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+ + + + + + + + + +
+ + diff --git a/variance_swap.ipynb b/variance_swap.ipynb new file mode 100644 index 0000000..0c4c304 --- /dev/null +++ b/variance_swap.ipynb @@ -0,0 +1,398 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Variance Swap for Heston Model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Model Setting\n", + "\n", + "### 1.1 Heston model\n", + "$$\n", + "\\left\\{\\begin{matrix}\n", + " dS_t=\\mu S_t dt+\\sqrt{v_t}S_t dB_t^S\\\\\n", + " dv_t=\\kappa(\\theta-v_t)dt+\\sigma_V\\sqrt{v_t}dB_t^V\n", + "\n", + "\\end{matrix}\\right.\n", + "$$\n", + "\n", + "$(dB_t^S,dB_t^V)=\\rho dt$\n", + "\n", + "Accordding to Heston (1993), these can be transfered to a risk-neutral probability measure:\n", + "$$\n", + "\\left\\{\\begin{matrix}\n", + " dS_t=\\mu S_t dt+\\sqrt{v_t}S_t d\\tilde B_t^S\\\\\n", + " dv_t=\\kappa^*(\\theta^*-v_t)dt+\\sigma_V\\sqrt{v_t}d\\tilde B_t^V\n", + "\n", + "\\end{matrix}\\right.\n", + "$$\n", + "\n", + "$\\kappa^*=\\kappa+\\lambda,\\quad \\theta^*=\\frac{\\kappa\\theta}{\\kappa+\\lambda}$\n", + "where $\\lambda$ is the premium of volatility risk\n", + "\n", + "\n", + "### 1.2 Variance Swap\n", + "the value of a variance swap at expiry:\n", + "$$\n", + "V_T=(\\sigma_R^2-K_{VAR})\\times L\n", + "$$\n", + "\n", + "- $\\sigma^2:$ annualized realized variance\n", + "- $K_{var}:$ annualized delivery price\n", + "- $L:$ notional amount of swap\n", + "\n", + "in risk neutral world: $V_t=E_t^Q[e^{-r(T-t)}(\\sigma_R^2-K_{var})L]$, therefore fair variance delivery price: $K_{var}=E_0^Q[\\sigma_R^2]$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Method Existed in PyFENG\n", + "**Method existed in PyFeng using log-return to calculate realized variance**\n", + "$$\n", + "K_{var}:=\\frac{1}{T}\\sum_{i=1}^N E[(ln\\frac{S_{t_{i+1}}}{S_{t_{t}}})^2]\n", + "$$\n", + "- `strike_var_swap_analytic()` function in heston.HestonABC()\n", + " - refers: Analytic fair strike of variance swap. Eq (11) in Bernard & Cui (2014)\n", + "- `return_var_realized()` function in heston_mc.HestonMcABC()\n", + " \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Method Added \n", + "Refer to [Bernard C, Cui Z (2014) Prices and Asymptotics for Discrete Variance Swaps. Applied Mathematical Finance 21:140–173. https://doi.org/10.1080/1350486X.2013.820524]() \n", + "and \n", + "[Song-Ping Zhu, Guang-Hua Lian (2011) A Closed-form Exact Solution for Pricing Variance Swaps with Stochastic Volatility]()\n", + "\n", + "where the realized variance is caculated by:\n", + "$$\n", + "K_{var}:=\\frac{1}{T}\\sum_{i=1}^N E[(\\frac{S_{t_{i+1}}}{S_{t_{t}}}-1)^2]\n", + "$$\n", + "\n", + "We implemented \n", + "- (eq 2.34) in Zhu & Lian (2011) \n", + "- (Proposition3.2) in Bernard & Cui (2014)\n", + "- percentage change return from MC method" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3.1 (eq 2.34) in Zhu & Lian (2011) \n", + "The fair strike price for the variance swap is given as:\n", + "$$K_{var}=E_0^Q[\\sigma_R^2]=\\frac{e^{r\\Delta t}}{T}[f(v_0)+\\sum_{i=2}^Nf_i(v_0)]$$\n", + "where r is interest rate, $\\Delta t$ is defined as $\\frac{T}{N}$ and N is the number of obersavation days.\n", + "\n", + "Function $f(v_0)$ and $f_i(v_0)$ are defined as:\n", + "$$f(v)=e^{\\tilde C(\\Delta t)+\\tilde D(\\Delta t)v}+e^{-r\\Delta t}-2$$\n", + "$$\\begin{aligned}f_{i}(v_{0})&=e^{\\tilde{C}(\\Delta t)+\\frac{c_{i}e^{-\\kappa^{*}t_{i-1}}}{c_{i}-\\tilde{D}(\\Delta t)}\\tilde{D}(\\Delta t)v_{0}}(\\frac{c_{i}}{c_{i}-\\tilde{D}(\\Delta t)})^{\\frac{2\\kappa^{*}\\theta^{*}}{\\sigma_{V}^{2}}}+e^{-r\\Delta t}-2\\end{aligned}$$\n", + "where $t_i = i\\Delta t$, and $\\kappa^{*}, \\theta^{*}, \\sigma_{V}$ are the parameters of Heston model under risk-neutral probability measure.\n", + "\n", + "Function $\\tilde{C}(\\Delta t)$ and $\\tilde{D}(\\Delta t)$ are derived from the generalized Fourier transform method which is used to solving the PDE of payoff. $\\tilde{C}(\\Delta t)$ and $\\tilde{D}(\\Delta t)$ are defined as:\n", + "$$\\left\\{\\begin{array}{ll}\\widetilde C(\\tau)=r\\tau+\\frac{\\kappa^*\\theta^*}{\\sigma_V^2}[(\\widetilde a+\\widetilde b)\\tau-2\\ln(\\frac{1-\\widetilde ge^{\\widetilde b\\tau}}{1-\\widetilde g})]\\\\\\\\\\widetilde D(\\tau)=\\frac{\\widetilde a+\\widetilde b}{\\sigma_V^2}(\\frac{1-e^{\\widetilde b\\tau}}{1-\\widetilde ge^{\\widetilde b\\tau}})\\\\\\\\\\widetilde a=\\kappa^*-2\\rho\\sigma_V,\\quad\\widetilde b=\\sqrt{\\widetilde a^2-2\\sigma_V^2},\\quad\\widetilde g=(\\frac{\\widetilde a}{\\sigma_V})^2-1+(\\frac{\\widetilde a}{\\sigma_V})\\sqrt{(\\frac{\\widetilde a}{\\sigma_V})^2-2}\\\\\\end{array}\\right.$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 3.2 (Proposition3.2) in Bernard & Cui (2014)\n", + "\n", + "$t_i=\\frac{iT}{n},i=0,1,...,n$, $\\Delta = T/n$, $\\alpha=2\\kappa\\theta/\\gamma^2-1\\geq 0$,\n", + "\n", + "Payoff $\\frac{1}{T}\\sum_{i=0}^{n-1}(\\frac{S_{t_{i+1}-S_{t_i}}}{S_{t_i}})^2$ equals to\n", + "$$\n", + "K_{var}(n) = \\frac{1}{T}(a_0+\\sum_{i=1}^{n-1}a_i)+\\frac{n-2ne^{r\\Delta}}{T}\n", + "$$\n", + "\n", + "$a_i=\\frac{e^{2r\\Delta}}{S_0^2}M(2,\\Delta)e^{q(2)V_0(\\frac{\\eta(t_i)e^{-\\kappa t_i}}{\\eta(t_i)-q(2)}01)}(\\frac{\\eta(t_i)}{\\eta(t_i)-q(2)})^{\\alpha+1}$\n", + "\n", + "where:\n", + "\n", + "$M(u,t)=E[e^{uX_t}]=S_0^u e^{\\frac{\\kappa\\theta}{\\gamma^2}((\\kappa-\\gamma\\rho u-d(u))t-2 ln(\\frac{1-g(u)e^{-d(u)t}}{1-g(u)}))}e^{V_0\\frac{\\kappa-\\gamma\\rho u-d(u)t}{\\gamma}\\frac{1-e^{-d(u)t}}{1-g(u)e^{-d(u)t}}}$\n", + "\n", + "$d(u)=\\sqrt{(\\kappa-\\gamma\\rho u)^2+\\gamma^2(u-u^2)}$\n", + "\n", + "$g(u)=\\frac{\\kappa-\\gamma\\rho u-d(u)}{\\kappa-\\gamma\\rho u+d(u)}$\n", + "\n", + "$q(u)=\\frac{\\kappa-\\gamma\\rho u -d(u)}{\\gamma}\\frac{1-e^{-d(u)\\Delta}}{1-g(u)e^{-d(u)\\Delta}}$\n", + "\n", + "$\\eta(u)=\\frac{2\\kappa}{\\gamma^2}(1-e^{-\\kappa u})^{-1}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### 3.3 MC\n", + "- added `return_pctvar_realized()` function in `heston_mc.py` to calcuate annualized variance" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 4. Experiments" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import sys\n", + "sys.path.insert(sys.path.index('')+1, r'C:\\Users\\LXY\\Desktop\\研究生课程\\ASP\\PyFENG')\n", + "import pyfeng as pf\n", + "import time\n", + "import numpy as np\n", + "import pandas as pd" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# model parameters\n", + "kwargs = {'sigma': 0.04, 'vov': 0.618, 'rho': -0.64, 'mr': 11.35, 'theta': 0.022, 'intr': 0.1}" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "Model = pf.HestonMcGlassermanKim2011(**kwargs)\n", + "CMCModel = pf.HestonMcAndersen2008(**kwargs)\n", + "BasicModel = pf.heston_mc.HestonMC(**kwargs)" + ] + }, + { + "attachments": { + "image-3.png": { + "image/png": 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" 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Result in Zhu & Lian\n", + "\n", + "table for $\\sigma_R^2=\\frac{1}{T}\\sum_{i=1}^N(\\frac{S_{t_i}}{S_{t_{i-1}}}-1)^2*100^2$\n", + "![image.png](attachment:image.png)\n", + "![image-3.png](attachment:image-3.png)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "starting simulation for dt = 0.25\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Zhu Lian's formula: 0.02632143084055675\n", + "Bernard Cui's formula: 0.02632143084055727\n", + "MC realized variance: 0.02599842698142366\n", + "MC realized variance std: 0.022263423919459322\n", + "time for Zhu Lian's formula: 0.0\n", + "time for Bernard Cui's formula: 0.0\n", + "time for MC simulation: 0.5713779926300049\n", + "----------------------------------\n", + "starting simulation for dt = 0.08333333333333333\n", + "Zhu Lian's formula: 0.024272086521686692\n", + "Bernard Cui's formula: 0.024272086521682112\n", + "MC realized variance: 0.02454482468030889\n", + "MC realized variance std: 0.015362925269449046\n", + "time for Zhu Lian's formula: 0.0\n", + "time for Bernard Cui's formula: 0.002378702163696289\n", + "time for MC simulation: 2.0986223220825195\n", + "----------------------------------\n", + "starting simulation for dt = 0.038461538461538464\n", + "Zhu Lian's formula: 0.023858347847937673\n", + "Bernard Cui's formula: 0.02385834784793417\n", + "MC realized variance: 0.02400852592320885\n", + "MC realized variance std: 0.012004495787884473\n", + "time for Zhu Lian's formula: 0.0\n", + "time for Bernard Cui's formula: 0.0010807514190673828\n", + "time for MC simulation: 5.90369176864624\n", + "----------------------------------\n", + "starting simulation for dt = 0.019230769230769232\n", + "Zhu Lian's formula: 0.023710973687990612\n", + "Bernard Cui's formula: 0.02371097368799724\n", + "MC realized variance: 0.023524935278655516\n", + "MC realized variance std: 0.009724459359170328\n", + "time for Zhu Lian's formula: 0.0012946128845214844\n", + "time for Bernard Cui's formula: 0.003013134002685547\n", + "time for MC simulation: 13.704880475997925\n", + "----------------------------------\n" + ] + } + ], + "source": [ + "times_zhu = []\n", + "times_bern = []\n", + "times_exactmc = []\n", + "times_cmc = []\n", + "times_mc = []\n", + "analytic_zhu = []\n", + "analytic_bern = []\n", + "exactmc_mean = []\n", + "cmc_mean = []\n", + "mc_mean = []\n", + "exactmc_std = []\n", + "cmc_std = [] \n", + "mc_std = []\n", + "\n", + "for dt in [1/4, 1/12, 1/26, 1/52]:\n", + " print('starting simulation for dt = ', dt)\n", + "\n", + " # analytic variance of Zhu's formula\n", + " start_time = time.time()\n", + " analytic_Zhu = Model.strike_var_swap_analytic_ZhuLian(texp=1, dt=dt)\n", + " end_time = time.time()\n", + " time_Zhu = end_time-start_time\n", + "\n", + " # analytic variance of Bernard Cui's formula\n", + " start_time = time.time()\n", + " analytic_Bern = Model.strike_var_swap_analytic_pctreturn(texp=1, dt=dt)\n", + " end_time = time.time()\n", + " time_Bern = end_time-start_time\n", + "\n", + " # get mc realized variance and time the simulation\n", + " CMCModel.set_num_params(dt=dt,n_path=200000)\n", + " start_time = time.time()\n", + " vars = CMCModel.return_pctvar_realized(texp=1)\n", + " mean_cmc = np.mean(vars)\n", + " std_cmc = np.std(vars)\n", + " end_time = time.time()\n", + " time_cmc = end_time-start_time\n", + "\n", + " Model.set_num_params(dt=dt,n_path=200000)\n", + " start_time = time.time()\n", + " vars = Model.return_pctvar_realized(texp=1)\n", + " mean_exactmc = np.mean(vars)\n", + " std_exactmc = np.std(vars)\n", + " end_time = time.time()\n", + " time_exactmc = end_time-start_time\n", + "\n", + " BasicModel.set_num_params(dt=dt,n_path=200000)\n", + " start_time = time.time()\n", + " vars = BasicModel.return_pctvar_realized(texp=1)\n", + " mean_mc = np.mean(vars)\n", + " std_mc = np.std(vars)\n", + " end_time = time.time()\n", + " time_mc = end_time-start_time\n", + "\n", + " \n", + "\n", + " # print results\n", + " print('Zhu Lian\\'s formula: ', analytic_Zhu)\n", + " print('Bernard Cui\\'s formula: ', analytic_Bern)\n", + " print('MC realized variance: ', mean_mc)\n", + " print('CMC realized variance: ', mean_cmc)\n", + " print('ExactMC realized variance: ', mean_exactmc)\n", + " print('MC realized variance std: ', std_mc)\n", + " print('CMC realized variance std: ', std_cmc)\n", + " print('ExactMC realized variance std: ', std_exactmc)\n", + " print('time for Zhu Lian\\'s formula: ', time_Zhu)\n", + " print('time for Bernard Cui\\'s formula: ', time_Bern)\n", + " print('time for MC simulation: ', time_mc)\n", + " print('time for CMC simulation: ', time_cmc)\n", + " print('time for ExactMC simulation: ', time_exactmc)\n", + " print('----------------------------------')\n", + " \n", + " analytic_zhu.append(analytic_Zhu)\n", + " analytic_bern.append(analytic_Bern)\n", + " cmc_mean.append(mean_cmc)\n", + " cmc_std.append(std_cmc)\n", + " times_zhu.append(time_Zhu)\n", + " times_bern.append(time_Bern)\n", + " times_cmc.append(time_cmc)\n", + "\n", + " time.sleep(1)\n", + " \n", + "res = pd.DataFrame({'dt': [1/4, 1/12, 1/26, 1/52], 'analytic_zhulian': analytic_zhu, 'analytic_bern': analytic_bern,\\\n", + " 'mc_mean': mc_mean, 'mc_std': mc_std, 'cmc_mean': cmc_mean, 'cmc_std': cmc_std, 'exactmc_mean': exactmc_mean, 'exactmc_std': exactmc_std, \\\n", + " 'time_ZhuLian': times_zhu, 'time_Bern': times_bern,'time_mc': times_mc, 'time_cmc': times_cmc, 'time_exactmc': times_exactmc})\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " dt analytic_zhulian analytic_bern mc_mean mc_std time_ZhuLian \\\n", + "0 0.250000 0.026321 0.026321 0.025998 0.022263 0.000000 \n", + "1 0.083333 0.024272 0.024272 0.024545 0.015363 0.000000 \n", + "2 0.038462 0.023858 0.023858 0.024009 0.012004 0.000000 \n", + "3 0.019231 0.023711 0.023711 0.023525 0.009724 0.001295 \n", + "\n", + " time_Bern time_mc \n", + "0 0.000000 0.571378 \n", + "1 0.002379 2.098622 \n", + "2 0.001081 5.903692 \n", + "3 0.003013 13.704880 \n" + ] + } + ], + "source": [ + "# good format for printing dataframe res\n", + "pd.options.display.float_format = '{:.6f}'.format\n", + "print(res)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.9" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 5bacd4fbbde3a0094873ef44d1b70cfa00b34661 Mon Sep 17 00:00:00 2001 From: Loiser Date: Thu, 18 Apr 2024 23:40:41 +0800 Subject: [PATCH 2/5] Add files via upload --- variance_swap.ipynb | 111 +++++++++++++++++++++++++++++--------------- 1 file changed, 74 insertions(+), 37 deletions(-) diff --git a/variance_swap.ipynb b/variance_swap.ipynb index 0c4c304..0338587 100644 --- a/variance_swap.ipynb +++ b/variance_swap.ipynb @@ -133,11 +133,18 @@ ] }, { + "attachments": { + "image.png": { + "image/png": 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" + } + }, "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3 MC\n", - "- added `return_pctvar_realized()` function in `heston_mc.py` to calcuate annualized variance" + "- added `return_pctvar_realized()` function in `heston_mc.py` to calcuate annualized variance\n", + "![image.png](attachment:image.png)\n", + "- take $v_t=max(0,v_t)$" ] }, { @@ -203,54 +210,72 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "starting simulation for dt = 0.25\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ + "starting simulation for dt = 0.25\n", "Zhu Lian's formula: 0.02632143084055675\n", "Bernard Cui's formula: 0.02632143084055727\n", - "MC realized variance: 0.02599842698142366\n", - "MC realized variance std: 0.022263423919459322\n", + "MC realized variance: 0.03487467662551381\n", + "CMC realized variance: 0.026499679482084662\n", + "ExactMC realized variance: 0.026408175790440937\n", + "MC realized variance std: 0.0340573875616237\n", + "CMC realized variance std: 0.019607639030466525\n", + "ExactMC realized variance std: 0.019721473127171013\n", "time for Zhu Lian's formula: 0.0\n", "time for Bernard Cui's formula: 0.0\n", - "time for MC simulation: 0.5713779926300049\n", + "time for MC simulation: 0.04999995231628418\n", + "time for CMC simulation: 0.10651612281799316\n", + "time for ExactMC simulation: 0.5356192588806152\n", "----------------------------------\n", "starting simulation for dt = 0.08333333333333333\n", "Zhu Lian's formula: 0.024272086521686692\n", "Bernard Cui's formula: 0.024272086521682112\n", - "MC realized variance: 0.02454482468030889\n", - "MC realized variance std: 0.015362925269449046\n", + "MC realized variance: 0.027859771492387844\n", + "CMC realized variance: 0.024006852994623754\n", + "ExactMC realized variance: 0.024261866608035636\n", + "MC realized variance std: 0.016591855073948374\n", + "CMC realized variance std: 0.013544965155115338\n", + "ExactMC realized variance std: 0.013922716579114067\n", "time for Zhu Lian's formula: 0.0\n", - "time for Bernard Cui's formula: 0.002378702163696289\n", - "time for MC simulation: 2.0986223220825195\n", + "time for Bernard Cui's formula: 0.0\n", + "time for MC simulation: 0.16114234924316406\n", + "time for CMC simulation: 0.30265140533447266\n", + "time for ExactMC simulation: 2.113616704940796\n", "----------------------------------\n", "starting simulation for dt = 0.038461538461538464\n", "Zhu Lian's formula: 0.023858347847937673\n", "Bernard Cui's formula: 0.02385834784793417\n", - "MC realized variance: 0.02400852592320885\n", - "MC realized variance std: 0.012004495787884473\n", + "MC realized variance: 0.025531523731592523\n", + "CMC realized variance: 0.02376758593632581\n", + "ExactMC realized variance: 0.023829697436999395\n", + "MC realized variance std: 0.011737187050216128\n", + "CMC realized variance std: 0.011328117771315259\n", + "ExactMC realized variance std: 0.011355118099651793\n", "time for Zhu Lian's formula: 0.0\n", - "time for Bernard Cui's formula: 0.0010807514190673828\n", - "time for MC simulation: 5.90369176864624\n", + "time for Bernard Cui's formula: 0.002004384994506836\n", + "time for MC simulation: 0.32060742378234863\n", + "time for CMC simulation: 0.6337699890136719\n", + "time for ExactMC simulation: 5.688959836959839\n", "----------------------------------\n", "starting simulation for dt = 0.019230769230769232\n", "Zhu Lian's formula: 0.023710973687990612\n", "Bernard Cui's formula: 0.02371097368799724\n", - "MC realized variance: 0.023524935278655516\n", - "MC realized variance std: 0.009724459359170328\n", - "time for Zhu Lian's formula: 0.0012946128845214844\n", - "time for Bernard Cui's formula: 0.003013134002685547\n", - "time for MC simulation: 13.704880475997925\n", + "MC realized variance: 0.024499030904000817\n", + "CMC realized variance: 0.023652189836766483\n", + "ExactMC realized variance: 0.023470922083224946\n", + "MC realized variance std: 0.00974403768485489\n", + "CMC realized variance std: 0.009863110682746281\n", + "ExactMC realized variance std: 0.00949484562057157\n", + "time for Zhu Lian's formula: 0.0005068778991699219\n", + "time for Bernard Cui's formula: 0.002004384994506836\n", + "time for MC simulation: 0.7216520309448242\n", + "time for CMC simulation: 1.268726110458374\n", + "time for ExactMC simulation: 13.508999109268188\n", "----------------------------------\n" ] } @@ -330,39 +355,51 @@ " \n", " analytic_zhu.append(analytic_Zhu)\n", " analytic_bern.append(analytic_Bern)\n", + " exactmc_mean.append(mean_exactmc)\n", + " exactmc_std.append(std_exactmc)\n", + " mc_mean.append(mean_mc)\n", + " mc_std.append(std_mc)\n", " cmc_mean.append(mean_cmc)\n", " cmc_std.append(std_cmc)\n", " times_zhu.append(time_Zhu)\n", " times_bern.append(time_Bern)\n", " times_cmc.append(time_cmc)\n", + " times_exactmc.append(time_exactmc)\n", + " times_mc.append(time_mc)\n", "\n", " time.sleep(1)\n", " \n", "res = pd.DataFrame({'dt': [1/4, 1/12, 1/26, 1/52], 'analytic_zhulian': analytic_zhu, 'analytic_bern': analytic_bern,\\\n", - " 'mc_mean': mc_mean, 'mc_std': mc_std, 'cmc_mean': cmc_mean, 'cmc_std': cmc_std, 'exactmc_mean': exactmc_mean, 'exactmc_std': exactmc_std, \\\n", + " 'mc_mean': mc_mean, 'cmc_mean': cmc_mean,'exactmc_mean': exactmc_mean, 'mc_std': mc_std, 'cmc_std': cmc_std, 'exactmc_std': exactmc_std, \\\n", " 'time_ZhuLian': times_zhu, 'time_Bern': times_bern,'time_mc': times_mc, 'time_cmc': times_cmc, 'time_exactmc': times_exactmc})\n" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - " dt analytic_zhulian analytic_bern mc_mean mc_std time_ZhuLian \\\n", - "0 0.250000 0.026321 0.026321 0.025998 0.022263 0.000000 \n", - "1 0.083333 0.024272 0.024272 0.024545 0.015363 0.000000 \n", - "2 0.038462 0.023858 0.023858 0.024009 0.012004 0.000000 \n", - "3 0.019231 0.023711 0.023711 0.023525 0.009724 0.001295 \n", + " dt analytic_zhulian analytic_bern mc_mean cmc_mean exactmc_mean \\\n", + "0 0.250000 0.026321 0.026321 0.034875 0.026500 0.026408 \n", + "1 0.083333 0.024272 0.024272 0.027860 0.024007 0.024262 \n", + "2 0.038462 0.023858 0.023858 0.025532 0.023768 0.023830 \n", + "3 0.019231 0.023711 0.023711 0.024499 0.023652 0.023471 \n", + "\n", + " mc_std cmc_std exactmc_std time_ZhuLian time_Bern time_mc time_cmc \\\n", + "0 0.034057 0.019608 0.019721 0.000000 0.000000 0.050000 0.106516 \n", + "1 0.016592 0.013545 0.013923 0.000000 0.000000 0.161142 0.302651 \n", + "2 0.011737 0.011328 0.011355 0.000000 0.002004 0.320607 0.633770 \n", + "3 0.009744 0.009863 0.009495 0.000507 0.002004 0.721652 1.268726 \n", "\n", - " time_Bern time_mc \n", - "0 0.000000 0.571378 \n", - "1 0.002379 2.098622 \n", - "2 0.001081 5.903692 \n", - "3 0.003013 13.704880 \n" + " time_exactmc \n", + "0 0.535619 \n", + "1 2.113617 \n", + "2 5.688960 \n", + "3 13.508999 \n" ] } ], From f27130242ff3d68df7c2fb3de02d1c6d70cd53c8 Mon Sep 17 00:00:00 2001 From: Loiser Date: Thu, 18 Apr 2024 23:41:58 +0800 Subject: [PATCH 3/5] Update heston_mc.py --- pyfeng/heston_mc.py | 115 +++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 114 insertions(+), 1 deletion(-) diff --git a/pyfeng/heston_mc.py b/pyfeng/heston_mc.py index 12bbe1a..5e7fb0e 100644 --- a/pyfeng/heston_mc.py +++ b/pyfeng/heston_mc.py @@ -179,7 +179,7 @@ def cond_log_return_var(self, dt, var_0, var_t, avgvar): mean_ln = self.rho / self.vov * ((var_t - var_0) + self.mr * dt * (avgvar - self.theta)) \ + (self.intr - self.divr - 0.5 * avgvar) * dt sigma_ln2 = (1.0 - self.rho**2) * dt * avgvar - return mean_ln**2 + sigma_ln2 + return mean_ln**2 + sigma_ln2 def draw_log_return(self, dt, var_0, var_t, avgvar): """ @@ -199,6 +199,25 @@ def draw_log_return(self, dt, var_0, var_t, avgvar): ln_sig = np.sqrt((1.0 - self.rho**2) * dt * avgvar) zn = self.rv_normal(spawn=5) return ln_m + ln_sig * zn + + def draw_pct_return(self, dt, var_0, var_t, avgvar): + """ + Samples log return, (S_t/S_0)-1 + + Args: + dt: time step + var_0: initial variance + var_t: final variance + avgvar: average variance + + Returns: + pct return + """ + ln_m = self.rho/self.vov * ((var_t - var_0) + self.mr * dt * (avgvar - self.theta)) \ + + (self.intr - self.divr - 0.5 * avgvar) * dt + ln_sig = np.sqrt((1.0 - self.rho**2) * dt * avgvar) + zn = self.rv_normal(spawn=5) + return np.exp(ln_m + ln_sig * zn)-1 def return_var_realized(self, texp, cond=False): """ @@ -239,6 +258,46 @@ def return_var_realized(self, texp, cond=False): var_0 = var_t return var_r / texp # annualized + + def return_pctvar_realized(self, texp, cond=False): + """ + Annualized realized return variance + + Args: + texp: time to expiry + cond: use conditional expectation without simulating price + + Returns: + + """ + tobs = self.tobs(texp) + n_dt = len(tobs) + dt = np.diff(tobs, prepend=0) + + var_r = np.zeros(self.n_path) + var_0 = np.full(self.n_path, self.sigma) + + tmp = self.rho/self.vov*self.mr - 0.5 + + for i in range(n_dt): + var_t, avgvar_inc, extra = self.cond_states_step(dt[i], var_0) + + if self.correct_martingale: + pois_avgvar_v = extra.get('pois_avgvar_v', None) + if pois_avgvar_v is not None: # missing variance: + var_r += (tmp*dt[i])**2 * pois_avgvar_v + qe_m_corr = extra.get('qe_m_corr', 0.0) + else: + qe_m_corr = 0.0 + + if cond: + var_r += np.exp(self.cond_log_return_var(dt[i], var_0, var_t, avgvar_inc))-1 + else: + var_r += (np.exp(self.draw_log_return(dt[i], var_0, var_t, avgvar_inc))-1 + qe_m_corr) ** 2 + + var_0 = var_t + + return var_r / texp # annualized def gamma_lambda(self, dt, kk=0): """ @@ -772,6 +831,60 @@ def cond_states_step(self, dt, var_0): return var_t, avgvar, {} +class HestonMC: + """ + Heston model with Monte-Carlo simulation + + Naive MC for Heston model based on Euler-Maruyama discretization scheme + + Underlying price follows a geometric Brownian motion, and variance of the price follows a CIR process. + + References: + - Song-Ping Zhu∗, Guang-Hua Lian(2011) SA Closed-form Exact Solution for Pricing Variance Swaps with Stochastic Volatility + """ + def __init__(self, **kwargs) -> None: + default_kwargs = {'sigma': 0.04, 'vov': 0.618, 'rho': -0.64,\ + 'mr': 11.35, 'theta': 0.022, 'intr': 0.1} + for key, value in default_kwargs.items(): + setattr(self, key, kwargs.get(key, value)) + + def set_num_params(self,dt=1/4,n_path=200000): + self.dt = dt + self.n_path = n_path + + def return_pctvar_realized(self, texp): + """ + Annualized realized return variance + + Args: + texp: time to expiry + Returns: + """ + n_dt = int(texp / self.dt) + dt = texp / n_dt + + var_r = np.zeros(self.n_path) + var_0 = np.full(self.n_path, self.sigma) + + for i in range(n_dt): + var_t, z1 = self.cond_states_step(dt, var_0) + var_r += (self.draw_pct_return(dt, var_0, z1) ) ** 2 + var_0 = var_t + + return var_r / texp # annualized + + def cond_states_step(self, dt, var_0): + z1 = np.random.normal(size=self.n_path) + z2 = np.random.normal(size=self.n_path) + zz = self.rho * z1 + np.sqrt(1 - self.rho**2) * z2 + var_t = var_0 + self.mr * (self.theta - var_0) * dt + np.sqrt(abs(var_0)) * self.vov * zz * np.sqrt(dt) + var_t = np.maximum(var_t, 0) + return var_t, z1 + + def draw_pct_return(self, dt, var_0, z1): + res = self.intr*dt+np.sqrt(abs(var_0))*z1*np.sqrt(dt) + return res + class HestonMcAndersen2008(HestonMcABC): """ From 6c80ab4a803a878a5cd0383f6d2b09367993cd18 Mon Sep 17 00:00:00 2001 From: Loiser Date: Fri, 19 Apr 2024 11:54:07 +0800 Subject: [PATCH 4/5] Update heston.py --- pyfeng/heston.py | 129 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 129 insertions(+) diff --git a/pyfeng/heston.py b/pyfeng/heston.py index c0847f3..87f1666 100644 --- a/pyfeng/heston.py +++ b/pyfeng/heston.py @@ -120,6 +120,135 @@ def strike_var_swap_analytic(self, texp, dt): return strike + def strike_var_swap_analytic_pctreturn(self, texp, dt): + """ + Analytic fair strike of variance swap. Proposition3.2 in Bernard & Cui (2014) + + Args: + texp: time to expiry + dt: observation time step (e.g., dt=1/12 for monthly) For continuous monitoring, set dt=0 + must in the form of 1/n for some integer n + + Returns: + Fair strike + + References: + - Bernard C, Cui Z (2014) Prices and Asymptotics for Discrete Variance Swaps. Applied Mathematical Finance 21:140–173. https://doi.org/10.1080/1350486X.2013.820524 + + """ + n = int(texp/dt) + delta = dt + kappa = self.mr + theta = self.theta + gamma = self.vov + rho = self.rho + V0 = self.sigma + r = self.intr + S0 = 1 + + + alpha = 2*kappa*theta/gamma**2-1 + + def d(u): + res = np.sqrt((kappa-gamma*rho*u)**2 + (u - u*2)*gamma**2) + return res + + def g(u): + res = (kappa - gamma*rho*u - d(u))/(kappa - gamma*rho*u + d(u)) + return res + + def q(u): + res = ((kappa - gamma*rho*u - d(u))/(gamma**2))*(1 - np.exp(-d(u)*delta))/(1 - g(u)*np.exp(-d(u)*delta)) + return res + + def eta(u): + res = (2*kappa)/((gamma**2)*(1 - np.exp(-u*kappa))) + return res + + def M(u,t): + e1 = np.exp((kappa*theta/gamma**2)*((kappa - gamma*rho*u - d(u))*t - 2*np.log((1 - g(u)*np.exp(-d(u)*t))/(1 - g(u))))) + e2 = np.exp(V0*(kappa-gamma*rho*u-d(u))*(1 - np.exp(-d(u)*t))/(gamma**2*(1 - g(u)*np.exp(-d(u)*t)))) + res = (S0**u)*e1*e2 + return res + + def ai(ti): + e1 = np.exp(q(2)*V0*(eta(ti)*np.exp(-kappa*ti)/(eta(ti)-q(2))-1)) + e2 = (eta(ti)/(eta(ti)-q(2)))**(alpha+1) + res = np.exp(2*r*delta)*M(2, delta)*e1*e2/(S0**2) + return res + + def K(n): + res = 0 + a = np.exp(2*r*delta)*M(2, delta)/S0**2 + res += a + for i in range(1,n): + ti = i*delta + res += ai(ti) + res = res/texp + (n-2*n*np.exp(r*delta))/texp + return res + + return K(n) + + def strike_var_swap_analytic_ZhuLian(self, texp, dt): + """ + Analytic fair strike of variance swap. eq (2.34) Lian & Zhu (2011) + + Args: + texp: time to expiry + dt: observation time step (e.g., dt=1/12 for monthly) For continuous monitoring, set dt=0 + must in the form of 1/n for some integer n + + Returns: + Fair strike + + References: + - Song-Ping Zhu, Guang-Hua Lian (2011) A Closed-form Exact Solution for Pricing Variance Swaps with Stochastic Volatility + + """ + kappa = self.mr + theta = self.theta + rho = self.rho + sigma_V = self.vov + v0 = self.sigma + r = self.intr + N = int(texp/dt) + T = texp + + def C_D_calculation(): + tilde_a = kappa - 2 * rho * sigma_V + tilde_b = np.sqrt(tilde_a ** 2 - 2 * sigma_V ** 2) + tilde_g = (tilde_a / sigma_V) ** 2 - 1 + (tilde_a / sigma_V) * np.sqrt((tilde_a / sigma_V) ** 2 - 2) + + term1 = r * dt + term2 = (kappa * theta) / (sigma_V ** 2) + term3 = (tilde_a + tilde_b) * dt + term4 = 2 * np.log((1 - tilde_g * np.exp(tilde_b * dt)) / (1 - tilde_g)) + + C = term1 + term2 * (term3 - term4) + + D = ((tilde_a + tilde_b) / sigma_V ** 2) * ((1 - np.exp(tilde_b * dt)) / (1 - tilde_g * np.exp(tilde_b * dt))) + return C, D + + def f(): + C, D = C_D_calculation() + return np.exp(C + D * v0) + np.exp(-r * dt) - 2 + + def sum_fi(): + C, D = C_D_calculation() + sum = 0 + for i in range(2, N + 1): + c_i = 2 * kappa / (sigma_V ** 2 * (1 - np.exp(-kappa * (i - 1) * dt))) + term1 = np.exp(C + c_i * np.exp(-kappa * (i - 1) * dt) / (c_i - D) * D * v0) + term2 = (c_i / (c_i - D)) ** (2 * kappa * theta / (sigma_V ** 2)) + sum += term1 * term2 + np.exp(-r * dt) - 2 + return sum + + + f_v0 = f() + sum_fi_v0 = sum_fi() + K_var = (np.exp(r * dt) / T) * (f_v0 + sum_fi_v0) + return K_var + class HestonUncorrBallRoma1994(HestonABC): """ From fc0cce2b742de7480ea2df33530b72fc2a9a83d2 Mon Sep 17 00:00:00 2001 From: Loiser Date: Fri, 19 Apr 2024 11:58:30 +0800 Subject: [PATCH 5/5] Add files via upload --- variance_swap.ipynb | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) diff --git a/variance_swap.ipynb b/variance_swap.ipynb index 0338587..50ff6be 100644 --- a/variance_swap.ipynb +++ b/variance_swap.ipynb @@ -203,8 +203,12 @@ "source": [ "#### Result in Zhu & Lian\n", "\n", - "table for $\\sigma_R^2=\\frac{1}{T}\\sum_{i=1}^N(\\frac{S_{t_i}}{S_{t_{i-1}}}-1)^2*100^2$\n", + "In Zhu & Lian's paper: \n", + "table3.1 for $\\sigma_R^2=\\frac{1}{T}\\sum_{i=1}^N(\\frac{S_{t_i}}{S_{t_{i-1}}}-1)^2*100^2$\n", "![image.png](attachment:image.png)\n", + "\n", + "\n", + "But Bernard & Cui's paper, they find the result for dt=1/4 in above table from Zhu & Lian's paper is not the same as their exact results. Our experient shows Bernard's number 263.2 is right.\n", "![image-3.png](attachment:image-3.png)" ] }, @@ -401,6 +405,14 @@ "2 5.688960 \n", "3 13.508999 \n" ] + }, + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mThe Kernel crashed while executing code in the the current cell or a previous cell. Please review the code in the cell(s) to identify a possible cause of the failure. Click here for more info. View Jupyter log for further details." + ] } ], "source": [