« View all new features in
Mathematica
9
◄
previous
|
next
►
New in
Mathematica
9
›
Time Series and Stochastic Differential Equations
Heston Model
In[5]:=
X
Rasterize[Framed[Show[\!\(\* GraphicsBox[{{}, {{}, {}, {RGBColor[0.24720000000000014`, 0.24, 0.6], LineBox[CompressedData[" 1:eJxV1nlYjWkfB/CEvKp5dQ0yr0y2EylLiUFXfO2UZQglMqFh7CpFY51RWTLI NEPZklJMFOG100ilRR2VspTT6VRnfZ7zPOecytZ4K7/7j/e+rq6ulnPf9+/7 ue/f8/Rfudl7lbmZmVl+61fb9/8fJuzokT5Dvj0Us85a7G9ex36ORIvH8Kmn j5pw2z5KO//2EUTmuy/PdWV//wNnNl4fY3nfiJPx7QP9wmSxDway/z+L0FmX RtQNM0E3v+03iWjpMutlroR9Phm9rZKyEj4ZYVmZFDTeMhUzuZhpDbZsvkto sb5wJ9nViCH+Rx83Ol6G+z/mt50+GGj+dDTkja4552BAcuunK5Ouwk19185z lYHWu4bf7ZL/6/DRALf2cR11/SLO2wwx0Po30LH+u39u9RCR3ejYusJNLC9p GOw6XKD93EKca6ef+vUW4P1lQTQmiTuO2wm0vzswKy1WhD0UIN/eNuFdlJue vlqiEWi/99FZstCxo4uA4LbtBT1AQ/ogaV02T/t/CK8HXg4Hh/L44pCFQvfp F7bnc1RPFhb9dk7bcweHme0L/I0HsmqrG34c1fc3bmelWq6RcmhbrXVJXM7L lhY+0lO92Qi/+5vv2mgO7eVUZmNLZ0k/z3wd1f8E+qtIX/lAh75t27HPwTqv hMqPSVrKIwcbP/j8uPmKGj+tbhu5cMjYfGt0s5ryyYM9fzA86JUGbbP1SM+D 7LUQvd5GS3k9RYEitJOTTIOmtukan+JzRkTsqGQN5ZePxZnX5/Wx1mBC+4QF CAo9MKJlrpryLMBSrzl/LpqgQvv2ogqxwG90svSYivItgpVk+z3rVSo8K2of WJQ53JpbpqK8n6H25xib5BlK9GzfYHFrXQ45E5eqKf9iHNQN1vK8Gu3T+Zdg 0kX5lqOPNOQhRY1PYf34MlaPFF3H1p9IqteQjxQ33SJnYh6rT4p94q2AokMa 8noO/x1mfkPLWL3PEfRtZH5Vrob8nmPJ7BMh2VZaqr8U4yZmWIyaoiPPUoRX 7wquPcNRHqXIfiyeS5vBk28ZJs3bp8hTcpRPGU6YbXWReerJuwzvnFLeRlfy lFc5bBVR9kONHPmX47bNlusHk3jKrxwnn35fEG2np/PwAr6O5mP4RTzl+QLr XMq9fTdwdD5e4NMwmxHb3nOUbwWE6s9xy7/l6bxUINdY4x/wNTvvFZCEcRPN Uzg6P5UYsHx60wIXjvKvxITZlXcGlXJ0nirR+ZFqp9VijjxeIiXpQIL5I448 XqIrPyjOM0VHHi9hN1hSIA3XkcdLvH5nt7LDSJ48XuGD16kutSc58niFourT S/Mm8+TxCqcNysWnbAXyeI3H53qb5pfqEdPu8RoH3FLcMxPZfX+N+F27BtlV C+TxBve9LqYlvBLI402rp7bf3L4iebxBH/WYAx/Gsf5QBVu73cX8JoE8qrBz d8NhryiBPKrgodNZ/JUokkc1PuyfWuo21UAe1RhrObV8QRjrX9XwibEcl8CJ 5PEWxYPibTbxInm8hU23i0P3DBDJ4y3SS5PWOp4TyUMGr9AI0/hwkTxk8I6Z 9bZvRwN5yHB2ZvrAir9E8qjBoeDqtD6jRaqnBlt8E1+uydaTTw0i9ipOlPUR qb4a/Jgxq0/gRoG8avA+8USHOn891VuDjkaL1KxoPfnVYO3sZR03eghUvxxT Alr2LXESyFOO9/f6B6V4ipSHHAkbTsYqXUTylePSJPfUZ3sEykeO4b9IQt8f E8hbDp/aXuL9FSyvWjTHbt3Xyd5A/rUoWJB9fE4yy68WtvFC6pQOBrqftVDO /iptvYHlWYsRrvwhP28DnY9adHJytHfhWL4KLJS8W7Z/sUjnRYGNJevrb8ew vBWtz1Mnm1N5Ip0fBXyaa2KPVIiUvwLdq8Q3F3LYeVKgwvtweORsA3nU4cwc 9PqzyEAedbhYOrKE22MgjzrkX7sQEjjQSB51iHrSLVGmNZJHHXxHnfSQtD4v v3jU4caKvZZp3Y3kUQezNR8L7VcbyKMeobKr/nEDDeRRj/SS4waHGuZRjzjP QCGmdb4vHvUY12v/+KSuRvKox0IhITBgE3s/qMepEQE7Q5aZyKMB6p5Sz8rv TOTRgDMeARW10SbyaID89eOwmBATeTQgYGBLyvd69v7RgIO/vugUGN1IHg3Y tmdBx74WJvJQYm5o/MqWqSbyUKK4saw8dbGRPJQI2ZWQOH2hkTyU8NlWeGdC fyN5KGExzeGa4pmBPJQYX396Tt9uRvJQ4bJVoM56EfNQ4aPzbmcrNfNQoUOT 6s5cd+ahwhnbJRumjGUeKpyPXt1/+xYTeahQlSvlL8xkHir88INz3TdbjeTR +hybOFzmITGShxouHRon3zvC+oUal82SvzEfzTzUCJ6wgDsczPqHGmVZ3cqK Z4vkoYbVTCFvb45AHhr4xVgiYA/rjxr4uqV3Xyhl90ODoF1uyp8fiNQvNdg/ yn2YR092PzSIaHaeXnme9U8NjJ69o4+lsfctLbpnbLbSBbN+qsVzufmqa6EC eWgxLVDvOe8U669apFbIB/w7lt0PLZztD7y9Esvuhxa/z5FcU0lYv9JhYWxg +RCR9SsdMq916X3ag3nosPWEJLhhBXs/1CEww/zqznKRPHSosrBJdnAVyUOH Qm7svCNzRfLQIfoXs/igjaxfc1jtllCQM0skDw5uRX2FFafZ/eCQsjiT/08m 61ccBux0bPQuYf2Kww2Dc7V7CvPgoBp41HHyTebBY8SVkW5ZfzAPHp/mdDvw 7muBPHjstB8/Omwy8+Ch/Jff4HMhzINH8rzS+dObWb/iEfcosvulQHY/9Hjy +eGE0LBG8tBjeM5X7taujeShx7YIedxebSN56KH8qPqck99EHnpsUpRVFT9s Ig894ntGLZXNaCIPAQqL7k1LUxvxP9v5W0k= "]]}, {RGBColor[0.6, 0.24, 0.4428931686004542], LineBox[CompressedData[" 1:eJxV1HtYjHkbB/DedWiRUMJa2uQQ1qENLUpfcliWJOWcdShFWaHsIrxCb46l Xiqh0CiUvJQo5S2dk7Zz6cBMNfM8M9OcnplIeG3lfv54n+uaa66Za+b3+93f z33/xmz3Wb3jGz09vaKuV/f7/z86+A9N+kV02A8bfkpyjF+opc+nUH6rUbf2 kBZPTQPlTk+Dobdq4IL/ufC/vwTXQy1n1+dpEXWl58H8+1saY4/wv4+Gs/+6 DfamOrQ5dX9zE4s/Ocf9Wc2vL0BO7ujk+DAt+tfG7p3XPx62gmEBC/z59e6C W9kyuQ5aTHINedE+MRGPTsXOHZ3G0fpJ0PccNTViGAdB179rY/8DRYCgZbyN hvZ7iCa9ZfLlHhrM6HmSYaRLf5znwtH+KXjJDTpqY88hp31i1w6P0bKoZFv+ PI7O8wQnk0L1V3zLYfXXDSGdNPK2R46GzpeGZw2zzpkHcRAd7l4wHVGfbZem nODovBl4tOFqpWojh33dx9ubibANz/9Z6qeh8z+HSW/J9OgaDb46ZOFm5/TP d735erJwbrPBW9l4Dkt7NshG5ZTUh2M4vr5sRMx8XGm2WIPu3bq2xGT5TusP Xny9OVj/6O69H55p0FNObQ6OPbF2ODiarz8XQ39Kzv2uQYMfuo9jmofODtNS QZKG8sjDtgtW68xNNPD06H7yMdU+3PFJgobyKcDc85lDLQI06F5taFIB1iSO 1e/oUFNehXgxZy3nMEmDd93LtRciwMLowK9v1ZRfEVKnel7xtNLArmfBYhRa 3TTeaKmhPItx5aTW78MIDj3HC3yJ8t/80mde1FC+JTCX6YendmjwqqTnwVIH 30fWe/i8XyHC2aV8RleeJj0HLIXTgLAk0Qu+f0rR+XxFUNgNLXqWc/0Lz7ZG 3/p3Hy15lGGcuVmCZ28d1VOGGrsGwz+NdORThl+8M47EzdZRfWW47WbYb5qt jrzKEflHvE1aqY7qLYfPjhOW3DZ+HsqBJykRVkE6qr8C9hMrhriN1ZFnBUKL Wz1tzXSURwW2rfGwv5qrI99KRIe6pV7boKN8KuE3edNIV1ZL3pWY/9i5/baz jvKqgum6oimhzvz8VUHTOMHOu5Kj/Kqgx3UOzBHx/VCNkEULf02s01Ce1dgX tenJ8wJ+Xqphc6czT/OzlvKtQTh3tyN7k5b6pQbxhv2mmCbz/V6DeY/T3MbU 8v1Ti5Qs86uVxznKvxaCuJI1HWs46qdaJNsZC886cuRRB7fXJ7b/HsnPYx36 bjU6szWVn5c6xI5YFPdKT0seXTdHzPnncQP5+XmNi1+G+J8v4Oe363Or2YPs oxx5vEaAz38Xtadz5FGPtBqDG1kGWlzs8ahHpGD4jX3P+Hmvx3GzdFZsz89b AxIaHIz69uH7tQEZx2eltZ3hyKMBZnb7E5Mk/P3QiOaVH6wN9fl5bESjXf2n wZf5fm7EKMe/RnsW8B5NKM7b/1v/A3x/N+H6wdkuNVt4jyZkfZOnU5/k+/0N htscDj96iiOPN7Bv6P8u+xu+/9/getbHQn9H/r57i9J+QywzD2rI4y2WNl3+ flaNmjze4sLV49cPKdTkIUTmgeUPJelqqkeIAYtU2w/n8vMvhOlY+Y7SHzVU nxAC7+Yxkbc05CVEwaGY9/ln1FSvECubRzwT9laTnxCnLp3zCFqoovpFXf+3 8FxXriRPEfRnvmGrlqooDxG+jftS/IdORb4i9HIw0he9V1I+Itz13fxxtr+a vEWomHUsyW29ivJqxu4LE7xW/6gi/2a0F7OnrD2UlF8z9Fctqx5soKL5bEaj QZHxWxM15dmMg5vkyQ8PqKk/mhHqqLdxQpSa8m3BfSNncauFmvqlBWHFOmcL fRXl3QLfbPs2JkRJ/dOCz+/uxAhlCsq/BbdXXN91115B/dSCiCV2c7jCNvJo xc6oMYY2uTLyaIWToFDj00tGHq3YUmM1XDRQSh6t+MfFJnNmOUserbAdN73P F1uWPFqxZLPVYmtvhjxaISov6gy6zJKHGKdTKu6Nn8aQhxgwOGJk6M6Shxg+ VsYZJuZS8hDjXXCTnlsHSx5iuNy6NjYlhyUPMTYnXT/fHsiQhwTi2GATRSJD HhJkmn28ud9RQh4SHAoRBp8OlJCHBGer/ULYXRLykGCQf9uDlCiGPCR4/dmi 97J0ljwYpDCW7lvvs+TBICf+pe2+TJY8GFS5W0b8y5EhDwZlBa/zyqwZ8mAg bDD+VCCQkAeDsFVmkoOmDHmwSFRK8ls3SsijKxeu0bxX13m/erCwKdztEVvC kAcL+6RdptfDxeTB4uOIPb93FIjJg8WHaTLT85yYPFiY+KomCtaIyUOKYNXu nYL9EvKQ4tw0rxv6jbyHFDNdOxPcnRjykCJ6waXTtQUS8pBiyfRC4Tpfhjyk iLHdNywxmPeQYXBg/Z0AY95DhveNMveEMt5DhunbIutvVTB0X8pwceLyPPcw KXnIkDF35LW1xSx5yLDx+9T4Z68l5CFHTMntp16DGPKQd9037h5z6hjykMPr 9uqh4bUS8pCjcoA4XTyD95Ajr8TJu3whQx5y7FF7W5a/YcmjDXuU17SmV1ny aENCgLjl+AwpebShMM4uP6arH796tCH/c4hD4UuGPNqQfDYq7XQVPx9tGNnv krQmkSWPNujbBp7wPSYlDwXGZ1xz3eEnJQ8F7p3+2O78hfdQwGdUv4DBR1ny UCDviefmPp8Y8lAgP04SOs6Vnw8FhqkKi0wSWPJQQiTYG+0gl5CHEo6Sny/P smXIQ4lH7/pun5PPeyjxndqr1knGkIcSE3wGJ1kO4D2U2HPovqC1VEYeKpRM HRL4IVJOHirMUSSsV96Rk4cKaY1BZ1eayclDBZdS0xmvLsjJQwX/K+8M2fly 8lAhZY99ygNf/r5S483p+YtcCxX4GzEKahk= "]]}, {RGBColor[0.6, 0.5470136627990908, 0.24], LineBox[CompressedData[" 1:eJxV1AdUVFcaB3Bb4oq9xoKFVQmo2BejCH+UCLKIXYhYsKxYE4qggOK6CJio AUQjKqIhoiBYUEBQShRFioAg0tubPjDD9GEAA+4A39tz9p4zZ857M+/e+/1/ 37tG+9w3HxjQr1+/Av2n5/v/hwanxj224/h7Y3DKpISzQ7V0HYQF86JyfzTX In1asGRTeii4dlY1NfHs71eRP9vCoTtSi5s3egcuO2x4N9+T/f9tBC63gk// Nkg39dyJQf+lQYH2Uvb5WFh4hc/M/6SFQdVdD0uDOCyOvhFT/L/5HuD2UION gYvaYLozLEdr8hCN2cYrpfZtNP9jeM0tMAzh6RCrf7rqbhI6Z+UZ5+iv+9Z7 Cgul9OaRf7VjSe9IhuGmmeULr7fT+iloO/BXzvn4DrzRmuhXSIXblae2JXM7 aD9p0OXHPIkKaMfmvgUxomNW9WGfdtrfC8weON56f6UOHP+eCV9i9PEJfyr3 t9N+M7E6ZmrZbI0Onj3b88jCqMr2r+cW62j/2dj73nKeUbUOfQ6v8PxO1cOu nWw9rzCrynbjW0cd1vYu8BrCuG7t7e/YPF/j4vN9YquINvSspl8SpScjbdMs tFTvG6S8EUmPrdeit5yqN4g2PnSv04/N/y3CTyfGjz2vwfSe7UzLxbgWqzEl aRrKIxcP6jQTA25qcNCtZ7zDpKg5tms61ZRPHgbP2TmhyliDntnGPc7DpWsW rv0T1JRXPiwfrU2MZVRo65lOm48sXQY3oVlF+RVAcmPDqrOT1bDqnbAQi74U ypU6NeVZiJBr4zKLNmnQu73g99hXODRu2yYt5VuEpmM/fXYv06C4qHdg1Psh 1g6JGsq7GF98Ei3uLNZgfO8GS5B3X8hfaqCh/EuQvsfDJUmsQu90Oz/g0DLD 4941SvIoRZMk5kzXLQXVUwrb+gE2G+cqyacUwSVfRVvMVlJ9pXibODrqer2C vMogdezKC3JQUr1lWJdTvNblnoL8yjBd/XndvDIF1f8Rr323LG3TP9/n+RER ijFBYeUKyuMjNv9kO/39dQX5lmPpthV/poUpKJ9ynHC8esVZriDvcrz6h0Xh JTcl5fUJcb5/Jd+ZoST/T2AC2vceUSooP/316XMLDUoV1A8VcDvqVhS+Xkl5 VuCRztI4zkVJ/VEB3oqJ92+dUlG+ldiirHDomqGifqmES4Xpby/yVZR3JbRJ y44iW0X9U4XUkFjBwKVqyr8KhjE5af9+oaZ+qkJ8oaAyxF9NHtWoAOdWVwrb X9VQOwVdXaXUkEc18q75Jga1asijGps3GXCbz2nJowZO67+tMdSw50sN4qZk mKRe1ZJHDcozTWwM9Nd9HrUIWB7epHupRXivRy1em3wo5U1oI49aDJ6bvzrV QUMedcjtKBi69ZKaPOowotOu5nGMmjzqoOh8Eq9LV5NHPfYULEoaqa+3z6Me fh8nm6+5wfZzPeI85VMvfFaTRwNq+BsnuRuryaMBv+d2b/30i4o8GrAy5MLo wCbWoxFFH0w8okNYj0YM+f6HD/xTrEcjzhg9y/raiPVowrmGzmbmrpI8mjBk /ORvZ09XkkcTEk76vItWKciDAd90VrJ3PwXVw+D+mAmXXe3Z94XBhuzI89vK 5VQfgxiZ0aJhH+XkxcDcxjDzzfcyqpdBgjbnqOiNlPwYGCDhWE2ClOrnwKjh woJdqa3kycESRfLBixYyyoODUQci/vlHmIx8OTA8fczTf7uc8uFAVXBP6ekl I28O6sKYE5eXySgvLgTGqkFeyXLy58ImJ3Js4A4F5cdF+xc75w8z2feTC35n /62ulkrKkwvHYT5yZRH7vnKxzsNlj+0qNl8eAtOs61PqVNQvPJhufOK1chB7 /vBwupFZeitQRf3DQ2HQV3+T27P58zBpYLEgo7+S+omH9gdhy55msB58jLbI W+xtwXrwYZWyznh9lJQ8+MiDmfvVLzLy4OPanPK8+6dbyYMP7rz0pNmbW8mD jx8N0iudlK3kwUfT2m9uxnuzHgIcbd0gjHSTkocA51ZcskmrkpCHAFa80dPi o1rIQ4DurvQUv0wJeQjQJQoymPBOQh4CDH9d3t9mSgt5CNGulnRkMc3kIcTC xutj4xPF5CFEqFVuc7iPiDyEsJ6+uFbmKyIPIXzPOp5XTxGThxCzkocP/jVD RB4i2G+9P8w7S0AeIkimnKg2HiUkDxFK/li//XKiiDxEOPQ2JGRotIg8RPBb 3pErWCgmD/39Z97xRUIReYjxteo/v6m3ichDjMLJZuKRaiF5iPGD2b3uy6tF 5CHG7RnxiV0CPnmIsS8mNMylQEQeYnDzbj+LchWRhxh7nOqNu8RC8mjGAWc7 n2BvIXk0I/Qmxzp0qpA8mpH92TL491ABeTSj+LuLhiO7+OTRjK7dUZ+Dj/PI oxkRt4bbJ5/kkEcLhqx12hFhzyGPFqTX7cF1Uw55tCAiIHKwVwCHzssWvFii qD1ixyWPFiyfbBpsOZAhjxYMuuHI8ZAy5CFBV1LVlpMBDHlIcGOicb9Vzgx5 SDA6dVJq3Ksm8pBgi3+JZL4nQx4SRBS6epnFMuQhgfvfl5gf9OWQhxRmvvIp Pp0c8tCfM7U+U58O5ZKHFE6doifVVxjykMIkI85lwwiGPKTYVXVhf11LE3lI kZ3t8sJ8YyN5SNHtaX9FOoAhj1bMWP0of6o7Qx6tKIiN/LXjPYc8WuG2JmnY 4hwuebRiZmZ25HFjHnm0otVv595vZKyHfr7nHa925/DIQwbnw4UHB8VwyUMG 83sOtfOfc8lDhsbd+57bPOKShwwjzOp3uQazHjKU3uUuc87ikocMDeqfm89b cclDDmXQS9m4n7nkIYfF4oe2x65xyEMOh6P7/K3153qfhxzbixKGDdjBesiR f8a58bBfE3nIEXLXquCXBQx5KKC7cqBkchSD/wLmfHDo "]]}, {RGBColor[0.24, 0.6, 0.33692049419863584`], LineBox[CompressedData[" 1:eJxV1gtUjekaB3AR4ph0VRIHYUJCJFH+mVwiRc0oQzNIoRGSaIRZdE4mWxcl Z3R0QuokSlLp4lZqIpd0v+1i7277+u3v2zuJqE6X9521zrdWq1V77/fy/J73 /+4ZnoddvUeOGDGidOBn8Pf/Px9wUu/uemFQADpW19cdXNhJ/v4nitelL7F6 2YncaSEyl9wInI2c/KExnb4eg7WRH05/H9aJf8cOPfByNB47l1GR98fjd6eI tyMVKshdBv9zA1YVHzecOkc/n4hrEVlHLew6Mb7upp/t+GR0mdZP2HdFRcZL geF/AtvfvlFhrkfksy7TVIgsz2mUi5Rk/Lv4Jjrr51J7JRIHPl138x5m+G1d zyxXkvkyUBbweXSMkRJLhp5MpEQd4/b+qCTzZ6FxjevEbn8lirpMB2bIhtMc Rl1/rZKsJweLck18W1gOrsMTYn7Pm82hDhxZXx6ux9biuwQOwqDBAfMRrKa3 NPgVR9b7CPkXQ343e8DiyODy/B5Dw3pU+oIyhqz/CXysJkVmu8ox7FAA7Wpb E+QwZD8FsJy9NCcfLByGJihE/6yaBoE7S/ZXCLXz+ZXJ33IYnG1gSpz0OlFR H8qS/RYhPjHb4esFFkPbqSvCvFu7dG0PsGT/xbBqKyjsfMvh74PLmfYnbPQL AzLHcaQef0Kwucdbfy+HfXsHnxKseH/+iN8jltTnOUrY56opcgUGR9O7+xx9 Zb08FyNarxdw2B59ZcVEDh8Hh+t6ga8LEiwaLFhSv1JkJv/hEC9lsGpowJdw avwhrcydIfV8iTlxy38+rctgaHkhr3BLV3PumC1yUt/XKA8UFPq3S/Hm9dAD vzOZ0a07JaTeb3DUcWqgc4kU+kMLLENComfc52MyUv8y8BYHJd23lWNoOI+3 SOn+tnWBi4J4lIPXF3Bzt4+C7Kcce3K9mkPyqE85Oo+Z2CzOUJD9lSNikXUh o8MQrwos2mk36eF6BdlvBXqvqtznFTLErwJ3DEpTGnro/ishvfq1oNhaQTwr cc2hIiOCUZB6VGKX2K1UYyVHfKswMsigb501R+pTBd8cydZnTzniXQXekVta nnzaj9UYZ7jdudOdI/7VWDk57vScmRypXzV0RodoLh9D+6EGHR59OeXaHKln DbJm9W/mxbCkP2rAaBuGzs9gSX1rcaZUT9jSw5J+qUXir7yH75dypN610H7V bO0QxpH+qcPu008tWsM5Uv86xH42k30w50g/1eFd6MbpwQqOeNRjxaEnu2p2 KYlHPV7XcwUGzvT812O97jvb5ztUxKMen4oCElY+UxGPBnwsGdM/9leaVw0w cOGvGZXUSTwawKufIL55oZN4NGLCRoP50f/oxMUhj0bcN171aWu8ing0YtmD 0AVTfqT5wsey2oR1EnMl8eDDb2GAZfkxJfHg4+GIkrRZGkri0QSvuCcL0EE9 mtBkeSe/wJB6NMG5YMkrnznUoxkhjX7ZCyNpnjTjdq1h6rMb1KMZyNfdLjrI EY93MGwoXBc2Q0k83sEpsbJmUjH1eIfQxZGldY40796jKfyET0899XiP+04f pTrR1OM9lvqutTsapSQeAujOjikqW073I0A7010gCafnX4B5xuqzojRo3grg +5xnKxrwHPYSQH/blrHe5nS/Atwx9nGfrEfzQoCNCdc9C//qRyG8rINjXYU0 D4WIF479JXQU7U8hVi3ewjBPaD4Lcar76ynzszTPhHjqFi5z59P8FMLz6NWl 51oZUq8WnNeNtuKb0fPYAtGmOanux+Wkfi2oTvUX5Z6TkfPZgv5+txWLr8lJ PVtgyYxx1oyg57UFmgdDM5hcBalvKyyM0pJPrVSQfmlF+ep0395gltS7FdOa beRevfQ8t+IX3neOpia0/q04tXebW9hxmuetCLfS7rTXouejDWMy7y5ZVk3P exsud6rv98umHm0wkYyrLhfSfmuDd0Fof/9+FfFow74TH8dFfqMiHm3o/lem p9ElJfFoQ2Gxf59tu5J4tCPuZFft9XR6vtpxMiLO2CBYRTza0SLJVt4XKolH O9xPBYaH7KP3bTuuu9h0/C2K3tcD7191Oo11VxKPDlR/uiM7pKskHh1osNTa P3UH7ecO3Mj9sozdSO+/DiSVeiVrCmh/dyCscvpMCwFLPDrw4lNe2eM26iHC ws023hH6NE9F8L/S3MOzoP0vwq3A2maXLOohQlrLcdfloB4iSHnq8RGXaN4O vO5wompRFUs8xOh228PvXssSDzH4Jlr37w3k47CHGE/45yxujKf3sRgeF3XK 1ZpY4iGG1wau20aLng8x7NaMD9knZoiHGOyljgvdhxniIcH+csf+2Ksy4iHB 7erqqsPTZMRDgtSnJpvO3JURDwn8A5M37kyWEw8JgjIPmtkXK4iHBDN0+A9e ZNN8l0Ljh7yaktEc8ZDiS5FekOiv7wdSPDL3CtZMV5C8lMJ+xyaD9IH6D3tI MffatttGI5XEQ4oNU1N25r6m94EMdVu+7xE0Uw8ZLvY765v2Ug8ZZNG/TWtp px4yuCW5N3oM5Muwhwx2LrwjqVNo3sowKsLr3gE1mldyaPloxsn+oB5yTDm7 IkE7g97vcsTgyx4FnyEecjAxXzKbAqmHHOajPyeZpSmIhxz2xif99H6ieSWH us8Jsc4ImlcM7B+Eh/WGK4gHg0etU/NmFiiIB4PsPWcfXyhiiAeD/IAopbVc RjwYXLy+N9YhT048GCQ51cXHimleKXB580+RfTdpXimw+uFE70JTev8qkGJ2 aKvdauqhgJqLuHZ2l4J4DOx7vvZ/rxrR768KbNPYevBMI/VgoZu0u5R3jXqw +K04Z9y6y9SDxQF1YUnxYerBIlbgccZXg54PFi2Olzyj3tK8YqFSm+4yI5ch HhzMDLOMeJly/A9mw2VM "]]}, {RGBColor[0.24, 0.3531726744018182, 0.6], LineBox[CompressedData[" 1:eJxV1ntYzHseB/BsWYQjG4dClLvUQzmVE73dKmFLZMPThEgISWWPbJykDrJE WSqUy+qwSZ0TOd2UkEpMSKLLzDRd5/ab+c3IZdV2+Xz/2N/zzNMzM8338nl9 Pp/v19wvaI3/n/T09Mp6Xr1////R4tCoDFdxeCi8RUeMJd7s/TEYTEp5YWel wwOzaJnng9MQBBz8WbhbR98n4FF159FXrTokJfY9eOt5P3NzJPv/K7DzmtgY YqiD3LP3k6vIihQ+Hm3Afn8DlicirIw+aWFYc33fQsM0LOzcNqjBUEvj3cLn q2tHtG/lMdPnzCPdjHSkpO8vNCvmafwMGMV+Lqi+o8GNnl/XXM+Evn/wiuLF PM2XhRSRiZn7EQ1s+57fsVtwyWGTREPzZyPHZUt9DniU6Gb0zHAPh0+5yH5L 19B6cmDwS5X9aj811vRPCL3q2SecKjla3x8IuaBXL4rkIA7vHTAXGTdvdg6e wNF687HccU7c4jgFgnuXt68AX8sE+e5JClp/IT5vFdYLhijR71AEqbD7zMdV HO2nCNpx684qAzks75ugGCOH3tRErOBof8Vw+S3we/MlHHpn65kS4bk/j4jf xNF+SxCjP3dY/iA1+rZTU4K6AaYltWvUtP/H2OJ4es5XLzUm9i7H7Anst85y NRqlpng8wdHPB38IiFYjYHvv8xRzRbs2ZJSoKT6lCLA0nGS+TI3e0UZllML7 9t/9kr5yFK9n8LayPe8RpsLH3uF0z5B8r8Xq2XwWvzIILpXsCo3l4NQ3YDke Hj7u4WinpniWQz8n98/xQWr0LS+6Ai8FVjcGnlBTfJ/jWsH1rGFmalQ+73uw zL6xctp4DcW7EjOvpAxvmqjB6L4FvoBju41xxhGWPy+QvMct0VGpQd9wPi+B ud2eK1bz5CGEJx/2dVeahvYjRAxSTsbv4MlHiBnmAZXfKjS0PyGWZ7//l8RF S15VMCysixFMZflcBY9Vv6wq9WD5WQUDm/te/xbytP9XCNw2Mf2nwzx5voLk +du4vSY8xeMV3AIb2n1rWD6/RlC4ZfRfrXmKz2uIFtk5bPqoIe/XyDE8lf58 DKufN9jou7XzzDae/N/gXmyzVJGnofi9wfEcoXuFN8uHakg0pi5X2tQUz2rk 7TaJ1N5n+VGNwP/4j5ywQU3xfYvl3b6Tul5ylC9vYdjxsmaflKN4v4X+oYj0 GRdY/tTA5sLe2XHpHMW/BhuLvxWui+con2ogMy+K2N6T//0e73Arw8Lgh10q 8niHR4OXHqjwV5HHO6SpLYL9brJ8e4cVB415RTmrn1r4G3+5V5bH8q8WXf90 XrRPn9VTLZ6mTA0IeqIij/fItHxeHLWXQ1yfx3ukOo9zSvRn+fkeS8ISBAvX s3r7AEMu/dXCJxx5fICp0TzzJdc48viAQKFuh0e+ijzqMKzhQ85uSxV51OHb PzrTT8UqyKMObwoeG3KJSvKox7TUqJVrRnPkUY8pdl0mDqkq8qjHpdnfZeSD I48GlBQ/NT4SzDwaIDfeLPljEPNoQNRdX2lpmYo8GpFhF+U09puKPHrel4QZ WhxhHo3ISf+bl8kX5iGC/rgdk52HsHoUQeqtOHb6Z1b/IuRteWAZ8EZJ+xOh e5Refu0uJXmJUJFwqiokX0n7FWHH7TG3HQo58hPhotHZ1d3nONq/GAOCi9yq g5inGA9tFVbK/Sw/xTAJMCuZM09DvmKMvbV4bWAj6+9ihJQtSHOXsfoTI+/Z uC63o1qKlwTeJryF8TZWjxI0xr6/MCKRp/hJED/XdHOxu5bqU4LpXoKDdy9o KZ4SFEmyf/S+oaX8kEC34HFZVQVP8W1CWdbd6KtRPOVLE0KGDHXzCuYp3k34 GFMxf1kBq+cmXJKEJhdn8hT/JsSZhy7M+8ZTPjVhRYGtammYljykSFlXmGDS qSUPKcb+3qo6sURLHlIUSWVFn1PZ+S6FafiAqEcROvKQYmOyaVTeLC15SLHN se6O1xIdeUjRHF7V6vYXHXk0Y+1q3zNzeZ48mqHuWiQ/a8aTRzOMLMY7+h7i yaMZWfs3pA3dqCWPZjgFD3lbu1dLHs2w9rRRWfWcx/0eLRgcMPScWyjzaMHK mNMjS8Qa8mjBMdOnimsTWb9swX6P/wbIVrL+3oL5y4db679g/bMFl776Oezh mUcrBAP3OSfpa8mjFWGhF+wm5DKPVpTvuWUxa6eWPFrhpy4+7VOtJY9W/Hp7 siZ8ho48WjFVdLnS4aiOPNpw7pgw09ZJRx5tsD8rNz5uxDzasH5g3Pm9nqwf t6H8sU9snB87X9oQ+mn9vQgF689tGH/+/C7r8Tx5tKF6+IEt01148miH67DG l+Jc5tGO4O4JJy9nMI92CCK3/2h7kXm0oygmY09OIvNoR6pxpl7ePObRjvkj hopf17P66IDf68Oy4C4teXQgp9t1R4q7jjw6YFL/Se+ktY76ZQeu3OVG70xi 9dEBwffDlxlMYR4dOHUgIVQTy+5bMhyNvLO40oadbzJkjsnuWLONnc8yJPi0 LP01S0MeMkzOWFmuDNaQhwyRiZW60i5235FhVmAyZ/pATR5yDGh4P8JQzu5n chwsSH9jLWH9So45gpkrj0dz5CFHoWPrd5fF7D4mx6i64ZvKdnLkIUda/aQP P1mxfiUHb2ShnJPN+pUCezcNLJzec170eyggXZDk/MCe9SsFxogarC6K2Hmk QHP2pGezbNj5qsBUH6+QgZFq8lAgN/mAwOkG6+9KaIf6p3tdZvcnJUrtp+93 3c36vRJVppdbtans/FJi0HNT96ynrP8rETV+PD/Sjd1flXjYtcBz7SKOPFSY Ujs63mU1O99UyDY7FDHfgp3XKrxelBM0cbaKPFTYLhA7l/fcZ/s9VHA9dySp eJqcPFQQflF+CJbLyIODZIvdtPCVMvwP78NTtQ== "]]}, {RGBColor[0.6, 0.24, 0.5632658430022722], LineBox[CompressedData[" 1:eJxV1XlUU1ceB3AEHdE6WhR1OIKoxQFXUBEoCl+3UYqiIGPLppY6CIy4URQH z9FRwAWVipUWcFwQBR0rWm0AVxBwgSoCIosIkhAgkISYl7z3CNZ2AvzuH3PP 4eQ8knfv/f0+v9+9k7/ZvjbM1MTEpMz41/f5/0OPvZa5K6RxMRBS/cvfd3P0 nIB7I1fbeCzToWBiotKvIBn2BdL1O8109P1pxC2O2Te2XoeM9P6Bkf+4aVni yn5/DvfdNL4/NnJQ+fX9JxPqU2cfm99j819CRkvh6JQxOgyvy9rhMTwHxR/v rxyp5Gi+qxjsXXHwv2YcpoV8V8w7/ITcGb/Ok4ZyNH8uAqyjOOsLHC4Z367L uol59YvDvDm23s94+rR0gtJXh3n94zbeRKT+zaSM7f8XnD3s4rv/Dx1KeAfj ChJc08zKW7uF7Scfy8Ns9hVKdFg7sCB22ojH5pazeO9AUuPnPapWB2lc34R3 MfVByN9Ljc8D+72PofHNMVF1Ouzs296OBxgUN9TNf5Ke9v8QcuucjmFuOgw4 FGFh9MOPlo9ZPEXo8h+mLT2mhVf/Ao8Q7XXa7pgzi+8Rhs0S4gL36tC3mnFJ 7Ck8Xn3tGUfxliB74Zcl6bs59IdTV4K5+5WGyzu1FH8p+DV/FcwGcbDt287E x5iYVme2s01L+XgMQ9rwLXumcwjf3DeeIL7D88mLQxzl5ykiXq6ZZG/OoW82 y9yncPtwZFax8f2BfD1Do0VybvIQDkLfdPwzVC7aFKNxZr5lmPLTbHcu7z08 +ycsx/xrJ2TZtlrKZzmGyF5VnTeu17+9xF/xOCUy21Wppfw+h8/q+X5bnDi8 eN4/kLpQ5hl6Wkv5foFjVn6h5oM5jO3fYAWiT4b3+nZrKf8VqJ5dseTbExz6 pwt5iWnVNw5LrTjyqMTKvX5H1FM4iqcSOxLG+OgX6MinEq7+w7UrwvQUXyXO jFrV9vQlT15V0BZlBbwexFO8VXjzm3LYpgo9+VVhSLqtXGzSU/zVSCpzcZdU 6smzGh7FEfvX7+QpH9U4LDcb0ezEk+8rbBgRgFt/Fig/ryBTh/ylqFUg71ew PJdlKhnRQ/mqQa6J1/NFTr3kX4PElLBdhyw+UP5qkPTo88aKYR+oHl5j0pyN t39b1kv5fI0rkj2ZY58ZqD5eY0NtdLd3eA/ltxZ2E74wMdzqoXqpRf2O8l7B zkD5rkVwk1XOd7sMVD91kJXdCbjtYqD812H3vBove42B6qkOG30L5+ZF9ZJH PUS3aenWHgbyqIfK8cSZNK1IHvUYXSv77LlUJI96hPnF2py5LpJHA+4nSh0C dQJ5NCDVPsg+861IHg2om7ngumKkSB5vcLo67OzVABEn+z3eIDB8nWOOZQ95 vMHTk/LtUVMN5NGIFO+hmaeUPeTRiKTO6MWq2B7yaIR9sNb2Wo5IHm+RUzY5 +5ajSB5vEesqjtx0WCCPtzho7RZeYSqQRxOs3e3uJRp48mjChfkmS1MTBPJo QuLNg0kOGoE8mlFu/8kfh+eI5NGMu0NCLJoOiuTRjGb39KP2CoE83sF3Q+X5 cUt48jA+39W/TbDmyeMdnFI4u+dr9eTRgnFBl7s99ugpnhb4/W455rKdnnxa UPik4Z8F0ex+acGGl/O3xPJ68mrB2G///eaE8Xkg3ha4aO+ecp/Bk18LQl9J vlce4Cl+KZpwdvUPPqy/pPjYpLwTCJYPKdQxe6vil7N+k+K5+a5H72x4yo8U S26HbPYqZP0nRUHGcIdBm/WULxmWTp92qrdIR/4yrM9wD2tX6yl/MuwfGZ8S /Iz1p/H3G/xTi4ay81yGGYeOWt5L1FN9yBDkMK1mjvF+HchvKzKj66svp+ip Xlph8XvOZucpLN+tKOa9pySU81Q/rXAsc90gD2b5b0Xw2PNOaSY81VMrnpX6 2DZb8eQhx9bcsR2/aZiHHDZBr+Kz8piHHNwcXeVND+YhR/64rS5aB5485Nij uCtG9jAPOTK7ipy/jmUecsy8EntpTQarxzYk+lid/hcvkEcbXkRMTJ0nF8ij DQnnIiRffcL6rQ3mB26argGr1zZo9kXtsPMUyKMNkwLntFw8z5NHO3JD2lxD F/Hk0Q7dmNWZX3vx5NFuvE+nKyeqePJoR/XbcuuPewXyaMfjo0NEKNj52Q4k f/HII5LVewcWrKqw+o+XQB4dyK4vi8w1vj/g0YEsdZVk+wJ2vnYgJ9/XMv8O 8+jANdHKpf0G8+iAPurMwZ5ZzEMB021Bqw3hAnkosOTjLt2Ebp48FLhSanth wmuePBRQFF7vHKJiHgrM+sqmeLwDOw8U8A+N2mG6kHkosH2FpGpai548OmGy +2LyliOsPzpxdKtn85YrrD86sXBy9gGXUtYfnfjeI73NW68nj06sdbg/NCuE J49O+LSMCJnYzDy6EFSZaC2zF8ijC0/yI0cczxHIowuPtpl3Nozn6bzsgkrq 6S71Y/3RhUUfnCuXRjKPLnwaIa7MP86ThxIt21U3LipYfyjBpzTGJyr15KHE zJoH0qtxrD+UuCPfWHL1gkAeSnjIpFHVm9n9pwQXNDxo/ByBPFTI3vci1U3C k4cKk86XbE8+IJCHCvKyWymfmrPzWAXHgNIkTbpAHiosXxuS8U09Tx4qpH50 GVNpXG/AQ4XOQw0HigNZf6gx+0vTh84r2P2jxta0cRaeV1l/qDFq2aUmsxrW H2pEbVb7J2SJ5KHGn5wkhx1H9ZCHGr+UrLKI+UEkj25s7B01OPBndl91G8/v 0KmVbey874bq/metsy3Z/dWNEYs7gvev6CGPbpzzW9zuLBfJoxshmim3a/NE 8tAg/NiDsHVxInloMDppeZ5nmkgeGvz4wXVbuB277zS4HL1u9eebeshDg6CK gGzH9yJ5aHDD9sqaikkG8ngPW6fsgjWcAf8DgcFe7Q== "]]}}, {}}, AspectRatio->0.6180339887498948, Axes->True, AxesLabel->{None, None}, AxesOrigin->{0, 0.4736458597280765}, ImageSize->250, Method->{}, PlotLabel->FormBox["\"Volatility of the asset\"", TraditionalForm], PlotRange->{{0, 1.}, {0.4736458597280765, 1.6917786203203786`}}, PlotRangeClipping->True, PlotRangePadding->{{0.02, 0.02}, {0.024362655211846045`, 0.024362655211846045`}}]\), ImageSize -> {144, 82}, AspectRatio -> 76/144, LabelStyle -> {FontSize -> 6}, PlotLabel -> Style["Volatility", FontFamily -> "Helvetica", 10, GrayLevel[.2]], Ticks -> False], FrameStyle -> GrayLevel[203/255], FrameMargins -> 2], "Image"]
Define an
ItoProcess
corresponding to the correlated 2D Wiener process.
In[1]:=
X
cW[\[Rho]_] := ItoProcess[{{0, 0}, IdentityMatrix[2]}, {{w1, w2}, {0, 0}}, t, {{1, \[Rho]}, {\[Rho], 1}}];
Define a Heston model by SDEs driven by the correlated 2D Wiener process.
In[2]:=
X
hm = ItoProcess[{ \[DifferentialD]s[t] == \[Mu] s[t] \[DifferentialD]t + Sqrt[r[t]] s[t] \[DifferentialD]Subscript[w, s][t], \[DifferentialD]r[ t] == \[Kappa] (\[Theta] - r[t]) \[DifferentialD]t + \[Xi] Sqrt[ r[t]] \[DifferentialD]Subscript[w, \[Nu]][t]}, {s[t], r[t]}, {{s, r}, {Subscript[s, 0], Subscript[r, 0]}}, t, {Subscript[w, s], Subscript[w, \[Nu]]} \[Distributed] cW[\[Rho]]];
Simulate the model using a stochastic Runge-Kutta scheme.
In[3]:=
X
td = BlockRandom[SeedRandom[1988]; RandomFunction[ hm /. {\[Mu] -> 0, \[Kappa] -> 2, \[Theta] -> 1, \[Xi] -> 1/2, \[Rho] -> -1/3, Subscript[s, 0] -> 25, Subscript[r, 0] -> 1.25}, {0, 1, 0.005}, 6, Method -> "StochasticRungeKutta"]];
Visualize the sample paths.
In[4]:=
X
Row[{ListLinePlot[td["PathComponent", 1], PlotLabel -> "Price of the asset", ImageSize -> 250], ListLinePlot[td["PathComponent", 2], PlotLabel -> "Volatility of the asset", ImageSize -> 250]}, Spacer[20]]
Out[4]=