3D plot in python from a csv file

import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from scipy.interpolate import griddata

Dim2	Dim1	Dim3
5	1	109.582
5	2	105.657
5	3	113.476
5	4	107.209
5	5	104.784
5	6	102.218
5	7	100.377
5	8	104.111
5	9	69.258
5	10	59.227
5	11	47.046
5	12	37.144
5	13	27.968
5	14	25.118
5	15	21
5	16	18.444
5	17	19.306
5	18	9.637
5	19	4.066
5	20	0.06
4	1	158.586
4	2	153.183
4	3	160.387
4	4	153.693
4	5	150.667
4	6	145.106
4	7	142.821
4	8	149.522
4	9	109.88
4	10	97.388
4	11	81.012
4	12	67.986
4	13	58.08
4	14	53.754
4	15	48.378
4	16	45.452
4	17	43.249
4	18	27.168
4	19	17.932
4	20	0.302
3	1	215.783
3	2	207.373
3	3	215.219
3	4	209.206
3	5	205.631
3	6	198.287
3	7	196.91
3	8	204.884
3	9	163.378
3	10	149.805
3	11	132.181
3	12	114.895
3	13	105.88
3	14	101.015
3	15	95.3
3	16	92.124
3	17	87.071
3	18	67.161
3	19	55.829
3	20	16.715
2	1	278.676
2	2	270.159
2	3	279.71
2	4	272.591
2	5	266.701
2	6	258.457
2	7	260.062
2	8	268.448
2	9	227.359
2	10	215.866
2	11	198.514
2	12	179.856
2	13	171.234
2	14	165.944
2	15	161.638
2	16	159.788
2	17	151.862
2	18	135.376
2	19	125.595
2	20	98.863
1	1	346.731
1	2	341.995
1	3	349.773
1	4	340.789
1	5	338.01
1	6	325.182
1	7	328.339
1	8	333.462
1	9	300.839
1	10	292.52
1	11	275.064
1	12	254.504
1	13	252.279
1	14	250.211
1	15	242.438
1	16	242.713
1	17	233.577
1	18	223.335
1	19	218.322
1	20	199.88

fig = plt.figure(figsize=plt.figaspect(0.5))
ax = fig.add_subplot(1, 2, 1, projection='3d')
# note this: you can skip rows!
my_data = np.genfromtxt('data.csv', delimiter=',',skip_header=1)
X = my_data[:,0]
Y = my_data[:,1]
Z = my_data[:,2]

xi = np.linspace(X.min(),X.max(),100)
yi = np.linspace(Y.min(),Y.max(),100)
# VERY IMPORTANT, to tell matplotlib how is your data organized
zi = griddata((X, Y), Z, (xi[None,:], yi[:,None]), method='cubic')

CS = plt.contour(xi,yi,zi,15,linewidths=0.5,color='k')
ax = fig.add_subplot(1, 2, 2, projection='3d')

xig, yig = np.meshgrid(xi, yi)

surf = ax.plot_surface(xig, yig, zi,
        linewidth=0)

plt.show()

Black Scholes "Option Payoff" versus "time" in Python

import math
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
mpl.rcParams['font.family'] = 'serif'
from scipy.integrate import quad

def dN(x):
    ''' Probability density function of standard normal random variable x.'''
    return math.exp(-0.5 * x ** 2) / math.sqrt(2 * math.pi)
def N(d):
    ''' Cumulative density function of standard normal random variable x. '''
    return quad(lambda x: dN(x), -20, d, limit=50)[0]
def d1f(St, K, t, T, r, sigma):
    ''' Black-Scholes-Merton d1 function.
        Parameters see e.g. BSM_call_value function. '''
    d1 = (math.log(St / K) + (r + 0.5 * sigma ** 2)
        * (T - t)) / (sigma * math.sqrt(T - t))
    return d1
#
# Valuation Functions
#
def BSM_call_value(St, K, t, T, r, sigma): 
    ''' Calculates Black-Scholes-Merton European call option value.86 DERIVATIVES ANALYTICS WITH PYTHON
    Parameters
    ==========
    St: float
    stock/index level at time t
    K: float
    strike price
    t: float
    valuation date
    T: float
    date of maturity/time-to-maturity if t = 0; T > t
    r: float
    constant, risk-less short rate
    sigma: float
    volatility
    Returns
    =======
call_value: float
European call present value at t
    '''
    d1 = d1f(St, K, t, T, r, sigma)
    d2 = d1 - sigma * math.sqrt(T - t)
    call_value = St * N(d1) - math.exp(-r * (T - t)) * K * N(d2)
    return call_value
def BSM_put_value(St, K, t, T, r, sigma):
    ''' Calculates Black-Scholes-Merton European put option value.
    Parameters
    ==========
    St: float
    stock/index level at time t
    K: float
    strike price
    t: float
    valuation date
    T: float
    date of maturity/time-to-maturity if t = 0; T > t
    r: float
    constant, risk-less short rate
    sigma: float
    volatility
    Returns
    =======
    put_value: float
        European put present value at t
    '''
    put_value = BSM_call_value(St, K, t, T, r, sigma) \
        - St + math.exp(-r * (T - t)) * K
    return put_value
#
# Plotting European Option Values
#
def plot_values(function):
    ''' Plots European option values for different parameters c.p. '''
    plt.figure(figsize=(10, 8.3))
    points = 100
#
# Model Parameters
#
    St = 100.0 # index level
    K = 100.0 # option strike
    t = 0.0 # valuation date
    T = 1.0 # maturity date
    r = 0.05 # risk-less short rate
    sigma = 0.2 # volatility
# C(T) plot
    plt.subplot(222)
    tlist = np.linspace(0.0001, 1, points)
    vlist = [function(St, K, t, T, r, sigma) for T in tlist]
    plt.plot(tlist, vlist)
    plt.grid(True)
    plt.xlabel('maturity $T$')

Black-Scholes model in R

stock=10858.7
rf=0.0743
strike=stock-100
sigma=0.1281
TTM=0.0039683
d1<-(log(stock/strike)+(rf+0.5*sigma^2)*TTM)/(sigma*sqrt(TTM))
d2<-d1-(sigma*sqrt(TTM))
BS.call<-stock*pnorm(d1,mean=0,sd=1)-strike*exp(-rf*TTM)*pnorm(d2,mean=0,sd=1)
BS.call
BS.put<-BS.call-stock+strike*exp(-rf*TTM)
BS.put
for(TTM<0.08) 
  {
  TTM<-(TTM*2)
  }
d1<-(log(stock/strike)+(rf+0.5*sigma^2)*TTM)/(sigma*sqrt(TTM))
d2<-d1-(sigma*sqrt(TTM))
BS.call<-stock*pnorm(d1,mean=0,sd=1)-strike*exp(-rf*TTM)*pnorm(d2,mean=0,sd=1)
BS.call
BS.put<-BS.call-stock+strike*exp(-rf*TTM)
BS.put

MC simulation of Black Scholes in R

stock=398.79

sigma=0.32

strike=300

TTM=2.5

rf=0.01

num.sim<-100000

R<-(rf-0.5*sigma^2)*TTM

R

SD<-sigma*sqrt(TTM)

SD

TTM.price<-stock*exp(R+SD*rnorm(num.sim,0,1))

TTM.call<-pmax(0,TTM.price-strike)

PV.call<-TTM.call*(exp(-rf*TTM))

mean(PV.call)

TTM.put<-pmax(0,strike-TTM.price)

PV.put<-TTM.put*(exp(-rf*TTM))

mean(PV.put)

#Let's calculate Black-Scholes value fr call and put option#

d1<-(log(stock/strike)+(rf+0.5*sigma^2)*TTM)/(sigma*sqrt(TTM))

d2<-d1-(sigma*sqrt(TTM))

BS.call<-stock*pnorm(d1,mean=0,sd=1)-strike*exp(-rf*TTM)*pnorm(d2,mean=0,sd=1)

BS.call

BS.put<-BS.call-stock+strike*exp(-rf*TTM)

BS.put

 #”ctrl+shft+enter” to process#

SPY versus BSM histogram plot in R

library("quantmod")
getSymbols("SPY")
#Stats of SPY
spy = Delt(as.numeric(SPY$SPY.Adjusted), k=20)
spy.mu= mean(spy, na.rm=TRUE)
spy.sd= sd(spy, na.rm=TRUE)
#Stats of SPY applied to Norm dist
norm = rnorm(1000, mean=spy.mu, sd=spy.sd)
#Visualize histograms
hist(spy, main="SPY versus Normal Distribution", breaks=50, col="blue", freq = FALSE, probability=TRUE)
hist(norm, col="yellow", breaks=50, add=T, freq = FALSE, probability=TRUE)

Plotting data from 2 columns in R

***load the excel/txt file from R-Studio manually using import option**

plot(d5[c(9,6)])

//d5 is name of the file, 'c' implies column, 9 and 6 are column nos to be plotted//

plot a line at x=31 with [y_min and y_max]

x=[31,31];
y=[0,70000];
plot(x,y)