기초자산 모델
개요
모델의 종류는 다음과 같다.
| 분류 | 모델 | 이름 | 요인 | 비고 |
|---|---|---|---|---|
| IR | HW | Hull-White | 1 | |
| IR | BK | Black-Karasinski | 2 | |
| EQ | GBM | Geometric Brownian Motion | 1 | |
| EQ | GBM_CONST | GBM (Constant Parameter) | 1 | |
| FX | GK | Garman–Kohlhagen | 1 |
이자율 모형
헐-화이트
수식 : dr = a(theta - r) ...
hw1f = xen.HullWhite1F('ir_rate1')
hw1f.fitting_curve.tenor = ['3M', '6M', '9M', '12M', '24M', '36M', '48M', '60M', '120M', '180M']
hw1f.fitting_curve.value = [0.0164, 0.0161, 0.0159, 0.0164, 0.0173, 0.0182, 0.0191, 0.0218, 0.0229, 0.0229]
hw1f.alpha_curve.tenor = ['36M']
hw1f.alpha_curve.value = [0.1]
hw1f.sigma_curve.tenor = ['12M', '24M', '36M']
hw1f.sigma_curve.value = [0.01, 0.01, 0.01]
블랙-카라진스키
수식 : dr = a(theta - r) ...
bk1f = xen.BK1F('ir_rate2')
bk1f.fitting_curve.tenor = ['3M', '6M', '9M', '12M', '24M', '36M', '48M', '60M', '120M', '180M']
bk1f.fitting_curve.value = [0.0164, 0.0161, 0.0159, 0.0164, 0.0173, 0.0182, 0.0191, 0.0218, 0.0229, 0.0229]
bk1f.alpha_curve.tenor = ['36M']
bk1f.alpha_curve.value = [0.1]
bk1f.sigma_curve.tenor = ['12M', '24M', '36M']
bk1f.sigma_curve.value = [0.01, 0.01, 0.01]
CIR 1 Factor
수식 : dr = a(theta - r) ...
cir1f = xen.CIR1F('ir_rate2')
cir1f.r0 = 0.03
cir1f.alpha = 0.1
cir1f.longterm = 0.1
cir1f.sigma = 0.01
주식 모형
GBM
수식 : dr = a(theta - r) ...
gbm = xen.GBM('index1')
gbm.x0 = 100
gbm.rf_curve.tenor = ['3M', '6M', '9M', '12M', '24M', '36M', '48M', '60M', '120M', '180M']
gbm.rf_curve.value = [0.0164, 0.0161, 0.0159, 0.0164, 0.0173, 0.0182, 0.0191, 0.0218, 0.0229, 0.0229]
gbm.div_curve.tenor = ['100Y']
gbm.div_curve.value = [0.005]
gbm.sigma_curve.tenor = ['5Y', '100Y']
gbm.sigma_curve.value = [0.3, 0.2]
GBM Const
수식 : dr = a(theta - r) ...
gbm_const = xen.GBMConst('index2')
gbm_const.x0 = 100
gbm_const.rf = 0.03
gbm_const.div = 0.01
gbm_const.sigma = 0.3
GBM LocalVol
수식 : dr = a(theta - r) ...
gbm_localvol = xen.GBMLocalVol('index3')
gbm_localvol.x0 = 100
gbm_localvol.rf_curve.tenor = ['3M', '6M', '9M', '12M', '24M', '36M', '48M', '60M', '120M', '180M']
gbm_localvol.rf_curve.value = [0.0164, 0.0161, 0.0159, 0.0164, 0.0173, 0.0182, 0.0191, 0.0218, 0.0229, 0.0229]
gbm_localvol.div_curve.tenor = ['100Y']
gbm_localvol.div_curve.value = [0.005]
gbm_localvol.sigma_surface.tenor = ['1Y', '2Y', '3Y', '4Y', '5Y', '100Y']
gbm_localvol.sigma_surface.strike = (gbm_localvol.x0 * np.array([0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4])).tolist()
gbm_localvol.sigma_surface.matrix = [[0.3, 0.29, 0.28, 0.27, 0.26, 0.26],
[0.3, 0.29, 0.28, 0.27, 0.26, 0.26],
[0.3, 0.29, 0.28, 0.27, 0.26, 0.26],
[0.3, 0.29, 0.28, 0.27, 0.26, 0.26],
[0.3, 0.29, 0.28, 0.27, 0.26, 0.26],
[0.3, 0.29, 0.28, 0.27, 0.26, 0.26],
[0.3, 0.29, 0.28, 0.27, 0.26, 0.26]]
환율 모형
갈만-콜하겐
수식 : dr = a(theta - r) ...
gk = xen.GarmanKohlhagen(process_name)
gk.sections["X0"] = 100
gk.dom_rf_curve.tenor = ['3M', '6M', '9M', '12M', '24M', '36M', '48M', '60M', '120M', '180M']
gk.dom_rf_curve.value = [0.0164, 0.0161, 0.0159, 0.0164, 0.0173, 0.0182, 0.0191, 0.0218, 0.0229, 0.0229]
gk.for_rf_curve.tenor = ['100Y']
gk.for_rf_curve.value = [0.005]
gk.sigma_curve.tenor = ['5Y', '100Y']
gk.sigma_curve.value = [0.3, 0.2]
상관관계
scen1.refresh_corr()
scen1.set_corr(gbm1, gbm3, 0.3)
scen1.set_corr(gbm1, gbm2, 0.5)
Supposing that $y >= 0$ and that $[\log x]$ represents the integer part of $\log x$, let:
$$\Phi (y) = \frac {1} {2 \pi i} \int_{2 - i \infty}^{2 + i \infty} \frac {y^{\omega} \mathrm{d} \omega} {\omega \left(1 + \frac {\omega} {(\log x)^{1.1}}\right)^{[ \log x ] + 1}}, x > 1$$
Obviously, when $0 <= y <= 1$, there is $\Phi(y) = 0$. For all $y >= 0$, $\Phi(y)$ is a non-decreasing function.
When $\log x>=10^4$ and $y>= e^{2{(\log x)}^{-0.1}}$, thus:
$$1 - x^{- 0.1} <= \Phi (y) <= 1$$