
i = 0
for ts_a, te, lamb in zip(ts_all, te_all, lamb_all):
for ts in ts_a:
#start = time()
print i
time_structure = arange(None, 0, ts + DELTA, DELTA)
maturity_structure = arange(None, 0, te, DELTA)
############# MODEL ###############
# Variance reduction technique - Antithetic Variates.
eps_tmp = randn(time_structure.shape[0] - 1, num_paths)
eps = concatenate(eps_tmp, -eps_tmp, 1)
# Forward LIBOR rates for the construction of the spot measure.
f_kk = zeros((time_structure.shape[0], 2*num_paths))
f_kk = assign(f_kk, np.s_[0, :], F_0)
# Plane kxN of simulated LIBOR rates.
f_kn = ones((maturity_structure.shape[0], 2*num_paths))*F_0
# Simulations of the plane f_kn for each time step.
for t in xrange(1, time_structure.shape[0]):
f_kn_new = f_kn[1:, :]*exp(lamb*mu(f_kn, lamb)*DELTA-0.5*lamb*lamb *
DELTA + lamb*eps[t - 1, :]*sqrt(DELTA))
f_kk = assign(f_kk, np.s_[t, :], f_kn_new[0])
f_kn = f_kn_new
############## PRODUCT ###############
# Value of zero coupon bonds.
zcb = ones((int((te-ts)/DELTA)+1, 2*num_paths))
f_kn_modified = 1 + DELTA*f_kn
for j in xrange(zcb.shape[0] - 1):
zcb = assign(zcb, np.s_[j + 1], zcb[j] / f_kn_modified[j])
# Swaption price at maturity.
last_row = zcb[zcb.shape[0] - 1, :].reshape((20, ))
swap_ts = maximum(1 - last_row - THETA*DELTA*expr.sum(zcb[1:], 0), 0)
# Spot measure used for discounting.
b_ts = ones((2*num_paths, ))
tmp = 1 + DELTA * f_kk
for j in xrange(int(ts/DELTA)):
b_ts *= tmp[j].reshape((20, ))
# Swaption price at time 0.
swaption = swap_ts/b_ts
# Save expected value in bps and std.
me = mean((swaption[0:num_paths] + swaption[num_paths:])/2) * 10000
st = std((swaption[0:num_paths] + swaption[num_paths:])/2)/sqrt(num_paths)*10000
swaptions.append([me.optimized().force(), st.optimized().force()])
#print time() - start
i += 1
return swaptions
def simulate(ts_all, te_all, lamb_all, num_paths):
"""Range over a number of independent products.
:param ts_all: DistArray
Start dates for a series of swaptions.
:param te_all: DistArray
End dates for a series of swaptions.
:param lamb_all: DistArray
Parameter values for a series of swaptions.
:param num_paths: Int
Number of paths used in random walk.
:rtype: DistArray
"""
swaptions = []
i = 0
for ts_a, te, lamb in zip(ts_all, te_all, lamb_all):
for ts in ts_a:
# start = time()
print i
time_structure = arange(None, 0, ts + DELTA, DELTA)
maturity_structure = arange(None, 0, te, DELTA)
############# MODEL ###############
# Variance reduction technique - Antithetic Variates.
eps_tmp = randn(time_structure.shape[0] - 1, num_paths)
eps = concatenate(eps_tmp, -eps_tmp, 1)
# Forward LIBOR rates for the construction of the spot measure.
f_kk = zeros((time_structure.shape[0], 2 * num_paths))
f_kk = assign(f_kk, np.s_[0, :], F_0)
# Plane kxN of simulated LIBOR rates.
f_kn = ones((maturity_structure.shape[0], 2 * num_paths)) * F_0
# Simulations of the plane f_kn for each time step.
for t in xrange(1, time_structure.shape[0]):
f_kn_new = f_kn[1:, :] * exp(
lamb * mu(f_kn, lamb) * DELTA - 0.5 * lamb * lamb * DELTA + lamb * eps[t - 1, :] * sqrt(DELTA)
)
f_kk = assign(f_kk, np.s_[t, :], f_kn_new[0])
f_kn = f_kn_new
############## PRODUCT ###############
# Value of zero coupon bonds.
zcb = ones((int((te - ts) / DELTA) + 1, 2 * num_paths))
f_kn_modified = 1 + DELTA * f_kn
for j in xrange(zcb.shape[0] - 1):
zcb = assign(zcb, np.s_[j + 1], zcb[j] / f_kn_modified[j])
# Swaption price at maturity.
last_row = zcb[zcb.shape[0] - 1, :].reshape((20,))
swap_ts = maximum(1 - last_row - THETA * DELTA * expr.sum(zcb[1:], 0), 0)
# Spot measure used for discounting.
b_ts = ones((2 * num_paths,))
tmp = 1 + DELTA * f_kk
for j in xrange(int(ts / DELTA)):
b_ts *= tmp[j].reshape((20,))
# Swaption price at time 0.
swaption = swap_ts / b_ts
# Save expected value in bps and std.
me = mean((swaption[0:num_paths] + swaption[num_paths:]) / 2) * 10000
st = std((swaption[0:num_paths] + swaption[num_paths:]) / 2) / sqrt(num_paths) * 10000
swaptions.append([me.optimized().force(), st.optimized().force()])
# print time() - start
i += 1
return swaptions