╨д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╨╡ ╨║╨╛╨╜╤В╤А╨░╨║╤В╤Л

╨з╤В╨╛ ╤В╨░╨║╨╛╨╡ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╨╡ ╨║╨╛╨╜╤В╤А╨░╨║╤В╤Л?

╨д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╨╣ ╨║╨╛╨╜╤В╤А╨░╨║╤В тАФ ╤Н╤В╨╛ ╨╕╨╜╨┤╨╕╨▓╨╕╨┤╤Г╨░╨╗╤М╨╜╤Л╨╣ ╨║╨╛╨╜╤В╤А╨░╨║╤В ╨╝╨╡╨╢╨┤╤Г ╨┤╨▓╤Г╨╝╤П ╤Б╤В╨╛╤А╨╛╨╜╨░╨╝╨╕ ╨╜╨░ ╨┐╨╛╨║╤Г╨┐╨║╤Г ╨╕╨╗╨╕ ╨┐╤А╨╛╨┤╨░╨╢╤Г ╨▒╨░╨╖╨╛╨▓╨╛╨│╨╛ ╨░╨║╤В╨╕╨▓╨░ ╨▓╨╛╨▓╤А╨╡╨╝╤П ╨╕ ╨┐╨╛ ╤Б╨╛╨│╨╗╨░╤Б╨╛╨▓╨░╨╜╨╜╨╛╨╣ ╤Б╨╡╨│╨╛╨┤╨╜╤П ╤Ж╨╡╨╜╨╡ (╨╕╨╖╨▓╨╡╤Б╤В╨╜╨╛╨╣ ╨║╨░╨║ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░).

╨Ю╨│╨╗╨░╨▓╨╗╨╡╨╜╨╕╨╡

• ╨з╤В╨╛ ╤В╨░╨║╨╛╨╡ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╨╡ ╨║╨╛╨╜╤В╤А╨░╨║╤В╤Л?
  • ╨б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░
  • ╨а╨░╤Б╤З╨╡╤В ╨┐╨╛ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨╝╤Г ╨║╨╛╨╜╤В╤А╨░╨║╤В╤Г
  • ╨Ъ╨░╨║ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╤В╤М ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╨╡ ╤Ж╨╡╨╜╤Л ╨▓ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨╡?
    • ╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ тДЦ1
    • ╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ тДЦ 2 (╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░ ╤Б ╤Г╤З╨╡╤В╨╛╨╝ ╤В╨╡╨║╤Г╤Й╨╕╤Е ╤А╨░╤Б╤Е╨╛╨┤╨╛╨▓)
    • ╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ тДЦ 3 (╤Н╤Д╤Д╨╡╨║╤В ╨╕╨╖╨▓╨╡╤Б╤В╨╜╨╛╨│╨╛ ╨┤╨╕╨▓╨╕╨┤╨╡╨╜╨┤╨░)
  • ╨Я╤А╨╡╨╕╨╝╤Г╤Й╨╡╤Б╤В╨▓╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╤Е ╨║╨╛╨╜╤В╤А╨░╨║╤В╨╛╨▓
  • ╨Э╨╡╨┤╨╛╤Б╤В╨░╤В╨║╨╕ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╤Е ╨║╨╛╨╜╤В╤А╨░╨║╤В╨╛╨▓
  • ╨Ю╨│╤А╨░╨╜╨╕╤З╨╡╨╜╨╕╤П
  • ╨Ч╨░╨║╨╗╤О╤З╨╡╨╜╨╕╨╡
  • ╨а╨╡╨║╨╛╨╝╨╡╨╜╨┤╤Г╨╡╨╝╤Л╨╡ ╤Б╤В╨░╤В╤М╨╕

• ╨Я╨╛╨║╤Г╨┐╨░╤В╨╡╨╗╤М ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ ╨╜╨░╨╖╤Л╨▓╨░╨╡╤В╤Б╤П ╨┤╨╗╨╕╨╜╨╜╤Л╨╝. ╨Я╨╛╨║╤Г╨┐╨░╤В╨╡╨╗╤М ╨┤╨╡╨╗╨░╨╡╤В ╤Б╤В╨░╨▓╨║╤Г ╨╜╨░ ╤В╨╛, ╤З╤В╨╛ ╤Ж╨╡╨╜╨░ ╨▓╤Л╤А╨░╤Б╤В╨╡╤В.
• ╨Я╤А╨╛╨┤╨░╨▓╨╡╤Ж ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ ╨╜╨░╨╖╤Л╨▓╨░╨╡╤В╤Б╤П ╨║╨╛╤А╨╛╤В╨║╨╕╨╝. ╨Я╤А╨╛╨┤╨░╨▓╨╡╤Ж ╨┤╨╡╨╗╨░╨╡╤В ╤Б╤В╨░╨▓╨║╤Г ╨╜╨░ ╤В╨╛, ╤З╤В╨╛ ╤Ж╨╡╨╜╨░ ╤Г╨┐╨░╨┤╨╡╤В.
• ╨Я╤А╨╕ ╤Н╤В╨╛╨╝ ╨╜╨╕╨║╨░╨║╨╕╨╡ ╨┤╨╡╨╜╤М╨│╨╕ ╨╜╨╡ ╨┐╨╡╤А╨╡╤Е╨╛╨┤╤П╤В ╨╕╨╖ ╤А╤Г╨║ ╨▓ ╤А╤Г╨║╨╕ ╨┤╨╛ ╨┤╨░╤В╤Л ╤А╨░╤Б╤З╨╡╤В╨╛╨▓╨Ф╨░╤В╨░ ╤А╨░╤Б╤З╨╡╤В╨╛╨▓╨Ф╨░╤В╨░ ╤А╨░╤Б╤З╨╡╤В╨╛╨▓ тАФ ╤Н╤В╨╛ ╨┤╨░╤В╨░, ╨║╨╛╨│╨┤╨░ ╨┤╨╡╨╜╨╡╨╢╨╜╤Л╨╡ ╤Б╤А╨╡╨┤╤Б╤В╨▓╨░ ╨╕ ╨░╨║╤В╨╕╨▓╤Л, ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨▒╤Л╨╗╨╕ ╨╛╨▒╨╝╨╡╨╜╨╡╨╜╤Л ╨╕╨╗╨╕ ╨┐╤А╨╛╨┤╨░╨╜╤Л, ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╤О╤В╤Б╤П ╨┐╤Г╤В╨╡╨╝ ╨╖╨░╤З╨╡╤В╨░ ╨┐╤А╨╛╤Ж╨╡╤Б╤Б╨░, ╨║╨╛╤В╨╛╤А╤Л╨╣ ╨┐╤А╨╛╨╕╨╖╨╛╤И╨╡╨╗ ╨╜╨╡╤Б╨║╨╛╨╗╤М╨║╨╛ ╨┤╨╜╨╡╨╣ ╨╜╨░╨╖╨░╨┤. ╨Ю╨▒╤Л╤З╨╜╨╛ ╨┤╨╗╤П ╨░╨║╤Ж╨╕╨╣ ╤Н╤В╨╛ ╨┤╨▓╨░ ╤А╨░╨▒╨╛╤З╨╕╤Е ╨┤╨╜╤П ╨┐╨╛╤Б╨╗╨╡ ╤Б╨┤╨╡╨╗╨║╨╕.╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡. ╨г╤Б╤В╨░╨╜╨░╨▓╨╗╨╕╨▓╨░╨╡╤В╤Б╤П ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░, ╨┐╨╛╤Н╤В╨╛╨╝╤Г ╨╜╨╕ ╨╛╨┤╨╜╨░ ╨╕╨╖ ╤Б╤В╨╛╤А╨╛╨╜ ╨╜╨╡ ╨┤╨╛╨╗╨╢╨╜╨░ ╨┐╨╗╨░╤В╨╕╤В╤М ╨┤╨╡╨╜╤М╨│╨╕ ╨┐╤А╨╕ ╨╖╨░╨║╨╗╤О╤З╨╡╨╜╨╕╨╕ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░.
• ╨Ю╨╜╨╕ ╨┐╨╛╨┤╨▓╨╡╤А╨╢╨╡╨╜╤Л ╤А╨╕╤Б╨║╤Г ╨┤╨╡╤Д╨╛╨╗╤В╨░ ╨╜╨╡╨╖╨░╨▓╨╕╤Б╨╕╨╝╨╛ ╨╛╤В ╨╕╤Е ╨╝╨╡╤В╨╛╨┤╨╛╨▓ ╤А╨░╤Б╤З╨╡╤В╨╛╨▓. ╨в╨╛╨╗╤М╨║╨╛ ╤Б╤В╨╛╤А╨╛╨╜╨░, ╨▓╨╗╨░╨┤╨╡╤О╤Й╨░╤П ╨▒╨╛╨╗╤М╤И╨╡╨╣ ╤Б╤Г╨╝╨╝╨╛╨╣, ╨╝╨╛╨╢╨╡╤В ╨╜╨╡ ╨▓╤Л╨┐╨╛╨╗╨╜╨╕╤В╤М ╤Б╨▓╨╛╨╕ ╨╛╨▒╤П╨╖╨░╤В╨╡╨╗╤М╤Б╤В╨▓╨░ ╨║╨░╨║ ╨┐╨╛ ╨┐╨╛╤Б╤В╨░╨▓╨╛╤З╨╜╤Л╨╝, ╤В╨░╨║ ╨╕ ╨┐╨╛ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╨╝ ╤Ж╨╡╨╜╨░╨╝ ╤Б ╤А╨░╤Б╤З╨╡╤В╨░╨╝╨╕ ╨╜╨░╨╗╨╕╤З╨╜╤Л╨╝╨╕.

╨б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╤Н╨║╤Б╨┐╨╡╨┤╨╕╤В╨╛╤А╤Б╨║╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░

╨Т ╨╝╨╛╨╝╨╡╨╜╤В ╨▓╤А╨╡╨╝╨╡╨╜╨╕ t = 0 ╨╗╨╛╨╜╨│ ╨╕ ╤И╨╛╤А╤В ╤Б╨╛╨│╨╗╨░╤И╨░╤О╤В╤Б╤П, ╤З╤В╨╛ ╤И╨╛╤А╤В ╨┐╨╛╤Б╤В╨░╨▓╨╕╤В ╨░╨║╤В╨╕╨▓ ╨╗╨╛╨╜╨│╤Г ╨▓ ╨╝╨╛╨╝╨╡╨╜╤В ╨▓╤А╨╡╨╝╨╡╨╜╨╕ T ╨┐╨╛ ╤Ж╨╡╨╜╨╡ F0 (T).

F0 (T) тАФ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░. ╨Х╤Б╨╗╨╕ ╨▒╨░╨╖╨╛╨▓╨░╤П ╤Ж╨╡╨╜╨░ ╤А╨░╨▓╨╜╨░ ST ╨▓ ╨╝╨╛╨╝╨╡╨╜╤В ╨▓╤А╨╡╨╝╨╡╨╜╨╕ T, ╨╗╨╛╨╜╨│ ╨╛╨▒╤П╨╖╨░╨╜ ╨╖╨░╨┐╨╗╨░╤В╨╕╤В╤М F0 (T) ╤И╨╛╤А╤В╤Г.

╨б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ ╨╜╨░ ╨╗╨╛╨╜╨│ ╨┐╨╛ ╤Н╨║╤Б╨┐╨╕╤А╨░╤Ж╨╕╨╕ = ST тАУ F0(T).

╨б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ ╨╜╨░ ╤И╨╛╤А╤В ╨╜╨░ ╨╝╨╛╨╝╨╡╨╜╤В ╤Н╨║╤Б╨┐╨╕╤А╨░╤Ж╨╕╨╕ = F0(T) тАУ ST.

╨а╨░╤Б╤З╨╡╤В ╨┐╨╛ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨╝╤Г ╨║╨╛╨╜╤В╤А╨░╨║╤В╤Г

╨Ъ╨╛╨│╨┤╨░ ╤Б╤А╨╛╨║ ╨┤╨╡╨╣╤Б╤В╨▓╨╕╤П ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ ╨╕╤Б╤В╨╡╨║╨░╨╡╤В, ╨╡╨│╨╛ ╨╝╨╛╨╢╨╜╨╛ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╤В╤М ╨┤╨▓╤Г╨╝╤П ╤Б╨┐╨╛╤Б╨╛╨▒╨░╨╝╨╕:

#1 тАУ ╨д╨╕╨╖╨╕╤З╨╡╤Б╨║╨░╤П ╨┤╨╛╤Б╤В╨░╨▓╨║╨░: ╨Я╤А╨╕ ╤А╨░╤Б╤З╨╡╤В╨╡ ╤Б ╤Д╨╕╨╖╨╕╤З╨╡╤Б╨║╨╛╨╣ ╨┐╨╛╤Б╤В╨░╨▓╨║╨╛╨╣ ╨╗╨╛╨╜╨│ ╨┐╨╗╨░╤В╨╕╤В ╤Б╨╛╨│╨╗╨░╤Б╨╛╨▓╨░╨╜╨╜╤Г╤О ╤Ж╨╡╨╜╤Г ╤И╨╛╤А╤В╤Г ╨╕ ╨┐╨╛╨╗╤Г╤З╨░╨╡╤В ╨▒╨░╨╖╨╛╨▓╤Л╨╣ ╨░╨║╤В╨╕╨▓ ╨╛╤В ╤И╨╛╤А╤В╨░.

#2 тАУ ╨а╨░╤Б╤З╨╡╤В ╨╜╨░╨╗╨╕╤З╨╜╤Л╨╝╨╕: ╤А╨░╤Б╤З╨╡╤В ╨╜╨░╨╗╨╕╤З╨╜╤Л╨╝╨╕: ╤А╨░╤Б╤З╨╡╤В ╨╜╨░╨╗╨╕╤З╨╜╤Л╨╝╨╕ тАУ ╤Н╤В╨╛ ╨▓╨░╤А╨╕╨░╨╜╤В ╤А╨░╤Б╤З╨╡╤В╨╛╨▓, ╤З╨░╤Б╤В╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╤Л╨╣ ╨▓ ╤В╨╛╤А╨│╨╛╨▓╤Л╤Е ╤Д╤М╤О╤З╨╡╤А╤Б╨╜╤Л╤Е ╨╕ ╨╛╨┐╤Ж╨╕╨╛╨╜╨╜╤Л╤Е ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░╤Е, ╨║╨╛╨│╨┤╨░ ╨▒╨░╨╖╨╛╨▓╤Л╨╡ ╨░╨║╤В╨╕╨▓╤Л ╤Д╨╕╨╖╨╕╤З╨╡╤Б╨║╨╕ ╨╜╨╡ ╨┐╨╛╤Б╤В╨░╨▓╨╗╤П╤О╤В╤Б╤П ╨▓ ╨┤╨░╤В╤Г ╨╕╤Б╤В╨╡╤З╨╡╨╜╨╕╤П ╤Б╤А╨╛╨║╨░ ╨┤╨╡╨╣╤Б╤В╨▓╨╕╤П. ╨Я╤А╨╕ ╤Н╤В╨╛╨╝ ╨╗╤О╨▒╨╛╨╣ ╨╕╨╖ ╤Б╤В╨╛╤А╨╛╨╜ ╨╛╨┐╨╗╨░╤З╨╕╨▓╨░╨╡╤В╤Б╤П ╤В╨╛╨╗╤М╨║╨╛ ╤А╨░╨╖╨╜╨╕╤Ж╨░ ╨▓ ╨╖╨░╨▓╨╕╤Б╨╕╨╝╨╛╤Б╤В╨╕ ╨╛╤В ╤А╤Л╨╜╨╛╤З╨╜╨╛╨│╨╛ ╨║╤Г╤А╤Б╨░.╤З╨╕╤В╨░╤В╤М ╨┤╨░╨╗╤М╤И╨╡ ╨Я╤А╨╕ ╨╜╨░╨╗╨╕╤З╨╜╨╛╨╝ ╤А╨░╤Б╤З╨╡╤В╨╡ ╨┐╨╛╨║╤Г╨┐╨░╤В╨╡╨╗╤М (╨┐╤А╨╛╨┤╨░╨▓╨╡╤Ж) ╨┐╨╛╨╗╤Г╤З╨░╨╡╤В ╤А╨░╨╖╨╜╨╕╤Ж╤Г ╨╝╨╡╨╢╨┤╤Г ╤А╤Л╨╜╨╛╤З╨╜╨╛╨╣ ╤Ж╨╡╨╜╨╛╨╣ ╨╕ ╨┤╨╛╨│╨╛╨▓╨╛╤А╨╜╨╛╨╣ ╤Ж╨╡╨╜╨╛╨╣, ╨╡╤Б╨╗╨╕ ╤А╤Л╨╜╨╛╤З╨╜╨░╤П ╤Ж╨╡╨╜╨░ ╨▓╤Л╤И╨╡ (╨╜╨╕╨╢╨╡) ╨┤╨╛╨│╨╛╨▓╨╛╤А╨╜╨╛╨╣ ╤Ж╨╡╨╜╤Л ╨╜╨░ ╨┤╨░╤В╤Г ╤А╨░╤Б╤З╨╡╤В╨░.

• ╨Ъ╨╛╨╜╤В╤А╨░╨║╤В╤Л ╤Б ╤А╨░╤Б╤З╨╡╤В╨╛╨╝ ╨╜╨░╨╗╨╕╤З╨╜╤Л╨╝╨╕ ╤З╨░╤Й╨╡ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╤О╤В╤Б╤П, ╨║╨╛╨│╨┤╨░ ╨┐╨╛╤Б╤В╨░╨▓╨║╨░ ╨╜╨╡╤Ж╨╡╨╗╨╡╤Б╨╛╨╛╨▒╤А╨░╨╖╨╜╨░, ╨╜╨░╨┐╤А╨╕╨╝╨╡╤А, ╨▓ ╤Н╨║╤Б╨┐╨╡╨┤╨╕╤Ж╨╕╨╛╨╜╨╜╤Л╤Е ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░╤Е ╨╜╨░ ╤Д╨╛╨╜╨┤╨╛╨▓╤Л╨╣ ╨╕╨╜╨┤╨╡╨║╤Б. /╤Ж╨╡╨╜╨╜╤Л╨╡ ╨▒╤Г╨╝╨░╨│╨╕ ╨╜╨░ ╤А╤Л╨╜╨║╨╡ ╨╕ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╨┤╨╛╤Е╨╛╨┤╨╜╨╛╤Б╤В╨╕ ╨░╨║╤Ж╨╕╨╣ ╤Б╨▓╨╛╨╕╤Е ╨╕╨╜╨▓╨╡╤Б╤В╨╕╤Ж╨╕╨╣. ╨Ш╨╜╨▓╨╡╤Б╤В╨╛╤А╤Л ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╤О╤В ╨╡╨│╨╛ ╨┤╨╗╤П ╨┐╨╛╨╗╤Г╤З╨╡╨╜╨╕╤П ╨╕╨╜╤Д╨╛╤А╨╝╨░╤Ж╨╕╨╕ ╨╛╨▒ ╤Н╤Д╤Д╨╡╨║╤В╨╕╨▓╨╜╨╛╤Б╤В╨╕ ╨╕╨╜╨▓╨╡╤Б╤В╨╕╤Ж╨╕╨╣ ╨╕ ╨┤╨╛╤Б╤В╤Г╨┐╨░ ╨║ ╨╛╨▒╤Й╨╡╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕, ╨║╨╛╤В╨╛╤А╨╛╨╣ ╨╛╨╜╨╕ ╨╛╨▒╨╗╨░╨┤╨░╤О╤В. ╤Б╨╛╨┤╨╡╤А╨╢╨╕╤В ╨║╨░╨╢╨┤╤Г╤О ╨╕╨╖ ╨░╨║╤Ж╨╕╨╣ ╨▓ ╤Д╨╛╨╜╨┤╨╛╨▓╨╛╨╝ ╨╕╨╜╨┤╨╡╨║╤Б╨╡, ╨┐╤А╨╛╨┐╨╛╤А╤Ж╨╕╨╛╨╜╨░╨╗╤М╨╜╤Г╤О ╨╡╨╡ ╨▓╨╡╤Б╤Г ╨▓ ╨╕╨╜╨┤╨╡╨║╤Б╨╡.
• ╨д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░ ╤Б ╤А╨░╤Б╤З╨╡╤В╨╛╨╝ ╨╜╨░╨╗╨╕╤З╨╜╤Л╨╝╨╕ ╤В╨░╨║╨╢╨╡ ╨╕╨╖╨▓╨╡╤Б╤В╨╜╨░ ╨║╨░╨║ ╨▒╨╡╤Б╨┐╨╛╤Б╤В╨░╨▓╨╛╤З╨╜╤Л╨╣ ╤Д╨╛╤А╨▓╨░╤А╨┤, ╤В.╨╡. NDF.

╨Ъ╨░╨║ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╤В╤М ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╨╡ ╤Ж╨╡╨╜╤Л ╨▓ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨╡?

╨Ь╨╛╨┤╨╡╨╗╤М ╤Ж╨╡╨╜╨╛╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╤П, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╨░╤П ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╤Е ╤Ж╨╡╨╜, ╨╕╤Б╤Е╨╛╨┤╨╕╤В ╨╕╨╖ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╨┤╨╛╨┐╤Г╤Й╨╡╨╜╨╕╨╣:

• ╨Э╨╕╨║╨░╨║╨╕╤Е ╤В╤А╨░╨╜╨╖╨░╨║╤Ж╨╕╨╛╨╜╨╜╤Л╤Е ╨╕╨╖╨┤╨╡╤А╨╢╨╡╨║ ╨╕╨╗╨╕ ╨╛╨│╤А╨░╨╜╨╕╤З╨╡╨╜╨╕╨╣ ╨╜╨░ ╨║╨╛╤А╨╛╤В╨║╨╕╨╡ ╨┐╤А╨╛╨┤╨░╨╢╨╕.
• ╨Ю╨┤╨╕╨╜╨░╨║╨╛╨▓╤Л╨╡ ╤Б╤В╨░╨▓╨║╨╕ ╨╜╨░╨╗╨╛╨│╨░ ╨╜╨░ ╨▓╤Б╤О ╤З╨╕╤Б╤В╤Г╤О ╨┐╤А╨╕╨▒╤Л╨╗╤М.
• ╨Ч╨░╨╕╨╝╤Б╤В╨▓╨╛╨▓╨░╨╜╨╕╨╡ ╨╕ ╨║╤А╨╡╨┤╨╕╤В╨╛╨▓╨░╨╜╨╕╨╡ ╨┐╨╛ ╨▒╨╡╨╖╤А╨╕╤Б╨║╨╛╨▓╨╛╨╣ ╤Б╤В╨░╨▓╨║╨╡╨С╨╡╨╖╤А╨╕╤Б╨║╨╛╨▓╨░╤П ╤Б╤В╨░╨▓╨║╨░╨С╨╡╨╖╤А╨╕╤Б╨║╨╛╨▓╨░╤П ╤Б╤В╨░╨▓╨║╨░ тАФ ╤Н╤В╨╛ ╨╝╨╕╨╜╨╕╨╝╨░╨╗╤М╨╜╨░╤П ╨╜╨╛╤А╨╝╨░ ╨┐╤А╨╕╨▒╤Л╨╗╨╕, ╨╛╨╢╨╕╨┤╨░╨╡╨╝╨░╤П ╨╕╨╜╨▓╨╡╤Б╤В╨╛╤А╨╛╨╝ ╨╛╤В ╨╕╨╜╨▓╨╡╤Б╤В╨╕╤Ж╨╕╨╣ ╤Б ╨╜╤Г╨╗╨╡╨▓╤Л╨╝ ╤А╨╕╤Б╨║╨╛╨╝. ╨н╤В╨╛ ╨│╨╛╤Б╤Г╨┤╨░╤А╤Б╤В╨▓╨╡╨╜╨╜╤Л╨╡ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╤А╨░╨╖╨▓╨╕╤В╤Л╤Е ╤Б╤В╤А╨░╨╜, ╨╗╨╕╨▒╨╛ ╨║╨░╨╖╨╜╨░╤З╨╡╨╣╤Б╨║╨╕╨╡ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨б╨и╨Р, ╨╗╨╕╨▒╨╛ ╨│╨╛╤Б╤Г╨┤╨░╤А╤Б╤В╨▓╨╡╨╜╨╜╤Л╨╡ ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕ ╨У╨╡╤А╨╝╨░╨╜╨╕╨╕. ╨е╨╛╤В╤П ╨╡╨│╨╛ ╨╜╨╡ ╤Б╤Г╤Й╨╡╤Б╤В╨▓╤Г╨╡╤В, ╨┐╨╛╤В╨╛╨╝╤Г ╤З╤В╨╛ ╨║╨░╨╢╨┤╨░╤П ╨╕╨╜╨▓╨╡╤Б╤В╨╕╤Ж╨╕╤П ╨╕╨╝╨╡╨╡╤В ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╜╤Г╤О ╨┤╨╛╨╗╤О ╤А╨╕╤Б╨║╨░. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡.
• ╨Р╤А╨▒╨╕╤В╤А╨░╨╢╨╜╤Л╨╡ ╨▓╨╛╨╖╨╝╨╛╨╢╨╜╨╛╤Б╤В╨╕ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╤О╤В╤Б╤П ╨┐╨╛ ╨╝╨╡╤А╨╡ ╨╕╤Е ╨▓╨╛╨╖╨╜╨╕╨║╨╜╨╛╨▓╨╡╨╜╨╕╤П.

╨Ф╨╗╤П ╤А╨░╨╖╤А╨░╨▒╨╛╤В╨║╨╕ ╨╝╨╛╨┤╨╡╨╗╨╕ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╤Ж╨╡╨╜╨╛╨╛╨▒╤А╨░╨╖╨╛╨▓╨░╨╜╨╕╤П ╨╝╤Л ╨▒╤Г╨┤╨╡╨╝ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╤В╤М ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╡ ╨╛╨▒╨╛╨╖╨╜╨░╤З╨╡╨╜╨╕╤П:

• T = ╨▓╤А╨╡╨╝╤П ╨┤╨╛ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П (╨▓ ╨│╨╛╨┤╨░╤Е) ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░.
• S0 = ╤Ж╨╡╨╜╨░ ╨▒╨░╨╖╨╛╨▓╨╛╨│╨╛ ╨░╨║╤В╨╕╨▓╨░ ╤Б╨╡╨│╨╛╨┤╨╜╤П (t = 0).
• F0 = ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░ ╤Б╨╡╨│╨╛╨┤╨╜╤П.
• r = ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨╛╨╡ ╨╜╨░╤З╨╕╤Б╨╗╨╡╨╜╨╕╨╡. ╨Э╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨╛╨╡ ╨╜╨░╤З╨╕╤Б╨╗╨╡╨╜╨╕╨╡. ╨д╨╛╤А╨╝╤Г╨╗╨░ ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨╛╨│╨╛ ╨╜╨░╤З╨╕╤Б╨╗╨╡╨╜╨╕╤П ╨╛╤В╤А╨░╨╢╨░╨╡╤В ╨┐╤А╨╛╤Ж╨╡╨╜╤В╤Л, ╨┐╨╛╨╗╤Г╤З╨░╨╡╨╝╤Л╨╡ ╨┐╤А╨╕ ╨┐╨╛╤Б╤В╨╛╤П╨╜╨╜╨╛╨╝ ╨╜╨░╤З╨╕╤Б╨╗╨╡╨╜╨╕╨╕ ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╛╨▓ ╨▓ ╤В╨╡╤З╨╡╨╜╨╕╨╡ ╨▒╨╡╤Б╨║╨╛╨╜╨╡╤З╨╜╨╛╨│╨╛ ╤З╨╕╤Б╨╗╨░ ╨┐╨╡╤А╨╕╨╛╨┤╨╛╨▓. ╨з╨╡╤В╤Л╤А╨╡ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╤Л╤Е, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╤Л╤Е ╨┤╨╗╤П ╨╡╨│╨╛ ╤А╨░╤Б╤З╨╡╤В╨░, — ╤Н╤В╨╛ ╨╛╤Б╨╜╨╛╨▓╨╜╨░╤П ╤Б╤Г╨╝╨╝╨░, ╨▓╤А╨╡╨╝╤П, ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╨░╤П ╤Б╤В╨░╨▓╨║╨░ ╨╕ ╨╜╨╛╨╝╨╡╤А ╨┐╨╡╤А╨╕╨╛╨┤╨░ ╨╜╨░╤З╨╕╤Б╨╗╨╡╨╜╨╕╤П ╤Б╨╗╨╛╨╢╨╜╤Л╤Е ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╛╨▓. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡ ╨▒╨╡╨╖╤А╨╕╤Б╨║╨╛╨▓╨░╤П ╨│╨╛╨┤╨╛╨▓╨░╤П ╤Б╤В╨░╨▓╨║╨░.

╨д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░ ╨╝╨╛╨╢╨╡╤В ╨▒╤Л╤В╤М ╨╖╨░╨┐╨╕╤Б╨░╨╜╨░ ╨║╨░╨║:

╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ тДЦ1

F0 = S0exp(rT)

╨Я╤А╨░╨▓╨░╤П ╤З╨░╤Б╤В╤М ╤Г╤А╨░╨▓╨╜╨╡╨╜╨╕╤П 1 ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨╖╨░╨╕╨╝╤Б╤В╨▓╨╛╨▓╨░╨╜╨╕╤П ╤Б╤А╨╡╨┤╤Б╤В╨▓ ╨┤╨╗╤П ╨▒╨░╨╖╨╛╨▓╨╛╨│╨╛ ╨░╨║╤В╨╕╨▓╨░. ╨С╨░╨╖╨╛╨▓╤Л╨╣ ╨░╨║╤В╨╕╨▓╨С╨░╨╖╨╛╨▓╤Л╨╡ ╨░╨║╤В╨╕╨▓╤Л ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╤О╤В ╤Б╨╛╨▒╨╛╨╣ ╤Д╨░╨║╤В╨╕╤З╨╡╤Б╨║╨╕╨╡ ╤Д╨╕╨╜╨░╨╜╤Б╨╛╨▓╤Л╨╡ ╨░╨║╤В╨╕╨▓╤Л, ╨╜╨░ ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨╛╨┐╨╕╤А╨░╤О╤В╤Б╤П ╨┐╤А╨╛╨╕╨╖╨▓╨╛╨┤╨╜╤Л╨╡ ╤Д╨╕╨╜╨░╨╜╤Б╨╛╨▓╤Л╨╡ ╨╕╨╜╤Б╤В╤А╤Г╨╝╨╡╨╜╤В╤Л. ╨в╨░╨║╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝, ╨╗╤О╨▒╨╛╨╡ ╨╕╨╖╨╝╨╡╨╜╨╡╨╜╨╕╨╡ ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╨╕ ╨┤╨╡╤А╨╕╨▓╨░╤В╨╕╨▓╨░ ╨╛╤В╤А╨░╨╢╨░╨╡╤В ╨║╨╛╨╗╨╡╨▒╨░╨╜╨╕╤П ╤Ж╨╡╨╜╤Л ╨╡╨│╨╛ ╨▒╨░╨╖╨╛╨▓╨╛╨│╨╛ ╨░╨║╤В╨╕╨▓╨░. ╨в╨░╨║╨╕╨╡ ╨░╨║╤В╨╕╨▓╤Л ╨▓╨║╨╗╤О╤З╨░╤О╤В ╨▓ ╤Б╨╡╨▒╤П ╨░╨║╤Ж╨╕╨╕, ╤В╨╛╨▓╨░╤А╤Л, ╤А╤Л╨╜╨╛╤З╨╜╤Л╨╡ ╨╕╨╜╨┤╨╡╨║╤Б╤Л, ╨╛╨▒╨╗╨╕╨│╨░╤Ж╨╕╨╕, ╨▓╨░╨╗╤О╤В╤Л ╨╕ ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╜╤Л╨╡ ╤Б╤В╨░╨▓╨║╨╕, ╨░ ╤В╨░╨║╨╢╨╡ ╨┐╨╡╤А╨╡╨╜╨╛╤Б ╨╕╤Е ╨╜╨░ ╨▓╤А╨╡╨╝╤П T. ╨г╤А╨░╨▓╨╜╨╡╨╜╨╕╨╡ 1 ╤Г╤В╨▓╨╡╤А╨╢╨┤╨░╨╡╤В, ╤З╤В╨╛ ╤Н╤В╨╕ ╨╖╨░╤В╤А╨░╤В╤Л ╨┤╨╛╨╗╨╢╨╜╤Л ╤А╨░╨▓╨╜╤П╤В╤М╤Б╤П ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨╣ ╤Ж╨╡╨╜╨╡. ╨Х╤Б╨╗╨╕ F0> S0.exp(rT), ╨░╤А╨▒╨╕╤В╤А╨░╨╢╨╡╤А╤Л ╨┐╨╛╨╗╤Г╤З╨░╤В ╨┐╤А╨╕╨▒╤Л╨╗╤М, ╨┐╤А╨╛╨┤╨░╨▓ ╤Д╨╛╤А╨▓╨░╤А╨┤ ╨╕ ╨║╤Г╨┐╨╕╨▓ ╨░╨║╤В╨╕╨▓ ╨╜╨░ ╨╖╨░╨╡╨╝╨╜╤Л╨╡ ╤Б╤А╨╡╨┤╤Б╤В╨▓╨░. ╨Х╤Б╨╗╨╕ F0< S0.exp(rT), ╨░╤А╨▒╨╕╤В╤А╨░╨╢╨╡╤А╤Л ╨┐╨╛╨╗╤Г╤З╨░╤В ╨┐╤А╨╕╨▒╤Л╨╗╤М, ╨┐╤А╨╛╨┤╨░╨▓ ╨░╨║╤В╨╕╨▓, ╤Б╤Б╤Г╨┤╨╕╨▓ ╨▓╤Л╤А╤Г╤З╨║╤Г ╨╕ ╨║╤Г╨┐╨╕╨▓ ╤Д╨╛╤А╨▓╨░╤А╨┤. ╨б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, ╤А╨░╨▓╨╡╨╜╤Б╤В╨▓╨╛ ╨▓ ╤Д╨╛╤А╨╝╤Г╨╗╨╡ ╨┤╨╛╨╗╨╢╨╜╨╛ ╨▓╤Л╨┐╨╛╨╗╨╜╤П╤В╤М╤Б╤П. ╨Ю╨▒╤А╨░╤В╨╕╤В╨╡ ╨▓╨╜╨╕╨╝╨░╨╜╨╕╨╡, ╤З╤В╨╛ ╤Н╤В╨░ ╨╝╨╛╨┤╨╡╨╗╤М ╨┐╤А╨╡╨┤╨┐╨╛╨╗╨░╨│╨░╨╡╤В ╤Б╨╛╨▓╨╡╤А╤И╨╡╨╜╨╜╤Л╨╡ ╤А╤Л╨╜╨║╨╕.

╨Я╤А╨╕╨╝╨╡╤А:

╨Я╤А╨╡╨┤╨┐╨╛╨╗╨╛╨╢╨╕╨╝, ╤Г ╨╜╨░╤Б ╨╡╤Б╤В╤М ╨░╨║╤В╨╕╨▓, ╨║╨╛╤В╨╛╤А╤Л╨╣ ╨▓ ╨╜╨░╤Б╤В╨╛╤П╤Й╨╡╨╡ ╨▓╤А╨╡╨╝╤П ╤Б╤В╨╛╨╕╤В 1000 ╨┤╨╛╨╗╨╗╨░╤А╨╛╨▓. ╨а╨░╤Б╤Б╤З╨╕╤В╨░╨╣╤В╨╡ ╤Ж╨╡╨╜╤Г 6-╨╝╨╡╤Б╤П╤З╨╜╨╛╨│╨╛ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ ╨╜╨░ ╤Н╤В╨╛╤В ╨░╨║╤В╨╕╨▓. ╨в╨╡╨║╤Г╤Й╨░╤П ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨╛ ╨╜╨░╤З╨╕╤Б╨╗╤П╨╡╨╝╨░╤П ╤Б╤В╨░╨▓╨║╨░ ╤Б╨╛╤Б╤В╨░╨▓╨╗╤П╨╡╤В 4% ╨┤╨╗╤П ╨▓╤Б╨╡╤Е ╤Б╤А╨╛╨║╨╛╨▓ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╤П.

F0 = $1,000.exp(0,04*0,5) = $1020,20.

╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ тДЦ 2 (╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░ ╤Б ╤Г╤З╨╡╤В╨╛╨╝ ╤В╨╡╨║╤Г╤Й╨╕╤Е ╤А╨░╤Б╤Е╨╛╨┤╨╛╨▓)

╨Х╤Б╨╗╨╕ ╨▒╨░╨╖╨╛╨▓╤Л╨╣ ╨░╨║╤В╨╕╨▓ ╨▓╤Л╨┐╨╗╨░╤З╨╕╨▓╨░╨╡╤В ╨╕╨╖╨▓╨╡╤Б╤В╨╜╤Г╤О ╤Б╤Г╨╝╨╝╤Г ╨┤╨╡╨╜╨╡╨╢╨╜╤Л╤Е ╤Б╤А╨╡╨┤╤Б╤В╨▓ ╨▓ ╤В╨╡╤З╨╡╨╜╨╕╨╡ ╤Б╤А╨╛╨║╨░ ╨┤╨╡╨╣╤Б╤В╨▓╨╕╤П ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░, ╨▓ ╤Г╤А╨░╨▓╨╜╨╡╨╜╨╕╨╡ 1 ╨▓╨╜╨╛╤Б╨╕╤В╤Б╤П ╨┐╤А╨╛╤Б╤В╨░╤П ╨║╨╛╤А╤А╨╡╨║╤В╨╕╤А╨╛╨▓╨║╨░. ╨Я╨╛╤Б╨║╨╛╨╗╤М╨║╤Г ╨▓╨╗╨░╨┤╨╡╨╗╨╡╤Ж ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ ╨╜╨╡ ╨┐╨╛╨╗╤Г╤З╨░╨╡╤В ╨╜╨╕╨║╨░╨║╨╕╤Е ╨┤╨╡╨╜╨╡╨╢╨╜╤Л╤Е ╨┐╨╛╤В╨╛╨║╨╛╨▓ ╨╛╤В ╨▒╨░╨╖╨╛╨▓╨╛╨│╨╛ ╨░╨║╤В╨╕╨▓╨░ ╨▓ ╨┐╨╡╤А╨╕╨╛╨┤ ╨╝╨╡╨╢╨┤╤Г ╤Н╤В╨╕ ╨┤╨╡╨╜╨╡╨╢╨╜╤Л╨╡ ╨┐╨╛╤В╨╛╨║╨╕ ╨┤╨╛╨╗╨╢╨╜╤Л ╨▒╤Л╤В╤М ╨▓╤Л╤З╤В╨╡╨╜╤Л ╨╕╨╖ ╤Б╨┐╨╛╤В╨╛╨▓╨╛╨╣ ╤Ж╨╡╨╜╤Л ╨┐╤А╨╕ ╤А╨░╤Б╤З╨╡╤В╨╡ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨╣ ╤Ж╨╡╨╜╤Л. ╨д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░╨д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░ тАУ ╤Н╤В╨╛ ╤Б╨╛╨│╨╗╨░╤Б╨╛╨▓╨░╨╜╨╜╨░╤П ╨▒╤Г╨┤╤Г╤Й╨░╤П ╤Ж╨╡╨╜╨░, ╨┐╨╛ ╨║╨╛╤В╨╛╤А╨╛╨╣ ╨┐╨╛╤Б╤В╨░╨▓╤Й╨╕╨║ ╨┐╨╛╤Б╤В╨░╨▓╨╕╤В ╨▒╨░╨╖╨╛╨▓╤Л╨╣ ╤Д╨╕╨╜╨░╨╜╤Б╨╛╨▓╤Л╨╣ ╨░╨║╤В╨╕╨▓ ╨╕╨╗╨╕ ╤В╨╛╨▓╨░╤А ╨┐╨╛╨║╤Г╨┐╨░╤В╨╡╨╗╤О. ╨Ю╨╜ ╨┐╨╛╨╗╨╜╨╛╤Б╤В╤М╤О ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В╤Б╤П ╤Б╨┐╨╛╤В╨╛╨▓╨╛╨╣ ╤Ж╨╡╨╜╨╛╨╣ ╨▒╨░╨╖╨╛╨▓╨╛╨│╨╛ ╤Д╨╕╨╜╨░╨╜╤Б╨╛╨▓╨╛╨│╨╛ ╨░╨║╤В╨╕╨▓╨░, ╨║╨╛╤В╨╛╤А╨░╤П ╨▓╨║╨╗╤О╤З╨░╨╡╤В ╨▓╤Б╨╡ ╤В╨╡╨║╤Г╤Й╨╕╨╡ ╤А╨░╤Б╤Е╨╛╨┤╤Л, ╤В╨░╨║╨╕╨╡ ╨║╨░╨║ ╤Г╨┐╤Г╤Й╨╡╨╜╨╜╤Л╨╡ ╤А╨░╤Б╤Е╨╛╨┤╤Л, ╨┐╤А╨╛╤Ж╨╡╨╜╤В╤Л ╨╕ ╤В. ╨┤. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡. ╨н╤В╨╛ ╨╗╨╡╨│╤З╨╡ ╨▓╤Б╨╡╨│╨╛ ╤Г╨▓╨╕╨┤╨╡╤В╤М, ╨║╨╛╨│╨┤╨░ ╨▒╨░╨╖╨╛╨▓╤Л╨╣ ╨░╨║╤В╨╕╨▓ ╨┐╤А╨╛╨╕╨╖╨▓╨╛╨┤╨╕╤В ╨┐╨╡╤А╨╕╨╛╨┤╨╕╤З╨╡╤Б╨║╨╕╨╣ ╨┐╨╗╨░╤В╨╡╨╢. ╨Ь╤Л ╨┐╨╛╨╖╨▓╨╛╨╗╤П╨╡╨╝/╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╨╝ ╤В╨╡╨║╤Г╤Й╤Г╤О ╤Б╤В╨╛╨╕╨╝╨╛╤Б╤В╤М ╨┤╨╡╨╜╨╡╨╢╨╜╨╛╨│╨╛ ╨┐╨╛╤В╨╛╨║╨░ ╨╖╨░ T ╨╗╨╡╤В. ╨в╨╛╨│╨┤╨░ ╤Д╨╛╤А╨╝╤Г╨╗╨░ 1 ╤Б╤В╨░╨╜╨╛╨▓╨╕╤В╤Б╤П:

F0 = (S0 тАУ I) exp(rT)

╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ тДЦ 3 (╤Н╤Д╤Д╨╡╨║╤В ╨╕╨╖╨▓╨╡╤Б╤В╨╜╨╛╨│╨╛ ╨┤╨╕╨▓╨╕╨┤╨╡╨╜╨┤╨░)

╨Ъ╨╛╨│╨┤╨░ ╨▒╨░╨╖╨╛╨▓╤Л╨╣ ╨░╨║╤В╨╕╨▓ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░ ╨▓╤Л╨┐╨╗╨░╤З╨╕╨▓╨░╨╡╤В ╨┤╨╕╨▓╨╕╨┤╨╡╨╜╨┤╤Л, ╨╝╤Л ╨┐╤А╨╡╨┤╨┐╨╛╨╗╨░╨│╨░╨╡╨╝, ╤З╤В╨╛ ╨┤╨╕╨▓╨╕╨┤╨╡╨╜╨┤╤Л ╨▓╤Л╨┐╨╗╨░╤З╨╕╨▓╨░╤О╤В╤Б╤П ╨╜╨╡╨┐╤А╨╡╤А╤Л╨▓╨╜╨╛. ╨Я╤Г╤Б╤В╤М q ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╨┐╨╛╤Б╤В╨╛╤П╨╜╨╜╨╛ ╨╜╨░╤З╨╕╤Б╨╗╤П╨╡╨╝╤Г╤О ╨┤╨╛╤Е╨╛╨┤╨╜╨╛╤Б╤В╤М ╨┐╨╛ ╨┤╨╕╨▓╨╕╨┤╨╡╨╜╨┤╨░╨╝. ╨Ф╨╛╤Е╨╛╨┤╨╜╨╛╤Б╤В╤М ╨┐╨╛ ╨┤╨╕╨▓╨╕╨┤╨╡╨╜╨┤╨░╨╝ ╨Ъ╨╛╤Н╤Д╤Д╨╕╤Ж╨╕╨╡╨╜╤В ╨┤╨╛╤Е╨╛╨┤╨╜╨╛╤Б╤В╨╕ ╨┐╨╛ ╨┤╨╕╨▓╨╕╨┤╨╡╨╜╨┤╨░╨╝ ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╨╛╤В╨╜╨╛╤И╨╡╨╜╨╕╨╡ ╤В╨╡╨║╤Г╤Й╨╕╤Е ╨┤╨╕╨▓╨╕╨┤╨╡╨╜╨┤╨╛╨▓ ╨║╨╛╨╝╨┐╨░╨╜╨╕╨╕ ╨║ ╤В╨╡╨║╤Г╤Й╨╡╨╣ ╤Ж╨╡╨╜╨╡ ╨╡╨╡ ╨░╨║╤Ж╨╕╨╣. ╨Ю╨╜ ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╨┐╨╛╤В╨╡╨╜╤Ж╨╕╨░╨╗╤М╨╜╤Л╨╣ ╨┤╨╛╤Е╨╛╨┤ ╨╛╤В ╨╕╨╜╨▓╨╡╤Б╤В╨╕╤Ж╨╕╨╣ ╨▓ ╨┤╨░╨╜╨╜╤Г╤О ╨░╨║╤Ж╨╕╤О. ╨С╨╛╨╗╨╡╨╡ ╤В╨╛╨│╨╛, ╨▓╤Л╨┐╨╗╨░╤З╨╕╨▓╨░╨╡╨╝╤Л╨╣ ╨▒╨░╨╖╨╛╨▓╤Л╨╝ ╨░╨║╤В╨╕╨▓╨╛╨╝, ╨▓╤Л╤А╨░╨╢╨╡╨╜╨╜╤Л╨╣ ╨▓ ╨│╨╛╨┤╨╛╨▓╨╛╨╝ ╨╕╤Б╤З╨╕╤Б╨╗╨╡╨╜╨╕╨╕, ╤Д╨╛╤А╨╝╤Г╨╗╨░ 1 ╨┐╤А╨╕╨╜╨╕╨╝╨░╨╡╤В ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╨╣ ╨▓╨╕╨┤:

F0 = S0 exp(rq)T

╨Я╤А╨╡╨╕╨╝╤Г╤Й╨╡╤Б╤В╨▓╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╤Е ╨║╨╛╨╜╤В╤А╨░╨║╤В╨╛╨▓

╨Э╨╡╨║╨╛╤В╨╛╤А╤Л╨╡ ╨╕╨╖ ╨┐╤А╨╡╨╕╨╝╤Г╤Й╨╡╤Б╤В╨▓ ╨╖╨░╨║╨╗╤О╤З╨░╤О╤В╤Б╤П ╨▓ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╡╨╝:

• ╨Ш╤Е ╨╝╨╛╨╢╨╜╨╛ ╤Б╨╛╨┐╨╛╤Б╤В╨░╨▓╨╕╤В╤М ╤Б ╨┐╨╡╤А╨╕╨╛╨┤╨╛╨╝ ╤Н╨║╤Б╨┐╨╛╨╖╨╕╤Ж╨╕╨╕ ╨╕ ╤А╨░╨╖╨╝╨╡╤А╨╛╨╝ ╨╜╨░╨╗╨╕╤З╨╜╨╛╤Б╤В╨╕.
• ╨Ю╨╜ ╨╛╨▒╨╡╤Б╨┐╨╡╤З╨╕╨▓╨░╨╡╤В ╨┐╨╛╨╗╨╜╨╛╨╡ ╤Е╨╡╨┤╨╢╨╕╤А╨╛╨▓╨░╨╜╨╕╨╡.
• ╨С╨╡╨╖╤А╨╡╤Ж╨╡╨┐╤В╤Г╤А╨╜╤Л╨╡ ╨┐╤А╨╛╨┤╤Г╨║╤В╤Л.
• ╨Ш╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╤Е ╨┐╤А╨╛╨┤╤Г╨║╤В╨╛╨▓ ╨╛╨▒╨╡╤Б╨┐╨╡╤З╨╕╨▓╨░╨╡╤В ╤Ж╨╡╨╜╨╛╨▓╤Г╤О ╨╖╨░╤Й╨╕╤В╤Г.
• ╨Ш╤Е ╨╗╨╡╨│╨║╨╛ ╨┐╨╛╨╜╤П╤В╤М.

╨Э╨╡╨┤╨╛╤Б╤В╨░╤В╨║╨╕ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╤Е ╨║╨╛╨╜╤В╤А╨░╨║╤В╨╛╨▓

╨Э╨╡╨║╨╛╤В╨╛╤А╤Л╨╡ ╨╕╨╖ ╨╜╨╡╨┤╨╛╤Б╤В╨░╤В╨║╨╛╨▓ ╨╖╨░╨║╨╗╤О╤З╨░╤О╤В╤Б╤П ╨▓ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╡╨╝:

• ╨Э╨╡╨╛╨▒╤Е╨╛╨┤╨╕╨╝╨░ ╨┐╤А╨╕╨▓╤П╨╖╨║╨░ ╨║╨░╨┐╨╕╤В╨░╨╗╨░. ╨Ф╨╛ ╤А╨░╤Б╤З╨╡╤В╨╛╨▓ ╨╜╨╡╤В ╨┐╤А╨╛╨╝╨╡╨╢╤Г╤В╨╛╤З╨╜╤Л╤Е ╨┤╨╡╨╜╨╡╨╢╨╜╤Л╤Е ╨┐╨╛╤В╨╛╨║╨╛╨▓.
• ╨Ю╨╜ ╨┐╨╛╨┤╨▓╨╡╤А╨╢╨╡╨╜ ╤А╨╕╤Б╨║╤Г ╨┤╨╡╤Д╨╛╨╗╤В╨░ ╨а╨╕╤Б╨║ ╨┤╨╡╤Д╨╛╨╗╤В╨░ ╨а╨╕╤Б╨║ ╨┤╨╡╤Д╨╛╨╗╤В╨░ тАФ ╤Н╤В╨╛ ╤Д╨╛╤А╨╝╨░ ╤А╨╕╤Б╨║╨░, ╨║╨╛╤В╨╛╤А╨░╤П ╨╕╨╖╨╝╨╡╤А╤П╨╡╤В ╨▓╨╡╤А╨╛╤П╤В╨╜╨╛╤Б╤В╤М ╨╜╨╡╨▓╤Л╨┐╨╛╨╗╨╜╨╡╨╜╨╕╤П ╨╛╨▒╤П╨╖╨░╤В╨╡╨╗╤М╤Б╤В╨▓, ╤В╨░╨║╨╕╤Е ╨║╨░╨║ ╨┐╨╛╨│╨░╤И╨╡╨╜╨╕╨╡ ╨╛╤Б╨╜╨╛╨▓╨╜╨╛╨╣ ╤Б╤Г╨╝╨╝╤Л ╨┤╨╛╨╗╨│╨░ ╨╕╨╗╨╕ ╨┐╤А╨╛╤Ж╨╡╨╜╤В╨╛╨▓, ╨╕ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╤П╨╡╤В╤Б╤П ╨╝╨░╤В╨╡╨╝╨░╤В╨╕╤З╨╡╤Б╨║╨╕ ╨╜╨░ ╨╛╤Б╨╜╨╛╨▓╨╡ ╨┐╤А╨╡╨┤╤Л╨┤╤Г╤Й╨╕╤Е ╨╛╨▒╤П╨╖╨░╤В╨╡╨╗╤М╤Б╤В╨▓, ╤Д╨╕╨╜╨░╨╜╤Б╨╛╨▓╤Л╤Е ╤Г╤Б╨╗╨╛╨▓╨╕╨╣, ╤А╤Л╨╜╨╛╤З╨╜╤Л╤Е ╤Г╤Б╨╗╨╛╨▓╨╕╨╣, ╨┐╨╛╨╖╨╕╤Ж╨╕╨╕ ╨╗╨╕╨║╨▓╨╕╨┤╨╜╨╛╤Б╤В╨╕ ╨╕ ╤В╨╡╨║╤Г╤Й╨╕╤Е ╨╛╨▒╤П╨╖╨░╤В╨╡╨╗╤М╤Б╤В╨▓. , ╤Б╤А╨╡╨┤╨╕ ╨┐╤А╨╛╤З╨╕╤Е ╤Д╨░╨║╤В╨╛╤А╨╛╨▓.╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡.
• ╨Ъ╨╛╨╜╤В╤А╨░╨║╤В╤Л ╨▒╤Л╨▓╨░╨╡╤В ╤В╤А╤Г╨┤╨╜╨╛ ╤А╨░╤Б╤В╨╛╤А╨│╨╜╤Г╤В╤М.
• ╨Э╨░╨╣╤В╨╕ ╨║╨╛╨╜╤В╤А╨░╨│╨╡╨╜╤В╨░ ╨╝╨╛╨╢╨╡╤В ╨▒╤Л╤В╤М ╤Б╨╗╨╛╨╢╨╜╨╛.

╨Ю╨│╤А╨░╨╜╨╕╤З╨╡╨╜╨╕╤П

• ╨а╨╕╤Б╨║ ╨╗╨╕╨║╨▓╨╕╨┤╨╜╨╛╤Б╤В╨╕╨а╨╕╤Б╨║ ╨╗╨╕╨║╨▓╨╕╨┤╨╜╨╛╤Б╤В╨╕╨а╨╕╤Б╨║ ╨╗╨╕╨║╨▓╨╕╨┤╨╜╨╛╤Б╤В╨╕ ╨╛╤В╨╜╨╛╤Б╨╕╤В╤Б╤П ╨║ ┬л╨╜╨╡╤Е╨▓╨░╤В╨║╨╡ ╨╜╨░╨╗╨╕╤З╨╜╨╛╤Б╤В╨╕┬╗ ╨▓ ╤В╨╡╤З╨╡╨╜╨╕╨╡ ╨▓╤А╨╡╨╝╨╡╨╜╨╜╨╛╨│╨╛ ╨╕╨╗╨╕ ╨║╤А╨░╤В╨║╨╛╤Б╤А╨╛╤З╨╜╨╛╨│╨╛ ╨┐╨╡╤А╨╕╨╛╨┤╨░, ╨╕ ╤В╨░╨║╨╕╨╡ ╤Б╨╕╤В╤Г╨░╤Ж╨╕╨╕, ╨║╨░╨║ ╨┐╤А╨░╨▓╨╕╨╗╨╛, ╨╜╨░╨╜╨╛╤Б╤П╤В ╤Г╤Й╨╡╤А╨▒ ╨╗╤О╨▒╨╛╨╝╤Г ╨▒╨╕╨╖╨╜╨╡╤Б╤Г ╨╕╨╗╨╕ ╨║╨╛╨╝╨╝╨╡╤А╤З╨╡╤Б╨║╨╛╨╣ ╨╛╤А╨│╨░╨╜╨╕╨╖╨░╤Ж╨╕╨╕. ╨б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, ╨▒╨╕╨╖╨╜╨╡╤Б-╨┤╨╛╨╝ ╨▓ ╨▒╨╛╨╗╤М╤И╨╕╨╜╤Б╤В╨▓╨╡ ╤Б╨╗╤Г╤З╨░╨╡╨▓ ╨╛╨║╨░╨╖╤Л╨▓╨░╨╡╤В╤Б╤П ╤Б ╨╛╤В╤А╨╕╤Ж╨░╤В╨╡╨╗╤М╨╜╤Л╨╝ ╨╛╨▒╨╛╤А╨╛╤В╨╜╤Л╨╝ ╨║╨░╨┐╨╕╤В╨░╨╗╨╛╨╝. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡.
• ╨а╨╕╤Б╨║ ╨║╨╛╨╜╤В╤А╨░╨│╨╡╨╜╤В╨░.

╨Я╤А╨╕╨╝╨╡╤З╨░╨╜╨╕╨╡:

╨б╤В╨╛╤А╨╛╨╜╤Л, ╤Г╤З╨░╤Б╤В╨▓╤Г╤О╤Й╨╕╨╡ ╨▓ ╤Н╨║╤Б╨┐╨╡╨┤╨╕╤В╨╛╤А╤Б╨║╨╕╤Е ╨┤╨╛╨│╨╛╨▓╨╛╤А╨░╤Е, ╨╜╨╡ ╨╕╨╝╨╡╤О╤В ╨▓╨╛╨╖╨╝╨╛╨╢╨╜╨╛╤Б╤В╨╕ ╨▓╤Л╨▒╨╛╤А╨░ ╤Б╨┐╨╛╤Б╨╛╨▒╨░ ╤А╨░╤Б╤З╨╡╤В╨░ (╤В. ╨╡. ╨┐╨╛╤Б╤В╨░╨▓╨║╨░ ╨╕╨╗╨╕ ╤А╨░╤Б╤З╨╡╤В ╨╜╨░╨╗╨╕╤З╨╜╤Л╨╝╨╕) ╨▓ ╨┤╨░╤В╤Г ╤А╨░╤Б╤З╨╡╤В╨░; ╤Б╨║╨╛╤А╨╡╨╡, ╤Н╤В╨╛ ╤Б╨╛╨│╨╗╨░╤Б╨╛╨▓╤Л╨▓╨░╨╡╤В╤Б╤П ╨╝╨╡╨╢╨┤╤Г ╤Б╤В╨╛╤А╨╛╨╜╨░╨╝╨╕ ╨▓ ╤Б╨░╨╝╨╛╨╝ ╨╜╨░╤З╨░╨╗╨╡.

╨Ч╨░╨║╨╗╤О╤З╨╡╨╜╨╕╨╡

• ╨Ф╨╗╨╕╨╜╨╜╨░╤П ╨┐╤А╨╕╨▒╤Л╨╗╤М, ╨╡╤Б╨╗╨╕ ╤Ж╨╡╨╜╨░ ╨░╨║╤В╨╕╨▓╨░ ╨▓╤Л╤И╨╡, ╤З╨╡╨╝ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░.
• ╨Ъ╨╛╤А╨╛╤В╨║╨░╤П ╨┐╤А╨╕╨▒╤Л╨╗╤М, ╨╡╤Б╨╗╨╕ ╤Ж╨╡╨╜╨░ ╨░╨║╤В╨╕╨▓╨░ ╨╝╨╡╨╜╤М╤И╨╡, ╤З╨╡╨╝ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨░╤П ╤Ж╨╡╨╜╨░.
• ╨Э╨╕ ╨╛╨┤╨╜╨░ ╨╕╨╖ ╤Б╤В╨╛╤А╨╛╨╜ ╨╜╨╡ ╨┐╨╗╨░╤В╨╕╤В ╨┐╤А╨╕ ╨╖╨░╨║╨╗╤О╤З╨╡╨╜╨╕╨╕ ╨║╨╛╨╜╤В╤А╨░╨║╤В╨░.

╨а╨╡╨║╨╛╨╝╨╡╨╜╨┤╤Г╨╡╨╝╤Л╨╡ ╤Б╤В╨░╤В╤М╨╕

╨н╤В╨╛ ╨▒╤Л╨╗ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╨╣ ╨║╨╛╨╜╤В╤А╨░╨║╤В ╨╕ ╨╡╨│╨╛ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡. ╨Ч╨┤╨╡╤Б╤М ╨╝╤Л ╨╛╨▒╤Б╤Г╨┤╨╕╨╝, ╨║╨░╨║ ╤А╨░╨▒╨╛╤В╨░╨╡╤В ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╤Л╨╣ ╨║╨╛╨╜╤В╤А╨░╨║╤В, ╨░ ╤В╨░╨║╨╢╨╡ ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╝ ╨┐╤А╨╕╨╝╨╡╤А ╨╕ ╨┐╨╛╨┤╤А╨╛╨▒╨╜╨╛╨╡ ╨╛╨▒╤К╤П╤Б╨╜╨╡╨╜╨╕╨╡. ╨Ь╤Л ╤В╨░╨║╨╢╨╡ ╨╛╨▒╤Б╤Г╨┤╨╕╨╝ ╨┐╤А╨╡╨╕╨╝╤Г╤Й╨╡╤Б╤В╨▓╨░ ╨╕ ╨╜╨╡╨┤╨╛╤Б╤В╨░╤В╨║╨╕. ╨Т╤Л ╨╝╨╛╨╢╨╡╤В╨╡ ╤Г╨╖╨╜╨░╤В╤М ╨▒╨╛╨╗╤М╤И╨╡ ╨╛ ╨▒╤Г╤Е╨│╨░╨╗╤В╨╡╤А╤Б╨║╨╛╨╝ ╤Г╤З╨╡╤В╨╡ ╨╕╨╖ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤Б╤В╨░╤В╨╡╨╣ тАУ

• ╨в╨╕╨┐╤Л ╨║╨╛╨╜╤В╤А╨░╨║╤В╨╛╨▓ Cost-Plus
• ╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Д╨╛╤А╨▓╨░╤А╨┤╨╜╨╛╨│╨╛ ╨║╤Г╤А╤Б╨░
• ╨д╨╛╤А╨▓╨░╤А╨┤╤Л ╨┐╤А╨╛╤В╨╕╨▓ ╤Д╤М╤О╤З╨╡╤А╤Б╨╛╨▓
• ╨в╨╛╨▓╨░╤А╨╜╤Л╨╡ ╨┤╨╡╤А╨╕╨▓╨░╤В╨╕╨▓╤Л