ich bin dabei für ein Projekt an der Universität , eine amerikanische Put Option zu bewerten.
Code: Alles auswählen
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)
#greeks = tf.gradients(npv, [S, r, sigma])
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]
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)
american_tf(100.,90.,[1.]*calldates,0.25,0.05,N,N_pricing)
Ich hab hierfür zwei Hilfsfunktionen eingebaut , einmal get_continuation_function welches die TensorFlow Operatoren herstellt und dann pricing_function
Mein npv Operator ist die Summe der optimalen Ausübungen.
Und die Preisbestimmung erfolgt mit der Funktion American_tf.
Ich führe die Funktion aus, um die Pfade zu erstellen, die exercise Values für den Trainingspfad. Dann durchlaufe ich rückwärts durch die training_functions und lerne den Wert und die Entscheidung an jedem Übungstag.
M sind die Zeitschritte
Soweit so gut , leider ist jetzt meine Fehlermeldung nicht nachvollziehbar für mich
InvalidArgumentError: In[0] is not a matrix
[[Node: MatMul_611 = MatMul[T=DT_FLOAT, transpose_a=false, transpose_b=false, _device="/job:localhost/replica:0/task:0/device:CPU:0"](Relu_241, w_65/read)]]
During handling of the above exception, another exception occurred:
InvalidArgumentError Traceback (most recent call last)
<ipython-input-636-2c998f9d6460> in <module>()
----> 1 american_tf(100.,90.,[1.]*calldates,0.25,0.05,N,N_pricing)
<ipython-input-634-01d7fd98f307> in american_tf(S_0, strike, M, impliedvol, riskfree_r, random_train, random_pricing)
26 exercise_values[:,i+1:i+2] = np.maximum(exercise_values[:,i+1:i+2],cont_value)
27
---> 28 npv = sess.run(npv, {S:S_0,K:strike,dts:M,r:riskfree_r,sigma:impliedvol,dW:N_pricing})