#
#?Valuation?of?European?call?options?in?Black-Scholes-Merton?model
#?incl.?Vega?function?and?implied?volatility?estimation
#?bsm_functions.py
#

#?Analytical?Black-Scholes-Merton?（BSM）?Formula


def?bsm_call_value（S0?K?T?r?sigma）:
????‘‘‘?Valuation?of?European?call?option?in?BSM?model.
????Analytical?formula.
????
????Parameters
????==========
????S0?:?float
????????initial?stock/index?level
????K?:?float
????????strike?price
????T?:?float
????????maturity?date?（in?year?fractions）
????r?:?float
????????constant?risk-free?short?rate
????sigma?:?float
????????volatility?factor?in?diffusion?term
????
????Returns
????=======
????value?:?float
????????present?value?of?the?European?call?option
????‘‘‘
????from?math?import?log?sqrt?exp
????from?scipy?import?stats

????S0?=?float（S0）
????d1?=?（log（S0?/?K）?+?（r?+?0.5?*?sigma?**?2）?*?T）?/?（sigma?*?sqrt（T））
????d2?=?（log（S0?/?K）?+?（r?-?0.5?*?sigma?**?2）?*?T）?/?（sigma?*?sqrt（T））
????value?=?（S0?*?stats.norm.cdf（d1?0.0?1.0）
????????????-?K?*?exp（-r?*?T）?*?stats.norm.cdf（d2?0.0?1.0））
??????#?stats.norm.cdf?-->?cumulative?distribution?function
??????#????????????????????for?normal?distribution
????return?value

#?Vega?function


def?bsm_vega（S0?K?T?r?sigma）:
????‘‘‘?Vega?of?European?option?in?BSM?model.
????
????Parameters
????==========
????S0?:?float
????????initial?stock/index?level
????K?:?float
????????strike?price
????T?:?float
????????maturity?date?（in?year?fractions）
????r?:?float
????????constant?risk-free?short?rate
????sigma?:?float
????????volatility?factor?in?diffusion?term
????
????Returns
????=======
????vega?:?float
????????partial?derivative?of?BSM?formula?with?respect
????????to?sigma?i.e.?Vega

????‘‘‘
????from?math?import?log?sqrt
????from?scipy?import?stats

????S0?=?float（S0）
????d1?=?（log（S0?/?K）?+?（r?+?0.5?*?sigma?**?2）?*?T）?/?（sigma?*?sqrt（T））
????vega?=?S0?*?stats.norm.pdf（d1?0.0?1.0）?*?sqrt（T）
????return?vega

#?Implied?volatility?function


def?bsm_call_imp_vol（S0?K?T?r?C0?sigma_est?it=100）:
????‘‘‘?Implied?volatility?of?European?call?option?in?BSM?model.
????
????Parameters
????==========
????S0?:?float
????????initial?stock/index?level
????K?:?float
????????strike?price
????T?:?float
????????maturity?date?（in?year?fractions）
????r?:?float
????????constant?risk-free?short?rate
????sigma_est?:?float
????????estimate?of?impl.?volatility
????it?:?integer
????????number?of?iterations
????
????Returns
????=======
????simga_est?:?float
????????numerically?estimated?implied?volatility
????‘‘‘
????for?i?in?range（it）:
????????sigma_est?-=?（（bsm_call_value（S0?K?T?r?sigma_est）?-?C0）
????????????????????????/?bsm_vega（S0?K?T?r?sigma_est））
????return?sigma_est

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2017-07-11?18:24??py4fi-master\
?????文件?????????690??2017-07-11?18:24??py4fi-master\.gitignore
?????文件????????1778??2017-07-11?18:24??py4fi-master\README.md
?????目錄???????????0??2017-07-11?18:24??py4fi-master\ipython\
?????文件???????45503??2017-07-11?18:24??py4fi-master\ipython\01_Why_Python_ipynb.ipynb
?????文件??????303643??2017-07-11?18:24??py4fi-master\ipython\03_Introductory_Examples.ipynb
?????文件???????65313??2017-07-11?18:24??py4fi-master\ipython\04_Data_Structures.ipynb
?????文件??????783006??2017-07-11?18:24??py4fi-master\ipython\05_Visualization.ipynb
?????文件??????560306??2017-07-11?18:24??py4fi-master\ipython\06_Financial_Time_Series.ipynb
?????文件??????285701??2017-07-11?18:24??py4fi-master\ipython\07_Input_Output.ipynb
?????文件??????107594??2017-07-11?18:24??py4fi-master\ipython\08_Performance_Python.ipynb
?????文件??????560298??2017-07-11?18:24??py4fi-master\ipython\09_Math_Tools.ipynb
?????文件??????692957??2017-07-11?18:24??py4fi-master\ipython\10_Stochastics.ipynb
?????文件??????661928??2017-07-11?18:24??py4fi-master\ipython\11_Statistics_a.ipynb
?????文件??????897769??2017-07-11?18:24??py4fi-master\ipython\11_Statistics_b.ipynb
?????文件???????36894??2017-07-11?18:24??py4fi-master\ipython\12_Excel_Integration.ipynb
?????文件??????104830??2017-07-11?18:24??py4fi-master\ipython\13_objects_GUIs.ipynb
?????文件???????64688??2017-07-11?18:24??py4fi-master\ipython\14_Web_Integration.ipynb
?????文件??????432419??2017-07-11?18:24??py4fi-master\ipython\15_DX_Library_ipynb.ipynb
?????文件???????83682??2017-07-11?18:24??py4fi-master\ipython\19_Volatility_Options.ipynb
?????文件???????58068??2017-07-11?18:24??py4fi-master\ipython\C_Dates_and_Times.ipynb
?????文件????????2693??2017-07-11?18:24??py4fi-master\ipython\bsm_functions.py
?????文件????????2092??2017-07-11?18:24??py4fi-master\ipython\bsm_option_class.py
?????目錄???????????0??2017-07-11?18:24??py4fi-master\ipython\data\
?????文件???????????0??2017-07-11?18:24??py4fi-master\ipython\data\.placeholder
?????目錄???????????0??2017-07-11?18:24??py4fi-master\ipython\images\
?????文件?????1513419??2017-07-11?18:24??py4fi-master\ipython\images\msft_1.html
?????文件?????3886998??2017-07-11?18:24??py4fi-master\ipython\images\msft_2.html
?????文件?????????828??2017-07-11?18:24??py4fi-master\ipython\mcs_full_vector_numpy.py
?????文件????????1041??2017-07-11?18:24??py4fi-master\ipython\mcs_pure_python.py
?????文件?????????837??2017-07-11?18:24??py4fi-master\ipython\mcs_vector_numpy.py
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