
    M/Ph4              
       
   d Z ddlZddlmZ  G d d          Z G d d          Z G d d          Z G d	 d
          Z	 G d d          Z
 G d d          Z G d d          Zd Zedk    rdZ ej        dez  de          ZdZdZdZdZdZdZ e            Ze                    eeeeeee          Z ej                      ej        ej                    ej        d           dZdZe                    eeeeeee          Z ej                      ej        ej                    ej        d           dZdZdZdZ dZ!dZ" e                                ee"eee e!ee          Z ej                      ej        ej                    ej        d            d!ZdZ#dZ" e                                ee"e#ee          Z ej                      ej        ej                    ej        d"           d#Z$dZ%d$Z& ee$e%e&          \  Z'Z(Z) e
                                e'e(e)ee          Z ej                      ej        ej                    ej        d%           dZ*d&Z#d'Z+d(Zd)Z,d*Zdez  Z ej        eez  ee          Z- e                                e*e#e+ee,e-ed*+          \  ZZ. ej                      ej        ej                    ej        d,            ej                      ej         ej/        e.          j                    ej        d-            ej                      ej0        d.d$d$            ej        ed                     ej        d/            ej0        d.d$d.            ej         ej/        e.d                               ej        d0           d!Z*d1Zd&Z#d$Z1d$Zd2Zdez  Z ej        eez  ee          Z- e                                e*e#e1eee-e          \  ZZ2Z3 ej                      ej        e-ej                    ej        d3            ej                      ej        e-e3j                    ej        d4            ej                      ej        e-e2j                    ej        d5            ej                      ej0        d.d$d$            ej        e-ed                     ej        d3            ej0        d.d$d.            ej        e-e3d         d67            ej        e-e2d         d87            ej4        d9:            ej        d           dS dS );a
   Diffusion 2: jump diffusion, stochastic volatility, stochastic time

Created on Tue Dec 08 15:03:49 2009

Author: josef-pktd   following Meucci
License: BSD

contains:

CIRSubordinatedBrownian
Heston
IG
JumpDiffusionKou
JumpDiffusionMerton
NIG
VG

References
----------

Attilio Meucci, Review of Discrete and Continuous Processes in Finance: Theory and Applications
Bloomberg Portfolio Research Paper No. 2009-02-CLASSROOM July 1, 2009
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1373102




this is currently mostly a translation from matlab of
http://www.mathworks.com/matlabcentral/fileexchange/23554-review-of-discrete-and-continuous-processes-in-finance
license BSD:

Copyright (c) 2008, Attilio Meucci
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:

    * Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright
      notice, this list of conditions and the following disclaimer in
      the documentation and/or other materials provided with the distribution

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.



TODO:

* vectorize where possible
* which processes are exactly simulated by finite differences ?
* include or exclude (now) the initial observation ?
* convert to and merge with diffusion.py (part 1 of diffusions)
* which processes can be easily estimated ?
  loglike or characteristic function ?
* tests ? check for possible index errors (random indices), graphs look ok
* adjust notation, variable names, more consistent, more pythonic
* delete a few unused lines, cleanup
* docstrings


random bug (showed up only once, need fuzz-testing to replicate)
  File "../diffusion2.py", line 375, in <module>
    x = jd.simulate(mu,sigma,lambd,a,D,ts,nrepl)
  File "../diffusion2.py", line 129, in simulate
    jumps_ts[n] = CumS[Events]
IndexError: index out of bounds

CumS is empty array, Events == -1


    Nc                       e Zd ZdZd Zd ZdS )JumpDiffusionMertonaX  

    Example
    -------
    mu=.00     # deterministic drift
    sig=.20 # Gaussian component
    l=3.45 # Poisson process arrival rate
    a=0 # drift of log-jump
    D=.2 # st.dev of log-jump

    X = JumpDiffusionMerton().simulate(mu,sig,lambd,a,D,ts,nrepl)

    plt.figure()
    plt.plot(X.T)
    plt.title('Merton jump-diffusion')


    c                     d S N selfs    b/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/sandbox/tsa/diffusion2.py__init__zJumpDiffusionMerton.__init__n           c                 6   |d         }t           j                            ||z  |df          }	g }
t          |          }t          j        ||f          }
t          |          D ]}|t           j                            |	|                   z  }t          j        |d          }||t           j                            |	|         d          z  z   }t          j	        |          }t          j        |          }t          |          D ]9}t          j
        |||         k              dz
  }d||<   |dk    r||         ||<   :||
|d d f<   t          j        ||f          }t          |          D ]h}||         }|dk    r||         ||dz
           z
  }||z  |t          j        |          z  t           j                            |          z  z   |d d |f<   it          j        t          j        |df          t          j	        |d          |
z   f          }|S N   sizer   )nprandompoissonlenzerosrangerandsortrandncumsumsumsqrthstack)r	   mslambdaDtsnreplTn_jumpsjumpsnobsjtSCumSjumps_tsnEventsD_DiffkDtxs                          r
   simulatezJumpDiffusionMerton.simulater   s   rF)##E!G5!*#==WWhd|$$u 	" 	"A")..,,,A!A Abioogaj3333A 9Q<<Dx~~H4[[ / /2a5))!+A::"&v,HQK "E!AAA#JJ 5,''t 	D 	DA!uBssa5AaC="q}RY__U-C-CCCF111Q3KKIrxq	**29VA+>+>u+DEFFr   N__name__
__module____qualname____doc__r   r7   r   r   r
   r   r   Z   s<         &  ( ( ( ( (r   r   c                       e Zd Zd Zd ZdS )JumpDiffusionKouc                     d S r   r   r   s    r
   r   zJumpDiffusionKou.__init__   r   r   c	                    |d         }	t           j                            ||	z  |df          }
g }t          |          }t          j        ||f          }t          |          D ]/}|	t           j                            |
|                   z  }t          j        |          }t           j                            d||
|                   }|t           j        	                    ||
|                   z  d|z
  t           j        	                    ||
|                   z  z
  }t          j
        |          }t          j        |          }t          |          D ]0}t          |||         k              dz
  }d||<   |r||         ||<   1|||d d f<   1t          j        ||f          }t          |          D ]i}||         }|dk    r||         ||dz
           z
  }||z  |t          j        |          z  t           j                            |          z  z   |d d |f<   jt          j        t          j        |df          t          j
        |d          |z   f          }|S r   )r   r   r   r   r   r   r   r   binomialexponentialr   r   r   normalr    )r	   r!   r"   r#   pe1e2r&   r'   r(   Nr*   r+   r,   r-   wwr.   r/   r0   r1   r2   r3   r4   r5   r6   s                            r
   r7   zJumpDiffusionKou.simulate   s=   
R&IeAgU1I66WWhd|$$u 	" 	"A	qt$$$AgajjA ##Aq!#66BRY**2QqT*;;;2..r1Q48889A 9Q<<Dx~~H4[[ - -Q1Xq - $VHQK!E!AAA#JJ5,''t 	J 	JA!uBssa5AaC="q}RY-=-=5-=-I-IIIF111Q3KKIrxq	**29VA+>+>u+DEFFr   N)r9   r:   r;   r   r7   r   r   r
   r>   r>      s2          ' ' ' ' 'r   r>   c                       e Zd ZdZd Zd ZdS )VGzvariance gamma process
    c                     d S r   r   r   s    r
   r   zVG.__init__   r   r   c           	         t          |          }t          j        ||f          }t          |          D ]}|d         dz
  }	|dk    r||         ||dz
           z
  }	|t          j                            |	|z  d|          z  }
t          j                            ||
z  d|t          j        |
          z  z             }||d d |f<   t          j        |d          }|S )Nr   r         ?r   ư>locscale)	r   r   r   r   r   gammarC   r   r   )r	   r!   r"   kappar&   r'   r(   dXsr-   dtd_taudXr6   s                r
   r7   zVG.simulate   s    
b''hay!!q 	 	A!uQwBssU2ac7]
 BIOOBuHReOEEEE
 !!agT!BGENN:J5J!KKBC!HHIc!r   Nr8   r   r   r
   rJ   rJ      s<               r   rJ   c                       e Zd ZdZd Zd ZdS )IGz%inverse-Gaussian ??? used by NIG
    c                     d S r   r   r   s    r
   r   zIG.__init__   r   r   c                 v   t           j                            |d          }|dz  }|d|z  |z  |z  |z  z   d|z  |z  t          j        d|z  |z  |z  ||z  |dz  z  z             z  z
  }t           j                            |d          }||||z   z  k    }||z  ||         z  ||<   |                                S )Nr            ?   )r   r   r   r   r   ravel)	r	   lr!   r'   rG   YXUinds	            r
   r7   zIG.simulate   s    IOOE!$$qDAa11Q!Aa!QT
0B(C(CCCINN5##1Q3i1QsV#wwyyr   Nr8   r   r   r
   rY   rY      s<           	 	 	 	 	r   rY   c                       e Zd ZdZd Zd ZdS )NIGznormal-inverse-Gaussian
    c                     d S r   r   r   s    r
   r   zNIG.__init__  r   r   c                    t          |          }t          j        ||f          }t          |          D ]}|d         dz
  }	|dk    r||         ||dz
           z
  }	d|z  |	dz  z  }
|	}t	                                          |
||          }t          j                            |          }||z  t          j        |          z  ||z  z   }||d d |f<   t          j	        |d          }|S )Nr   r   r\   )
r   r   r   r   rY   r7   r   r   r   r   )r	   thr4   r"   r&   r'   r(   DXsr-   r5   lfracr!   DSrG   DXr6   s                   r
   r7   zNIG.simulate  s    GGhay!!q 	 	A!uQwBssa5AaC=aCQKEAua//B	&&A1RWR[[2b5(BC!HHIc!r   Nr8   r   r   r
   rf   rf      s<               r   rf   c                        e Zd ZdZd ZddZdS )Hestonz!Heston Stochastic Volatility
    c                     d S r   r   r   s    r
   r   zHeston.__init__  r   r   rM   c	                    |d         }	t          |          }
t          j        |
          }|d         dz
  |d<   t          j        |          |dd <   t          j        ||
f          }t          j        |          t          j                            ||
          z  }t          j        |          t          j                            ||
          z  }||z  t          j        d|dz  z
            |z  z   }|t          j        |          z  }g }t          j        ||
f          }t          j        ||
f          }t          |
          D ]}|||z
  z  ||         z  |t          j        |          z  |d d |f         z  z   }|||         z  t          j        |||         z            |d d |f         z  z   }||z   }||d d |f<   ||d d |f<   t          j	        |d          }||fS )Nr   r   r   r\   )
r   r   r   diffr   r   r   onesr   r   )r	   r!   rS   etar#   rr&   r'   tratior(   r+   rU   rj   dB_1dB_2udB_2vtvrT   vtsr-   dvrW   r6   s                           r
   r7   zHeston.simulate   s   rF2wwXd^^1a1122hd|$$wr{{RY__U4888biooeD999v!Q$--
hd|$$hd|$$t 	 	AB1%uRWR[['8aaac'BBB2a5272be8,,tAAAaCy88BbBC!HC!HHIc!#vr   N)rM   r8   r   r   r
   ro   ro     sA                r   ro   c                       e Zd ZdZd Zd ZdS )CIRSubordinatedBrownianz%CIR subordinated Brownian Motion
    c                     d S r   r   r   s    r
   r   z CIRSubordinatedBrownian.__init__@  r   r   c                    |d         }t          |          }	t          j        |	          }
|d         dz
  |
d<   t          j        |          |
dd <   t          j        ||	f          }t          j        |
          t          j                            ||	          z  }d}t          j        ||	f          }t          j        ||	f          }t          j        ||	f          }t          |	          D ]}|
|         }|||z
  z  |z  |t          j        |          z  |d d |f         z  z   }t          j        ||z   d          }t          j        ||z  d          }t          j        	                    ||z  |t          j        |          z            }||d d |f<   ||d d |f<   ||d d |f<   t          j
        |d          }t          j
        |d          }|||fS )Nr   r   r   rM   g|=rN   rO   )r   r   r   rr   r   r   r   r   maximumrC   r   )r	   r!   rS   T_dotr#   sigmar&   r'   r(   r+   dtarrrj   dBytrT   dtausyr-   rU   dydtaurW   taur6   s                           r
   r7   z CIRSubordinatedBrownian.simulateC  s   rF2wwa57aGBKKabb	hd|$$WU^^biooeD999hd|$$%&&HeD\""t 
	 
	AqBb!"$uRWR[['8AAAaC'@@BBrE%((B:beT**D!!afE"'$--4G!HHBAaaacFE!!!A#JC!HHia  Ic!#qyr   Nr8   r   r   r
   r   r   <  s<               r   r   c                     ||z  t          j        | dz  |dz  z
            z  }d|t          j        | dz  |dz  z
            z  z  }t          j        |t          j        | dz  |dz  z
            z            }|||fS )Nr\   r   )r   r   )r$   bdri   r4   r"   s         r
   schout2contankr   b  s    	
1RWQT!Q$Y	B	1RWQT!Q$Y A
"'!Q$q!t)$$$%%Aa6Mr   __main__g     o@rM      g{Gz?g{Gz?g     @A@g?zMerton jump-diffusiong@g        g      @r]   g333333?z'double exponential (Kou jump diffusion)g?zvariance gammag @r   znormal-inverse-Gaussiang333333?g
ףp=
?g      ?gffffffg      4@)rv   zHeston Stochastic Volatilityz'Heston Stochastic Volatility - CIR Vol.r\   z$Heston Stochastic Volatility processzCIR Volatilityg?g      $@zCIRSubordinatedBrownian processzCIRSubordinatedBrownian - CIRz*CIRSubordinatedBrownian - stochastic time CIR)labelzstoch. timez
upper left)rP   )5r<   numpyr   matplotlib.pyplotpyplotpltr   r>   rJ   rY   rf   ro   r   r   r9   r+   linspacer&   r'   mur   r#   r$   r%   jdr7   r6   figureplotr(   titlerD   rE   rF   sigrS   albederi   r4   r"   r!   rt   ru   tshr|   r   subplotr   r   r   legendr   r   r
   <module>r      s  R Rj          @ @ @ @ @ @ @ @D, , , , , , , ,^       >       &       8! ! ! ! ! ! ! !F$ $ $ $ $ $ $ $L   z D
"+bgr4
(
(B
EBEEAA				B
BuU1Qr%00ACJLLLCHQSMMMCI%&&&EE
BuU1Qr%00ACJLLLCHQSMMMCI%&&&
 
B
EA	B	B
C##Bs52bEBBACJLLLCHQSMMMCI7888 
BE
C
bU2e,,ACJLLLCHQSMMMCI 
B	
B	
B^Br"%%FBqr!Ab''ACJLLLCHQSMMMCI'(((
 	AE
CEAA6D2;qvq$''CVXXqE!S%LLFAsCJLLLCHQSMMMCI,---CJLLLCHWRWS\\^CI7888CJLLLCK!ACHQqTNNNCI4555CK!ACHWRWSV__CI
 	A
E
E
E
E 	A6D2;qvq$''C''))221eU5PSUZ[[IAsACJLLLCHS!#CI/000CJLLLCHS!#CI-...CJLLLCHS#%CI:;;;CJLLLCK!ACHS!A$CI/000CK!ACHS!A$e$$$$CHS#a&....CJ<    CI'(((((U r   