{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Black Scholes valuation methods\n",
"\n",
"[*Black Scholes model WIKI*](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model). \n",
"\n",
"\n",
"The purpose of this notebook is to review the most common algorithms and implement them numerically. \n",
"\n",
"## Contents\n",
" - [European option](#sec1)\n",
" - [Put-Call parity](#sec1.1)\n",
" - [Numerical integration](#sec2)\n",
" - [Monte Carlo method](#sec3)\n",
" - [Binomial tree](#sec4)\n",
" - [Limits of the model](#sec5)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from FMNM.BS_pricer import BS_pricer\n",
"from FMNM.Parameters import Option_param\n",
"from FMNM.Processes import Diffusion_process\n",
"\n",
"import numpy as np\n",
"import scipy.stats as ss\n",
"from scipy.integrate import quad\n",
"from functools import partial\n",
"\n",
"import matplotlib.pyplot as plt\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## European option\n",
"\n",
"Under the Black-Scholes (BS) model, the best method to price a vanilla European option is to use the [BS closed formula](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model).\n",
"\n",
"The **BS formula** for a call is:\n",
"\n",
"$$ C(t,T,S,K,r,\\sigma) = S \\, N(d_1) - K e^{-r(T-t)} N(d_2) $$\n",
"\n",
"with \n",
"\n",
"$$ d_1 = \\frac{1}{\\sigma \\sqrt{T-t}} \\biggl[ \\log \\biggl( \\frac{S}{K} \\biggr) + \\biggl(r + \\frac{\\sigma^2}{2} \\biggr) (T-t) \\biggr] \\quad \\text{and} \\quad d_2 = d_1 - \\sigma \\sqrt{T-t} $$\n",
"\n",
"where $N$ is the cumulative distribution function of a standard normal random variable. \n",
"The formula for a put is similar and can be found in the wiki page.\n",
"\n",
"The value of an option can be also computed as the discounted expectation of a future payoff in this way:\n",
"\n",
"$$\\begin{aligned}\n",
" C(s,K,t, T) &= e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ (S_T - K)^+ \\bigg| S_t=s \\biggr] \\\\\n",
" &= e^{-r(T-t)} \\int_0^{\\infty}\\, (s' - K)^+ \\, f(s'|s) \\, ds' \\\\\n",
" &= e^{-r(T-t)} \\int_K^{\\infty}\\, (s' - K) \\, f(s'|s) \\, ds' \n",
"\\end{aligned}$$\n",
"\n",
"where $f(s'|s)$ is the risk neutral transition probability of the process $\\{S_u\\}_{u\\in [t,T]}$ starting at $S_t=s$. This is a log-normal density function \n",
"\n",
"$$ f(s'|s) = \\frac{1}{s' \\sigma \\sqrt{2\\pi (T-t)}} \\; e^{- \\frac{ \\biggl[\\log(s') - \\bigl(\\log(s) + (r-\\frac{1}{2} \\sigma^2)(T-t) \\bigr) \\biggr]^2}{2\\sigma^2 (T-t)}} $$\n",
"\n",
"\n",
"#### Comment:\n",
"Usually in statistics random variables are indicated by capital letters, and non-random variables are indicated with small letters. However, it is very common to indicate the stock price in the Black-Scholes formula with a capital letter e.g [wiki notation](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#Notation). I'm going to use a capital letters to indicate random variables, and small letters for non random. However there will be exceptions where it will be clear from the context e.g. strike K and maturity T are non random, or $S_0$ most of the time is a fixed variable."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Let us analyze better the previous formulas\n",
"\n",
"\n",
"\n",
"\\begin{align*}\n",
" C(s,t,K,T) &= e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ (S_T - K)^+ \\bigg| S_t=s \\biggr] \\\\\n",
" &= e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ S_T \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] \n",
" - e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ K \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] \\\\\n",
" &= e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ S_T \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] \n",
" - e^{-r(T-t)} K \\, \\underbrace{\\mathbb{Q}\\biggl[ S_T >K \\bigg| S_t=s \\biggr]}_{N(d_2)} \\\\ \n",
"\\end{align*}\n",
"\n",
"Let us introduce the following change of measure (under the stock numeraire):\n",
"\n",
"$$ \\begin{aligned}\n",
"\\frac{d \\tilde{\\mathbb{Q}} }{ d \\mathbb{Q} } &= \\frac{S_T}{\\mathbb{E}^\\mathbb{Q}[S_T | S_t]} = \\frac{S_T}{S_t e^{r(T-t)}} \\\\ \n",
" &= \\frac{S_t e^{(r -\\frac{1}{2}\\sigma^2)(T-t) + \\sigma W_{T-t}} }{S_t e^{r(T-t)}} \\\\\n",
" &= e^{ -\\frac{1}{2}\\sigma^2(T-t) + \\sigma W_{T-t} } \\quad \\text{(exponential martingale)} \n",
"\\end{aligned} $$\n",
"\n",
"By [Girsanov theorem](https://en.wikipedia.org/wiki/Girsanov_theorem), under $\\tilde{\\mathbb{Q}}$ the driving Brownian motion has the new dynamics \n",
"\n",
"$$ \\tilde{W_t} = W_t - \\sigma t $$\n",
"\n",
"and the corresponding stock dynamics becomes\n",
"\n",
"$$\\begin{aligned}\n",
" \\frac{dS_t}{S_t} &= r dt + \\sigma dW_t \\\\\n",
" &= (r+\\sigma^2) dt + \\sigma d\\tilde{W}_t \n",
"\\end{aligned}$$\n",
"\n",
"The first term is\n",
"\n",
"$$ \\begin{aligned}\n",
" e^{-r(T-t)} \\mathbb{E}^{\\mathbb{Q}}\\biggl[ S_T \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] =& e^{-r(T-t)} \\mathbb{E}^{\\tilde{\\mathbb{Q}}} \n",
" \\biggl[ \\frac{d \\mathbb{Q} }{ d \\tilde{\\mathbb{Q}}} S_T \\mathbb{1}_{S_T >K} \\bigg| S_t=s \\biggr] \\\\\n",
" =& e^{-r(T-t)} \\mathbb{E}^{\\tilde{\\mathbb{Q}}} \n",
" \\biggl[ \\frac{e^{r(T-t)}S_t}{S_T} S_T \\mathbb{1}_{S_T > K} \\bigg| S_t=s \\biggr] \\\\ \n",
" =& \\; s \\, \\underbrace{\\tilde{\\mathbb{Q}} ( S_T > K | S_t=s)}_{N(d_1)}\n",
"\\end{aligned}$$\n",
"\n",
"We have just seen how to interpret the terms $N(d_1)$ and $N(d_2)$. These are the risk neutral probabilities of $S_T > K$ in the stock and money market numeraires respectively."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I implemented the BS closed formula in the class `BS_pricer`. \n",
"Let us consider the following set of parameters, that will be recurrent in all the next notebooks. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"S0 = 100.0 # spot stock price\n",
"K = 100.0 # strike\n",
"T = 1.0 # maturity\n",
"r = 0.1 # risk free rate\n",
"sig = 0.2 # diffusion coefficient or volatility"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Call price: 13.269676584660893\n",
"Put price: 3.753418388256833\n"
]
}
],
"source": [
"call = BS_pricer.BlackScholes(\"call\", S0, K, T, r, sig)\n",
"put = BS_pricer.BlackScholes(\"put\", S0, K, T, r, sig)\n",
"print(\"Call price: \", call)\n",
"print(\"Put price: \", put)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"### Put-Call parity\n",
"\n",
"This is an important formula [wiki page](https://en.wikipedia.org/wiki/Put%E2%80%93call_parity)\n",
"\n",
"$$ Call - Put = S_0 - K e^{-rT} $$\n",
"\n",
"Let us check if it works:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"13.269676584660893\n",
"13.269676584660886\n"
]
}
],
"source": [
"print(call)\n",
"print(put + S0 - K * np.exp(-r * T))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## Numerical integration\n",
"\n",
"I want to play a bit with the different formulas written above. \n",
"\n",
"Let us compute the option prices by integrating the log-normal density:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"e_ret = np.log(S0) + (r - 0.5 * sig**2) * T # expected return of the log-price\n",
"vol = sig * np.sqrt(T) # standard deviation of the log-price\n",
"\n",
"\n",
"# log-normal density (defined above)\n",
"def log_normal(x, e_ret, vol):\n",
" return 1 / (x * vol * np.sqrt(2 * np.pi)) * np.exp(-((np.log(x) - e_ret) ** 2) / (2 * vol**2))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8, 5))\n",
"x = np.linspace(30, 190, 100)\n",
"plt.plot(x, log_normal(x, e_ret, vol))\n",
"plt.title(\"Lognormal distribution, conditioned on $S_0=100$\")\n",
"plt.xlabel(\"$S_T$\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The function `log_normal(x, e_ret, vol)` defined above, corresponds to the scipy.stats function: \n",
"```\n",
"ss.lognorm.pdf(x, vol, scale=np.exp(e_ret) ).\n",
"```\n",
"\n",
"In the next calculation, I'm going to use the scipy function. \n",
"Let us perform the integration with the `scipy.integrate` function [quad](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html):"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Call price: 13.269676584660926 \n",
"Put price: 3.753418388256828 \n"
]
}
],
"source": [
"def integrand_LN(S, strike, e_ret, vol, payoff):\n",
" if payoff == \"call\":\n",
" return (S - strike) * ss.lognorm.pdf(S, vol, scale=np.exp(e_ret))\n",
" elif payoff == \"put\":\n",
" return (strike - S) * ss.lognorm.pdf(S, vol, scale=np.exp(e_ret))\n",
"\n",
"\n",
"call = quad(integrand_LN, K, np.inf, args=(K, e_ret, vol, \"call\"))[0] * np.exp(-r * T)\n",
"put = quad(integrand_LN, 0, K, args=(K, e_ret, vol, \"put\"))[0] * np.exp(-r * T)\n",
"\n",
"print(\"Call price: {} \\nPut price: {} \".format(call, put))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The put option payoff $(K-S_T)^+$ is positive for $S_T < K$. \n",
"- In the call case, the integration is from $K$ to $\\infty$.\n",
"- In the put case, the integration is from $0$ to $K$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What if we use the change of measure proposed above? In this way the integrations are simpler. \n",
"Let us compute $\\tilde{\\mathbb{Q}}( S_T > K )$ and $\\mathbb{Q}( S_T > K )$."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Risk neutral probability under stock numeraire,\n",
" Q1 = 0.7257468822499276\n",
"Risk neutral probability under money market numeraire,\n",
" Q2 = 0.6554217416103069\n",
"BS call price: 13.26967658466257\n"
]
}
],
"source": [
"# expected return of the log-price under the new measure\n",
"e_ret_1 = np.log(S0) + (r + 0.5 * sig**2) * T\n",
"\n",
"Q1 = quad(lambda S: ss.lognorm.pdf(S, vol, scale=np.exp(e_ret_1)), K, np.inf)[0]\n",
"print(\"Risk neutral probability under stock numeraire,\\n Q1 =\", Q1)\n",
"Q2 = quad(lambda S: ss.lognorm.pdf(S, vol, scale=np.exp(e_ret)), K, np.inf)[0]\n",
"print(\"Risk neutral probability under money market numeraire,\\n Q2 =\", Q2)\n",
"\n",
"print(\"BS call price: \", S0 * Q1 - K * np.exp(-r * T) * Q2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is quite common to compute the Black-Scholes formula using $N(d_1)$ and $N(d_2)$. \n",
"The reason is that the cumulative function of the standard Normal distribution is more accessible (I guess). In the `BS_pricer` class I used the function `scipy.stats.norm.cdf`. \n",
"\n",
"For completeness, let me recall that if $X_T$ is a Normal random variable, then $S_T = S_0 e^{X_T}$ is Log-Normal. Therefore we have:\n",
"\n",
"$$ \\mathbb{Q}( S_T > K ) = \\mathbb{Q}\\biggl( S_0 e^{X_T} > K \\biggr) = \\mathbb{Q}\\biggl( X_T > \\log \\frac{K}{S_0} \\biggr). $$\n",
"\n",
"This permits to use the Normal cumulative function."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## Monte Carlo method\n",
"\n",
"I'm going to simulate the random variables: \n",
"\n",
"$$ S_T^i = S_0 e^{(r -\\frac{1}{2}\\sigma^2)T + \\sigma W_{T}^i} $$\n",
"\n",
"for $1 \\leq i \\leq N$. \n",
"Then use the approximation for a call option:\n",
"\n",
"$$ \\mathbb{E}^{\\mathbb{Q}}\\biggl[ (S_T - K)^+ \\bigg| S_0 \\biggr] \\; \n",
"\\approx \\; \\frac{1}{N} \\sum_{i=1}^N (S_T^i - K)^+\n",
"$$\n",
"\n",
"For a put option I use this payoff $(K - S_T )^+$ inside the expectation."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(seed=44) # seed for random number generation\n",
"N = 10000000 # Number of random variables\n",
"\n",
"W = ss.norm.rvs((r - 0.5 * sig**2) * T, np.sqrt(T) * sig, N)\n",
"S_T = S0 * np.exp(W)\n",
"\n",
"call = np.mean(np.exp(-r * T) * np.maximum(S_T - K, 0))\n",
"put = np.mean(np.exp(-r * T) * np.maximum(K - S_T, 0))\n",
"call_err = ss.sem(np.exp(-r * T) * np.maximum(S_T - K, 0)) # standard error\n",
"put_err = ss.sem(np.exp(-r * T) * np.maximum(K - S_T, 0)) # standard error"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Call price: 13.263338006636662, with error: 0.005093638687208466\n",
"Put price: 3.7553894006350093, with error: 0.002214066662789331\n"
]
}
],
"source": [
"print(\"Call price: {}, with error: {}\".format(call, call_err))\n",
"print(\"Put price: {}, with error: {}\".format(put, put_err))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### BS_pricer\n",
"\n",
"In the next notebooks I will present better the class `BS_pricer`. But now let's have a look at the prices obtained by different pricing methods:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# Creates the object with the parameters of the option\n",
"opt_param = Option_param(S0=100, K=100, T=1, exercise=\"European\", payoff=\"call\")\n",
"# Creates the object with the parameters of the process\n",
"diff_param = Diffusion_process(r=0.1, sig=0.2)\n",
"# Creates the pricer object\n",
"BS = BS_pricer(opt_param, diff_param)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"13.269676584660893"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"BS.closed_formula()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"13.269676584660623"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"BS.Fourier_inversion()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([13.26753511]), array([0.00294085]), 0.679786205291748)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"BS.MC(N=30000000, Err=True, Time=True)\n",
"# output is: price, standard error and execution time"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"BS.mesh_plt() # PDE method"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The PDE approach is the topic of the notebook **2.1**."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## Binomial tree\n",
"\n",
"\n",
"Of course I cannot forget about the Binomial model!\n",
"This is a simple but very powerful numerical method!\n",
"\n",
"I expect you to be familiar with this model. If not, have a look at the [wiki page](https://en.wikipedia.org/wiki/Binomial_options_pricing_model). \n",
"Although I said I expect you to know the model, I'm not expecting that you have already implemented it! \n",
"Therefore, here I present an efficient implementation:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"BS Tree Price: 13.269537371978052\n"
]
}
],
"source": [
"N = 15000 # number of periods or number of time steps\n",
"payoff = \"call\" # payoff\n",
"\n",
"dT = float(T) / N # Delta t\n",
"u = np.exp(sig * np.sqrt(dT)) # up factor\n",
"d = 1.0 / u # down factor\n",
"\n",
"V = np.zeros(N + 1) # initialize the price vector\n",
"\n",
"# price S_T at time T\n",
"S_T = np.array([(S0 * u**k * d ** (N - k)) for k in range(N + 1)])\n",
"\n",
"a = np.exp(r * dT) # risk free compounded return\n",
"p = (a - d) / (u - d) # risk neutral up probability\n",
"q = 1.0 - p # risk neutral down probability\n",
"\n",
"if payoff == \"call\":\n",
" V[:] = np.maximum(S_T - K, 0.0)\n",
"else:\n",
" V[:] = np.maximum(K - S_T, 0.0)\n",
"\n",
"for i in range(N - 1, -1, -1):\n",
" # the price vector is overwritten at each step\n",
" V[:-1] = np.exp(-r * dT) * (p * V[1:] + q * V[:-1])\n",
"\n",
"print(\"BS Tree Price: \", V[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The stock price on each node of a binomial tree is\n",
"$$ S_n^{(k)} = u^{k} d^{n-k} S_0 \\quad \\text{for} \\quad k \\in \\{ 0, ..., n \\} \\quad \\text{and} \\quad n \\in \\{ 0, ..., N \\}$$\n",
"where the price at $S_n^{(k)}$ is obtained starting from $S_0^{(0)}$ := $S_0$ and applying $k$ up factors and $(n-k)$ down factors. \n",
"\n",
"In a (recombining) binomial tree at each time point $n$ there are $i+1$ nodes.\n",
"The total number of nodes of a binomial tree is\n",
"\n",
"\\begin{align}\n",
" \\sum_{i=0}^N (1+i) &= \\sum_{i=0}^N 1 + \\sum_{i=0}^N i \\\\\n",
" &= (N+1) + N(N+1)/2 \\\\\n",
" &= (N+1)(N+2)/2.\n",
"\\end{align}\n",
"\n",
"Since $u = 1/d$, we can rewrite the formula above as\n",
"$$ S_n^{(k)} = u^{2k - n}\\, S_0 \\quad \\text{for} \\quad k \\in \\{ 0, ..., n \\} \\quad \\text{and} \\quad n \\in \\{ 0, ..., N \\}$$\n",
"\n",
"In this way, we can decrease the number of operations and increase the speed of the program:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2.64 ms ± 37.9 µs per loop (mean ± std. dev. of 10 runs, 20 loops each)\n"
]
}
],
"source": [
"%%timeit -n 20 -r 10\n",
"S_T = np.array([(S0 * u**j * d ** (N - j)) for j in range(N + 1)]) # price S_T at time T"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.59 ms ± 24.1 µs per loop (mean ± std. dev. of 10 runs, 20 loops each)\n"
]
}
],
"source": [
"%%timeit -n 20 -r 10\n",
"S_0N = S0 / u**N\n",
"S_T = np.array([S_0N * u ** (2 * j) for j in range(N + 1)]) # price S_T at time T"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.49 ms ± 25 µs per loop (mean ± std. dev. of 10 runs, 20 loops each)\n"
]
}
],
"source": [
"%%timeit -n 20 -r 10\n",
"S_0N = S0 / u**N\n",
"S_T = np.array([S_0N * u ** (j) for j in range(0, 2 * N + 1, 2)]) # price S_T at time T"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The last approach for the computation of $S_T$ is the fastest."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## Limits of the model"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"BS_sigma = partial(BS_pricer.BlackScholes, \"call\", S0, K, T, r) # binding the function\n",
"sigmas = np.linspace(0.01, 10, 1000)\n",
"\n",
"plt.plot(sigmas, BS_sigma(sigmas))\n",
"plt.xlabel(\"sig\")\n",
"plt.ylabel(\"price\")\n",
"plt.title(\"Black-Scholes price as function of volatility\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The BS formula is an increasing function of the volatility. \n",
"However, for higher volatilities, the graph becomes almost flat!!\n",
"\n",
"We can conclude that the model is reliable for volatilities in the range $0 - 400\\%$.\n"
]
}
],
"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": "3.11.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}