In [15]: log_returns.mean() * M + 0.5 * sigma ** 2
➊
Out[15]: 0.05000000000000005
In [16]: log_returns.std() * math.sqrt(M)
➋
Out[16]: 0.20000000000000015
➊
이토 항
2
수정 후의 연율화된 평균 로그 수익률
➋
연율화된 변동성. 로그 수익률의 연율화된 표준편차
전체
12
,
500
,
000
개의 데이터가 대부분 +/–
0
.
15
사이에 있음을 알 수 있다. 또한 평균 수익률
과 표준편차를 연율화하면
0
.
05
,
0
.
2
가 되는 것을 예상할 수 있다(
1
년을
50
개의 구간으로 나누
었기 때문에 연율화하기 위해서는 평균값에
50
을, 표준편차에는
50
을 곱한다). 모멘트가 잘
맞는 이유는 난수를 생성할 때 분산 감소 방법을 썼기 때문이다.
[그림
13
-
2
]에서는 시뮬레이션된 로그 수익률 분포와 주어진
r
,
sigma
값에 대한 정규분포의
확률 밀도 함수를 비교했다. 사용된 함수는 ...
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