def up_call(s0,x,T,r,sigma,n_simulation,barrier):
"""
Objective: output up_and_out_call and
up_and_in_call
"""
import scipy as sp
import p4f
n_steps=100.
dt=T/n_steps
inTotal=0
outTotal=0
for j in range(0, n_simulation):
sT=s0
inStatus=False
outStatus=True
for i in range(0,int(n_steps)):
e=sp.random.normal()
sT*=sp.exp((r-0.5*sigma*sigma)*dt+sigma*e*sp.sqrt(dt))
if sT>barrier:
outStatus=False
inStatus=True
#print 'sT=',sT
#print 'j=',j ,'out=',out
if outStatus==True:
outTotal+=p4f.bs_call(s0,x,T,r,sigma)
else:
inTotal+=p4f.bs_call(s0,x,T,r,sigma)
return outTotal/n_simulation, inTotal/n_simulation
def up_call(s0, x, T, r, sigma, n_simulation, barrier):
import scipy as sp
import p4f
n_steps = 100.
dt = T / n_steps
inTotal = 0
outTotal = 0
for j in range(0, n_simulation):
sT = s0
inStatus = False
outStatus = True
for i in range(0, int(n_steps)):
e = sp.random.normal()
sT *= sp.exp((r - 0.5 * sigma * sigma) * dt +
sigma * e * sp.sqrt(dt))
if (sT > barrier):
outStatus = False
inStatus = True
#print 'sT=',sT
#print 'j=', j, 'out=',out
if outStatus == True:
outTotal += p4f.bs_call(s0, x, T, r, sigma)
else:
inTotal += p4f.bs_call(s0, x, T, r, sigma)
return outTotal / n_simulation, inTotal / n_simulation
def upCall(s, x, T, r, sigma, nSimulation, barrier):
import scipy as sp
import p4f
n_steps = 100
dt = T / n_steps
inTotal = 0
outTotal = 0
for j in range(0, nSimulation):
sT = s
inStatus = False
outStatus = True
for i in range(0, int(n_steps)):
e = sp.random.normal()
sT *= sp.exp((r - 0.5 * sigma * sigma) * dt +
sigma * e * sp.sqrt(dt))
if sT > barrier:
outStatus = False
inStatus = True
if outStatus == True:
outTotal += p4f.bs_call(s, x, T, r, sigma)
else:
inTotal += p4f.bs_call(s, x, T, r, sigma)
return outTotal / nSimulation, inTotal / nSimulation
def up_and_out_call(s0,x,T,r,sigma,n_simulation,barrier):
n_steps=100.
dt=T/n_steps
total=0
for j in range(0, n_simulation):
sT=s0
out=False
for i in range(0,int(n_steps)):
e=sp.random.normal()
sT*=sp.exp((r-0.5*sigma*sigma)*dt+sigma*e*sp.sqrt(dt))
if sT>barrier:
out=True
if out==False:
total+=p4f.bs_call(s0,x,T,r,sigma)
return total/n_simulation
def up_and_out_call(s0,x,T,r,sigma,n_simulation,barrier):
n_steps=100.
dt=T/n_steps
total=0
for j in range(0,n_simulation):
sT=s0
out=False
for i in range(0,int(n_steps)):
e=sp.random.normal()
sT*=sp.exp((r-0.5*sigma*sigma)*dt+sigma*e*sp.sqrt(dt))
if ssT>barrier:
out=True
if out ==False:
total+=p4f.bs_call(s0,x,T,r,sigma)
return total/n_simulation
def lookback_min_price_as_strike(s,T,r,sigma,n_simulation):
n_steps=100.
dt=T/n_steps
total=0
for j in range(n_simulation):
min_price=100000.
sT=s
for i in range(int(n_steps)):
e=sp.random.normal()
sT*=sp.exp((r-0.5*sigma*sigma)*dt+sigma*e*sp.sqrt(dt))
if sT<min_price:
min_price=sT
#print 'j=',j,'i=',i,'total=',total
total+=p4f.bs_call(s,min_price,T,r,sigma)
return total/n_simulation
def lookback_min_price_as_strike(s, T, r, sigma, n_simulation):
n_steps = 100.
dt = T / n_steps
total = 0
for j in range(n_simulation):
min_price = 100.
sT = s
for i in range(int(n_steps)):
e = sp.random.normal()
sT *= sp.exp((r - 0.5 * sigma * sigma) * dt +
sigma * e * sp.sqrt(dt))
if sT < min_price:
min_price = sT
#print 'j=',j,'i=',i,'total=',total
total += p4f.bs_call(s, min_price, T, r, sigma)
return total / n_simulation
import matplotlib.pyplot as plt
#
s = 9.25 # stock price at time zero
x = 9.10 # exercise price
barrier = 10.5 # barrier
T = 0.5 # maturity date (in years)
n_steps = 30 # number of steps
r = 0.05 # expected annual return
sigma = 0.2 # volatility (annualized)
sp.random.seed(125) # seed()
n_simulation = 5 # number of simulations
#
dt = T / n_steps
S = sp.zeros([n_steps], dtype=float)
time_ = range(0, int(n_steps), 1)
c = p4f.bs_call(s, x, T, r, sigma)
sp.random.seed(124)
outTotal, inTotal = 0., 0.
n_out, n_in = 0, 0
for j in range(0, n_simulation):
S[0] = s
inStatus = False
outStatus = True
for i in time_[:-1]:
e = sp.random.normal()
S[i + 1] = S[i] * sp.exp((r - 0.5 * pow(sigma, 2)) * dt +
sigma * sp.sqrt(dt) * e)
if S[i + 1] > barrier:
outStatus = False
inStatus = True
for j in range(0, n_simulation):
sT = s0
inStatus = False
outStatus = True
for i in range(0, int(n_steps)):
e = sp.random.normal()
sT *= sp.exp((r - 0.5 * sigma * sigma) * dt +
sigma * e * sp.sqrt(dt))
if (sT > barrier):
outStatus = False
inStatus = True
#print 'sT=',sT
#print 'j=', j, 'out=',out
if outStatus == True:
outTotal += p4f.bs_call(s0, x, T, r, sigma)
else:
inTotal += p4f.bs_call(s0, x, T, r, sigma)
return outTotal / n_simulation, inTotal / n_simulation
s0 = 40.
x = 40.
barrier = 42
T = 0.5
r = 0.05
sigma = 0.2
n_simulation = 100
upoutCall, upInCall = up_call(s0, x, T, r, sigma, n_simulation, barrier)
print 'upOutCall=', round(upoutCall, 2), 'upinCall=', round(upInCall, 2)
print 'Black-Scholes call', round(p4f.bs_call(s0, x, T, r, sigma), 2)
# -*- coding: utf-8 -*- """ Name : c10_31_plot_call_vs_one_inut.py Book : Python for Finance (2nd ed.) Publisher: Packt Publishing Ltd. Author : Yuxing Yan Date : 6/6/2017 email : [email protected] [email protected] """ import numpy as np import p4f as pf import matplotlib.pyplot as plt s0 = 30 T0 = 0.5 sigma0 = 0.2 r0 = 0.05 x0 = 30 sigma = np.arange(0.05, 0.8, 0.05) T = np.arange(0.5, 2.0, 0.5) call_0 = pf.bs_call(s0, x0, T0, r0, sigma0) call_sigma = pf.bs_call(s0, x0, T0, r0, sigma) call_T = pf.bs_call(s0, x0, T, r0, sigma0) plt.plot(sigma, call_sigma, 'b') plt.plot(T, call_T) plt.show()
import p4f
sT = arange(20,70,5)
s=40;x=40;T1=0.5;T2=1;sigma=0.3;r=0.05
payoff=(abs(sT-x)+sT-x)/2
call_01 = p4f.bs_call(s,x,T1,r,sigma) #short
call_02=pdf.bs_call(s,x,T2,r,sigma) # long
profit_01=payoff-call_01
call_03=pdf.bs_call(sT,x,(T2-T1),r,sigm)
calender_spread=call_03-payoff+call_01 -call_02
y0=zeros(len(sT))
ylim(-20,20)
xlim(20,60)
plot(sT,call_03,'b-.')
plot(sT,call_02-call_01-payoff,'b-.')
plot(sT,calender_spread,'r')
plot([x,x],[-20,-15])
title("Calender spread with calls")
xlabel('Stock price at maturity (sT)')
ylabel('Profit (loss)')
plt.annotate('Buy a call with T1 and sell a call with T2', xy=(25,16))
plt.annotate('where T1<T2', xy=(25,14))
plt.annotate('Calender spread', xy=(25,-3), xytext=(22,-15),
arrowprops=dict(facecolor='red',shrink=0.01),)
plt.annotate('Value of the call (T2) at maturity', xy=(45,7), xytest=(25,10), arrowprops=dict(facecolor='red',shrink=0.01),)
plt.annotate('Profit/loss with call 1 only', xy=(50,-10), xytext(30,-10),
arrowprops=dict(facecolor='blue',shrink=0.01),)
plt.annotate('Excercise price', xy=(x+0.5,-20+0.5))
show()
Author : Yuxing Yan Date : 12/26/2013 email : [email protected] [email protected] """ import matplotlib.pyplot as plt import p4f sT = arange(20,70,5) s=40 x=40 T1=0.5 T2=1 sigma=0.3 r=0.05 payoff=(abs(sT-x)+sT-x)/2 call_01=p4f.bs_call(s,x,T1,r,sigma) # short call_02=p4f.bs_call(s,x,T2,r,sigma) # long profit_01=payoff-call_01 call_03=p4f.bs_call(sT,x,(T2-T1),r,sigma) calendar_spread=call_03-payoff+call_01 -call_02 y0=zeros(len(sT)) ylim(-20,20) xlim(20,60) plot(sT,call_03,'b-.') plot(sT,call_02-call_01-payoff,'b-.') plot(sT,calendar_spread,'r') plot([x,x],[-20,-15]) title("Calendar spread with calls") xlabel('Stock price at maturity (sT)') ylabel('Profit (loss)') plt.annotate('Buy a call with T1 and sell a call with T2', xy=(25,16))
k = 190 # Strike price of the May 26th 2015 and July 28th 2015 Call Option
cs = 7.50
# Premium of the Short call on May 2nd, 2015
cl = 20.70
# Premium of the Long call on May 2nd, 2015
shares = 100 # Shares per lot
sT = np.arange(0, 2 * s0, 5) # Stock Price at expiration of the Call
sigma = 0.4 # Historical Volatility
r = 0.08 # Risk-free interest rate
t = datetime(2015, 7, 28) - datetime(2015, 5, 26)
T = t.days / 365
# Payoff from the May 26th 2015 Short Call Option at Expiration
y1 = np.where(sT > k, ((k - sT) + cs) * shares, cs * shares)
# Value of the July 28th 2015 long Call Option on May 26th 2015
lc_value = p4f.bs_call(sT, k, T, r, sigma) * shares
# Payoff from the Calendar Call
y2 = y1 + (lc_value - cl)
# Create a plot using matplotlib
fig, ax = plt.subplots()
ax.spines['top'].set_visible(False) # Top border removed
ax.spines['right'].set_visible(False) # Right border removed
ax.spines['bottom'].set_position('zero') # Sets the X-axis in the center
ax.tick_params(top=False, right=False) # Removes the tick-marks on the RHS
plt.plot(sT, y1, lw=1.5, label='Short Call')
plt.plot(sT, lc_value, lw=1.5, label='Long Call')
plt.plot(sT, y2, lw=1.5, label='Calendar Call')
plt.title('Calendar Call')
plt.xlabel('Stock Prices')
from math import exp
import matplotlib.pyplot as pl
S0 = 9.15
x = 9.15
barrier = 10.15
T = 0.5
n_steps = 30.
r = 0.05
sigma = 0.2
sp.random.seed(125)
n_simulation = 5
dt = T / n_steps
S = sp.zeros([n_steps], dtype=float)
time_ = range(0, int(n_steps), 1)
c = p4f.bs_call(S0, x, T, r, sigma)
sp.random.seed(124)
outTotal, inTotal = 0., 0.
n_out, n_in = 0, 0
for j in range(0, n_simulation):
S[0] = S0
inStatus = False
outStatus = True
for i in time_[:-1]:
e = sp.random.normal()
S[i +
1] = S[i] * exp((r - 0.5 * pow(sigma, 2)) * dt + sigma * sp.sqrt(dt) * e)
if S[i + 1] > barrier:
outStatus = False
inStatus = True
pl.plot(time_, S)
for j in range(0, n_simulation):
sT=s0
inStatus=False
outStatus=True
for i in range(0,int(n_steps)):
e=sp.random.normal()
sT*=sp.exp((r-0.5*sigma*sigma)*dt+sigma*e*sp.sqrt(dt))
if (sT>barrier) :
outStatus=False
inStatus=True
#print 'sT=',sT
#print 'j=', j, 'out=',out
if outStatus==True:
outTotal+=p4f.bs_call(s0,x,T,r,sigma)
else:
inTotal+=p4f.bs_call(s0,x,T,r,sigma)
return outTotal/n_simulation, inTotal/n_simulation
s0=40.
x=40.
barrier=42
T=0.5
r=0.05
sigma=0.2
n_simulation=100
upoutCall,upInCall=up_call(s0,x,T,r,sigma,n_simulation,barrier)
print 'upOutCall=', round(upoutCall,2),'upinCall=',round(upInCall,2)
print 'Black-Scholes call', round(p4f.bs_call(s0,x,T,r,sigma),2)
plt.annotate('x1 = 50, x2 =55, x3=60', xy=(45,12))
plt.annotate('c1=10, c2= 7, c3=5', xy=(45,10))
plt.show()
## 입력값과 옵션값의 관계 -> 변동성과 c, p 가격 차이 ##
#변동성이 커지면 옵션값은 올라간다#
#만기가 증가하면 K가 낮아서 콜증가, 풋감소 + 변동성 증가의 가능성을 증가시켜 옵션가격 증가시킨다#
s0 = 30
T0 = 0.5
sigma0 = 0.2
r0= 0.05
x0 = 30
sigma = np.arange(0.05, 0.8, 0.05)
T = np.arange(0.5 , 2.0 , 0.5)
call_0 = p4f.bs_call(s0,x0,T0,r0, sigma0)
call_sigma = p4f.bs_call(s0,x0,T0,r0,sigma)
call_T = p4f.bs_call(s0,x0,T,r0, sigma0)
plt.title("Relationship between sigma and call, T, and call")
plt.plot(sigma, call_sigma,'b')
plt.plot(T, call_T, 'r')
plt.annotate('x=Sigma, y=call price', xy=(0.6,5), xytext=(1,6), arrowprops=dict(facecolor = 'blue', shrink = 0.01),)
plt.annotate('x=T(maturity), y=call price',xy =(1,3), xytext=(0.8,1), arrowprops=dict(facecolor = 'red', shrink = 0.01),)
plt.ylabel("Call premium")
plt.xlabel("Volatiltiy or T")
plt.show()
#### 풋콜패러티 ####
x = 10
""" Name : 4375OS_09_14_sigma_against_call.py Book : Python for Finance Publisher: Packt Publishing Ltd. Author : Yuxing Yan Date : 12/26/2013 email : [email protected] [email protected] """ import numpy as np import p4f as pf s0 = 30 T0 = 0.5 r0 = 0.05 x0 = 30 sigma = np.arange(0.05, 0.8, 0.05) call = pf.bs_call(s0, x0, T0, r0, sigma) plot(sigma, call, 'b') show()
import numpy as np import p4f as pf s0=30;T0=0.5;sigma0=0.2;r0=0.05;x0=30 sigma=np.arange(0.5,2.0,0.5) call_0=pf.bs_call(s0,x0,T0,r0,sigma) call_sigma=pf.bs_call(s0,x0,T0,r0,sigma) call_T=pf.bs_call(s0,x0,Tr0,sigma0) plot(sigma,call_sigma,'b') plot(T,call_T)
""" Name : 4375OS_10_15_for_loop_implied_vol_p4f.py Book : Python for Finance Publisher: Packt Publishing Ltd. Author : Yuxing Yan Date : 12/26/2013 email : [email protected] [email protected] """ import p4f S=40 K=40 T=0.5 r=0.05 c=3.30 for i in range(200): sigma=0.005*(i+1) diff=c-p4f.bs_call(S,K,T,r,sigma) if abs(diff)<=0.01: print(i,sigma, diff)
import numpy as np
from datetime import datetime
import matplotlib.pyplot as plt
s0 = 187 # Initial stock price on May 2nd, 2015
k = 190 # Strike price of the May 26th 2015 and July 28th 2015 Call Option
cs = 7.50; # Premium of the Short call on May 2nd, 2015
cl = 20.70; # Premium of the Long call on May 2nd, 2015
shares = 100 # Shares per lot
sT = np.arange(0,2*s0,5) # Stock Price at expiration of the Call
sigma = 0.4 # Historical Volatility
r = 0.08 # Risk-free interest rate
t = datetime(2015,7,28) - datetime(2015,5,26) ; T = t.days / 365;
# Payoff from the May 26th 2015 Short Call Option at Expiration
y1 = np.where(sT > k,((k - sT) + cs) * shares, cs * shares)
# Value of the July 28th 2015 long Call Option on May 26th 2015
lc_value = p4f.bs_call(sT,k,T,r,sigma) * shares
# Payoff from the Calendar Call
y2 = y1 + (lc_value - cl)
# Create a plot using matplotlib
fig, ax = plt.subplots()
ax.spines['top'].set_visible(False) # Top border removed
ax.spines['right'].set_visible(False) # Right border removed
ax.spines['bottom'].set_position('zero') # Sets the X-axis in the center
ax.tick_params(top=False, right=False) # Removes the tick-marks on the RHS
plt.plot(sT,y1,lw=1.5,label='Short Call')
plt.plot(sT,lc_value,lw=1.5,label='Long Call')
plt.plot(sT,y2,lw=1.5,label='Calendar Call')
plt.title('Calendar Call')
plt.xlabel('Stock Prices')
plt.ylabel('Profit/loss')
plt.grid(True)
email : [email protected] [email protected] """ import p4f import numpy as np import matplotlib.pyplot as plt sT = np.arange(20, 70, 5) s = 40 x = 40 T1 = 0.5 T2 = 1 sigma = 0.3 r = 0.05 payoff = (abs(sT - x) + sT - x) / 2 call_01 = p4f.bs_call(s, x, T1, r, sigma) # short call_02 = p4f.bs_call(s, x, T2, r, sigma) # long profit_01 = payoff - call_01 call_03 = p4f.bs_call(sT, x, (T2 - T1), r, sigma) calendar_spread = call_03 - payoff + call_01 - call_02 y0 = np.zeros(len(sT)) plt.ylim(-20, 20) plt.xlim(20, 60) plt.plot(sT, call_03, 'b-.') plt.plot(sT, call_02 - call_01 - payoff, 'b-.') plt.plot(sT, calendar_spread, 'r') plt.plot([x, x], [-20, -15]) plt.title("Calendar spread with calls") plt.xlabel('Stock price at maturity (sT)') plt.ylabel('Profit (loss)')
""" Name : 4375OS_09_14_sigma_against_call.py Book : Python for Finance Publisher: Packt Publishing Ltd. Author : Yuxing Yan Date : 12/26/2013 email : [email protected] [email protected] """ import numpy as np import p4f as pf s0 = 30 T0 = 0.5 r0 = 0.05 x0 = 30 sigma = np.arange(0.05, 0.8, 0.05) call = pf.bs_call(s0, x0, T0, r0, sigma) plot(sigma, call, "b") show()
