option

Author: bottler

README.md

@@ -3,6 +3,8 @@ Some fairly standalone python scripts
 
 * crank_nicholson: basic Crank-Nicholson solver for a parabolic PDE on an interval
 
+* european_option: demonstrates valuing an option using crank_nicholson
+
 * readSketchnet: tool to read data from the sketch-a-net dataset http://cybertron.cg.tu-berlin.de/eitz/projects/classifysketch/
 
 * oncampus: Should graphs be sent from a warwick computer to the screen or a file.

european_option.py

@@ -0,0 +1,75 @@
+from crank_nicholson import crank_nicholson
+import numpy as np
+from math import log, exp, sqrt
+from scipy.stats import norm
+import scipy
+
+from distutils.version import LooseVersion
+
+if LooseVersion(scipy.__version__)>=LooseVersion("0.18.0"):
+    have_CubicSpline = True
+    from scipy.interpolate import CubicSpline
+else:
+    have_CubicSpline = False
+    from scipy.interpolate import spline
+
+
+def priceOptionBS(term, vol, rate, spot, strike, put=False):
+    fwd = spot * exp(rate*term)
+    d1 = (log(fwd/strike)+0.5*vol*vol*term)/(vol*sqrt(term))
+    d2 = d1-vol*sqrt(term)
+    if put:
+        price = norm.cdf(-d2)*strike*exp(-rate*term) - norm.cdf(-d1)*spot
+        itm_prob = norm.cdf(-d2)
+    else:
+        price = norm.cdf(d1)*spot - norm.cdf(d2)*strike*exp(-rate*term)
+        itm_prob = norm.cdf(d2)
+    return price, itm_prob
+
+def priceEuropeanWithPDE(spot,payoff,gridCentre,stdDevs,term,vol,rate,
+                         do_discounting=True):
+    nx=100
+    nt=100
+    centralLogSpot=log(gridCentre)
+    sd=vol*sqrt(term)
+    minGridLogSpot=centralLogSpot-sd*stdDevs
+    maxGridLogSpot=centralLogSpot+sd*stdDevs
+    logGrid = np.linspace(minGridLogSpot,maxGridLogSpot,nx)
+    payoff_values=payoff(np.exp(logGrid))
+    growth = lambda v: (-rate if do_discounting else 0)*v
+
+    time_0_vals = crank_nicholson(payoff_values,
+                                  maxGridLogSpot-minGridLogSpot,
+                                  term,
+                                  nt,
+                                  0.5*vol*vol,
+                                  rate-0.5*vol*vol,
+                                  growth
+                                  )
+    if have_CubicSpline:
+        val = CubicSpline(logGrid,time_0_vals)(log(spot)).item()
+    else:
+        val = spline(xk=logGrid,yk=time_0_vals,xnew=log(spot)).item()
+    return val
+
+if __name__=="__main__":
+    vol=0.12
+    term = 4
+    rate=0.01
+    spot=100
+    strike=99
+    put=True
+
+    print(priceOptionBS(term,vol,rate,spot,strike,put))
+
+    payoff = lambda x: np.maximum(0,strike-x if put else x-strike)
+    #payoff = lambda x : np.ones_like(x)
+    pde_val = priceEuropeanWithPDE(spot, payoff,
+                                   strike,4,term,vol, rate)
+    itm_payoff = lambda x:(strike>x if put else x>strike)
+    itm_prob = priceEuropeanWithPDE(spot, itm_payoff,
+                                    strike,4,term,vol, rate, False)
+
+    print((pde_val, itm_prob))
+
+