add Black-Scholes examples

examples/stocks/options/black-scholes.kg

@@ -0,0 +1,20 @@
+.pyf("math";["erf" "sqrt"]);.pyf("numpy";["log" "sqrt" "exp"])
+
+:" normal cdf "
+ncdf::{(1+erf(x%sqrt(2)))%2}
+
+:" Option delta computed via Black-Scholes "
+optiondelta::{[s k r t iv];s::x@0;k::x@1;r::x@2;t::x@3;iv::x@4;ncdf((log(s%k)+(r+0.5*iv^2)*t)%(iv*sqrt(t)))}
+
+:" Option price computed via Black-Scholes "
+d::optiondelta([[100] [100] [0.05] [1] [0.2]])
+.d("expecting: 0.6368306511756191 computed: ");.p(d)
+
+d1fn::{(log(s%k)+(r+0.5*iv^2)*t)%(iv*sqrt(t))}
+d2fn::{d1-iv*sqrt(t)}
+pricefn::{(s*ncdf(d1))-(k*exp((-r)*t)*ncdf(d2))}
+optionprice::{[s k r t iv d1 d2];s::x@0;k::x@1;r::x@2;t::x@3;iv::x@4;d1::d1fn();d2::d2fn();pricefn()}
+
+d::optionprice([100 100 0.05 1 0.2])
+.d("expecting: 10.4506 computed: ");.p(d)
+

examples/stocks/options/black-scholes.py

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+import numpy as np
+import math
+#from scipy.stats import norm
+
+
+def _get_option_delta(s, k, r, t, sigma):
+    d1 = (np.log(s / k) + (r + 0.5 * sigma ** 2) * t) / (sigma * np.sqrt(t))
+    delta = norm.cdf(d1)
+    return delta
+
+def _get_option_price(s, k, r, t, sigma):
+    d1 = (np.log(s / k) + (r + 0.5 * sigma ** 2) * t) / (sigma * np.sqrt(t))
+    d2 = d1 - sigma * np.sqrt(t)
+    option_price = s * norm.cdf(d1) - k * np.exp(-r * t) * norm.cdf(d2)
+    return option_price
+
+def norm_cdf(x, mu=0, sigma=1):
+    #return (1 + np.erf((x - mu) / (sigma * np.sqrt(2)))) / 2
+    return (1 + math.erf(x / math.sqrt(2))) / 2 
+
+def get_option_delta(s, k, r, t, sigma):
+    d1 = (np.log(s / k) + (r + 0.5 * sigma ** 2) * t) / (sigma * np.sqrt(t))
+    #delta = norm.cdf(d1)
+    delta = norm_cdf(d1)
+    return delta
+
+def get_option_price(s, k, r, t, sigma):
+    d1 = (np.log(s / k) + (r + 0.5 * sigma ** 2) * t) / (sigma * np.sqrt(t))
+    d2 = d1 - sigma * np.sqrt(t)
+    #option_price = s * norm.cdf(d1) - k * np.exp(-r * t) * norm.cdf(d2)
+    option_price = s * norm_cdf(d1) - k * np.exp(-r * t) * norm_cdf(d2)
+    return option_price
+
+
+def test_get_option_delta():
+    assert np.isclose(get_option_delta(100, 100, 0.05, 1, 0.2), 0.6368306511756191, rtol=1e-5)
+
+def test_get_option_price():
+    assert np.isclose(get_option_price(100, 100, 0.05, 1, 0.2), 10.4506, rtol=1e-4)
+
+test_get_option_delta()
+test_get_option_price()
+
+from py_vollib.black_scholes import black_scholes
+from py_vollib.black_scholes.greeks.analytical import delta
+
+
+def test_get_option_delta():
+    s = 100
+    k = 100
+    r = 0.05
+    t = 1
+    sigma = 0.2
+    expected_delta = delta('c', s, k, t, r, sigma)
+    assert np.isclose(get_option_delta(s, k, r, t, sigma), expected_delta, rtol=1e-5)
+
+def test_get_option_price():
+    s = 100
+    k = 100
+    r = 0.05
+    t = 1
+    sigma = 0.2
+    expected_price = black_scholes('c', s, k, t, r, sigma)
+    assert np.isclose(get_option_price(s, k, r, t, sigma), expected_price, rtol=1e-4)
+
+
+test_get_option_delta()
+test_get_option_price()
+