Python不同的正则/解析函数

Question

为了执行衍生，我开发了以下代码：

import matplotlib.pyplot as plt
import numpy as np
from math import *

xi = jnp.linspace(-3,3)

def f(x):
  a = x**3+5
  return a


g1i = jax.vmap(jax.grad(f))(xi)
g2i = jax.vmap(jax.grad(jax.grad(f)))(xi)
g3i = jax.vmap(jax.grad(jax.grad(jax.grad(f))))(xi)
plt.plot(xi,yi,  label = "f")
plt.plot(xi,g1i, label = "f'")
plt.plot(xi,g2i, label = "f''")
plt.plot(xi,g3i, label = "f'''")
plt.legend()

此代码有效，但现在我感兴趣的是应用以下代码计算买入价相对于标的资产（即delta）的一阶导数，尝试使用以下代码，但不起作用：

import scipy.stats as si
import sympy as sy
import sys
xi = jnp.linspace(1,1.5)
def analytical_call(s0):
    T=1.
    q=0.
    r=0.
    k=1.
    sigma=0.4
    Kt = k*exp((q-r)*T)
    d = (log(Kt/s0)+(sigma**2)/2*T)/sigma
    result = (Kt * si.norm.cdf((d / sqrt(T)), 0.0, 1.0)  - s0 * si.norm.cdf(((d - sigma * T) / sqrt(T)), 0.0, 1.0)  ) * exp(-q * T) + exp(-q * T) * (s0 - Kt)
    return result
print(analytical_call(1))

g1i = jax.vmap(jax.grad(analytical_call))(xi)
g2i = jax.vmap(jax.grad(jax.grad(analytical_call)))(xi)
plt.plot(xi,yi,  label = "f")
plt.plot(xi,g1i, label = "f'")
plt.legend()

你有什么提示吗？提前谢谢

Answer 1

正如在注释中已经提到的，您不能在jax库之外使用像scipy.stats.norm.cdf这样的方法。改用^{}。类似地，用jax等价物jnp.exp和jnp.sqrt替换exp和sqrt：

from jax import jit, grad, vmap
import jax.numpy as jnp
from jax.scipy.stats.norm import cdf

def analytical_call(s0):
    T, q, r, k, sigma = 1.0, 0.0, 0.0, 1.0, 0.4
    Kt = k*jnp.exp((q-r)*T)
    d = (jnp.log(Kt/s0)+(sigma**2)/2*T)/sigma
    result = (Kt * cdf((d / jnp.sqrt(T)), 0.0, 1.0)  - s0 * cdf(((d - sigma * T) / jnp.sqrt(T)), 0.0, 1.0)  ) * jnp.exp(-q * T) + jnp.exp(-q * T) * (s0 - Kt)
    return result

g = vmap(grad(analytical_call))
h = vmap(grad(grad(analytical_call)))
xi = jnp.linspace(1,1.5)

然后，您可以计算g(xi)和h(xi)