4.2

Python

(added on 2015-04-11.)

code

# 4.2.py
# 17:49 2015-04-11
#
# s, current spot rate curve
# s2, next year's spot rate curve

def sd(i): # next year's spot rate curve
  j = i + 1
  return ((1 + s[j])**j / (1 + s[1]))**(1 / (j - 1)) - 1

print("current spot rate curve")
s = [0, 5.0, 5.3, 5.6, 5.8, 6.0, 6.1]
print("s=", [s[i] for i in range(1, len(s))])

s = list(map(lambda x: x / 100, s))

print("calculating without function")
fmt = "{:10.3f}"
print(fmt.format(((1 + s[2])**2 / (1 + s[1]))**(1 / (2-1)) - 1))
print(fmt.format(((1 + s[3])**3 / (1 + s[1]))**(1 / (3-1)) - 1))
print(fmt.format(((1 + s[4])**4 / (1 + s[1]))**(1 / (4-1)) - 1))
print(fmt.format(((1 + s[5])**5 / (1 + s[1]))**(1 / (5-1)) - 1))
print(fmt.format(((1 + s[6])**6 / (1 + s[1]))**(1 / (6-1)) - 1))

s2 = [0]
for i in range(1, len(s) - 1):
  s2.append(round(sd(i), 3))

print("calculating with function")
for i in range(1, len(s) - 1):
  print(fmt.format(s2[i]))

print("next year's spot rate curve")
print("s'=", [round(s2[i] * 100, 1) for i in range(1, len(s) - 1)])
# eof

output

current spot rate curve
s= [5.0, 5.3, 5.6, 5.8, 6.0, 6.1]
calculating without function
     0.056
     0.059
     0.061
     0.063
     0.063
calculating with function
     0.056
     0.059
     0.061
     0.063
     0.063
next year's spot rate curve
s'= [5.6, 5.9, 6.1, 6.3, 6.3]

JavaScript

コードを次のリンクに示す。node.jsで動作確認済。

4.2.js

Gauche

コードを次のリンクに示す。

4.2.scm

Fortran

コードを次のリンクに示す。

4.2.f90

appendix

以下の計算は、間違っています。(2015-04-11)

p.103の式(4.1)を用いてs'_j-1を求める。

s'₁ = [(1 + s₂)² / (1 + s₁)]^1/1 - 1 = 0.047 = 4.7%
s'₂ = [(1 + s₃)³ / (1 + s₁)]^1/2 - 1 = 0.059 = 5.9%
s'₃ = [(1 + s₄)⁴ / (1 + s₁)]^1/3 - 1 = 0.061 = 6.1%
s'₄ = [(1 + s₅)⁵ / (1 + s₁)]^1/4 - 1 = 0.063 = 6.3%
s'₅ = [(1 + s₆)⁶ / (1 + s₁)]^1/5 - 1 = 0.063 = 6.3%
∴s'=(4.7, 5.9, 6.1, 6.3, 6.3)

history

2004-05-23 create, 2015-04-11 revise, add Python code.
2021-02-17 change XHTML to html5, change shift-jis to utf-8, add viewport.
2024-10-26 add a JavaScript code, a Gauche code and a Fortran code.