所以我想做的是用Monte Carlo模拟美国期权（股票）并使用TensorFlow对其定价。
我使用两个帮助函数 get_continuation_function 创建TF运算符。然后 pricing_function 创建定价的计算图。
npv 运算符是最佳运动决策的总和。每次我检查行使值是否大于预测的连续值（换句话说，期权是否在货币中）。
而实际的定价功能是 american_tf 。我执行该功能以创建路径，即训练路径的运动值。然后，我向后遍历training_functions，并在每个练习日期学习其价值和决定。
def get_continuation_function():
X = tf.placeholder(tf.float32, (None,1),name="X")
y = tf.placeholder(tf.float32, (None,1),name="y")
w = tf.Variable(tf.random_uniform((1,1))*0.1,,name="w")
b = tf.Variable(initial_value = tf.ones(1)*1,name="b")
y_hat = tf.add(tf.matmul(X, w), b)
pre_error = tf.pow(y-y_hat,2)
error = tf.reduce_mean(pre_error)
train = tf.train.AdamOptimizer(0.1).minimize(error)
return(X, y, train, w, b, y_hat)
def pricing_function(number_call_dates):
S = tf.placeholder(tf.float32,name="S")
# First excerise date
dts = tf.placeholder(tf.float32,name="dts")
# 2nd exersice date
K = tf.placeholder(tf.float32,name="K")
r = tf.placeholder(tf.float32,,name="r")
sigma = tf.placeholder(tf.float32,name="sigma")
dW = tf.placeholder(tf.float32,name="dW")
S_t = S * tf.cumprod(tf.exp((r-sigma**2/2) * dts + sigma * tf.sqrt(dts) * dW), axis=1)
E_t = tf.exp(-r * tf.cumsum(dts)) * tf.maximum(K-S_t, 0)
continuationValues = []
training_functions = []
previous_exersies = 0
npv = 0
for i in range(number_call_dates-1):
(input_x, input_y, train, w, b, y_hat) = get_continuation_function()
training_functions.append((input_x, input_y, train, w, b, y_hat))
X = tf.keras.activations.relu(S_t[:, i])
contValue = tf.add(tf.matmul(X, w),b)
continuationValues.append(contValue)
inMoney = tf.cast(tf.greater(E_t[:,i], 0.), tf.float32)
exercise = tf.cast(tf.greater(E_t[:,i], contValue[:,0]), tf.float32) * inMoney * (1-previous_exersies)
previous_exersies += exercise
npv += exercise*E_t[:,i]
# Last exercise date
inMoney = tf.cast(tf.greater(E_t[:,-1], 0.), tf.float32)
exercise = inMoney * (1-previous_exersies)
npv += exercise*E_t[:,-1]
npv = tf.reduce_mean(npv)
return([S, dts, K, r, sigma,dW, S_t, E_t, npv, training_functions])
def american_tf(S_0, strike, M, impliedvol, riskfree_r, random_train, random_pricing):
n_exercise = len(M)
with tf.Session() as sess:
S,dts,K,r,sigma,dW,S_t,E_t,npv,training_functions = pricing_function(n_exercise)
sess.run(tf.global_variables_initializer())
paths, exercise_values = sess.run([S_t,E_t], {
S: S_0,
dts: M,
K: strike,
r: riskfree_r,
sigma: impliedvol,
dW: random_train
})
for i in range(n_exercise-1)[::-1]:
(input_x,input_y,train,w,b,y_hat) = training_functions[i]
y= exercise_values[:,i+1:i+2]
X = paths[:,i]
print(input_x.shape)
print((exercise_values[:,i]>0).shape)
for epochs in range(100):
_ = sess.run(train, {input_x:X[exercise_values[:,i]>0],
input_y:y[exercise_values[:,i]>0]})
cont_value = sess.run(y_hat, {input_x:X, input_y:y})
exercise_values[:,i+1:i+2] = np.maximum(exercise_values[:,i+1:i+2], cont_value)
npv = sess.run(npv, {S: S_0, K: strike, r: riskfree_r, sigma: impliedvol, dW: N_pricing})
return npv
N_samples_learn = 1000
N_samples_pricing = 1000
calldates = 12
N = np.random.randn(N_samples_learn,calldates)
N_pricing = np.random.randn(N_samples_pricing,calldates)
american_tf(100., 90., [1.]*calldates, 0.25, 0.05, N, N_pricing)
Calldates是步骤数
训练样本集= 1000
测试样本大小= 1000
但是我的错误很奇怪
---> 23 nput_y:y[exercise_values[:,i]>0]})
ValueError: Cannot feed value of shape (358,) for Tensor 'Placeholder_441:0', which has shape '(?, 1)'
答案 0 :(得分：0)
有一堆在评论与@ hallo12讨论的事情。我只想上传一个包含所有更改的工作版本。该代码经过测试，可以正常运行。但是，为了确保最终的培训输出是正确的，你可能需要比较对一些标杆。
一般注释：在这种类型的应用程序中，最好将变量和时间维度分开，尤其是当您只有1个变量时。例如，您的输入数组应为
的3D[time, training sample, input variable]
而不是使用[训练样本，时间]进行2D。这样，当你遍历时间维度，尺寸的其余部分保持不变。
import tensorflow as tf
import numpy as np
def get_continuation_function():
X = tf.placeholder(tf.float32, (None,1),name="X")
y = tf.placeholder(tf.float32, (None,1),name="y")
w = tf.Variable(tf.random_uniform((1,1))*0.1,name="w")
b = tf.Variable(initial_value = tf.ones(1)*1,name="b")
y_hat = tf.add(tf.matmul(X, w), b)
pre_error = tf.pow(y-y_hat,2)
error = tf.reduce_mean(pre_error)
train = tf.train.AdamOptimizer(0.1).minimize(error)
return(X, y, train, w, b, y_hat)
def pricing_function(number_call_dates):
S = tf.placeholder(tf.float32,name="S")
# First excerise date
dts = tf.placeholder(tf.float32,name="dts")
# 2nd exersice date
K = tf.placeholder(tf.float32,name="K")
r = tf.placeholder(tf.float32,name="r")
sigma = tf.placeholder(tf.float32,name="sigma")
dW = tf.placeholder(tf.float32,name="dW")
S_t = S * tf.cumprod(tf.exp((r-sigma**2/2) * dts + sigma * tf.sqrt(dts) * dW), axis=1)
E_t = tf.exp(-r * tf.cumsum(dts)) * tf.maximum(K-S_t, 0)
continuationValues = []
training_functions = []
previous_exersies = 0
npv = 0
for i in range(number_call_dates-1):
(input_x, input_y, train, w, b, y_hat) = get_continuation_function()
training_functions.append((input_x, input_y, train, w, b, y_hat))
X = tf.keras.activations.relu(S_t[:, i:i+1])
contValue = tf.add(tf.matmul(X, w),b)
continuationValues.append(contValue)
inMoney = tf.cast(tf.greater(E_t[:,i], 0.), tf.float32)
exercise = tf.cast(tf.greater(E_t[:,i], contValue[:,0]), tf.float32) * inMoney * (1-previous_exersies)
previous_exersies += exercise
npv += exercise*E_t[:,i]
# Last exercise date
inMoney = tf.cast(tf.greater(E_t[:,-1], 0.), tf.float32)
exercise = inMoney * (1-previous_exersies)
npv += exercise*E_t[:,-1]
npv = tf.reduce_mean(npv)
return([S, dts, K, r, sigma,dW, S_t, E_t, npv, training_functions])
def american_tf(S_0, strike, M, impliedvol, riskfree_r, random_train, random_pricing):
n_exercise = len(M)
with tf.Session() as sess:
S,dts,K,r,sigma,dW,S_t,E_t,npv,training_functions = pricing_function(n_exercise)
sess.run(tf.global_variables_initializer())
paths, exercise_values = sess.run([S_t,E_t], {
S: S_0,
dts: M,
K: strike,
r: riskfree_r,
sigma: impliedvol,
dW: random_train
})
for i in range(n_exercise-1)[::-1]:
(input_x,input_y,train,w,b,y_hat) = training_functions[i]
y= exercise_values[:,i+1:i+2]
X = paths[:,i]
print(input_x.shape)
print((exercise_values[:,i]>0).shape)
for epochs in range(100):
_ = sess.run(train, {input_x:(X[exercise_values[:,i]>0]).reshape(len(X[exercise_values[:,i]>0]),1),
input_y:(y[exercise_values[:,i]>0]).reshape(len(y[exercise_values[:,i]>0]),1)})
cont_value = sess.run(y_hat, {input_x:X.reshape(len(X),1), input_y:y.reshape(len(y),1)})
exercise_values[:,i+1:i+2] = np.maximum(exercise_values[:,i+1:i+2], cont_value)
npv = sess.run(npv, {S: S_0, K: strike, dts:M, r: riskfree_r, sigma: impliedvol, dW: N_pricing})
return npv
N_samples_learn = 1000
N_samples_pricing = 1000
calldates = 12
N = np.random.randn(N_samples_learn,calldates)
N_pricing = np.random.randn(N_samples_pricing,calldates)
print(american_tf(100., 90., [1.]*calldates, 0.25, 0.05, N, N_pricing))