$$\text{Call Payoff = MAX(S-X, 0)}$$

$$\text{S = Stock Price}$$
$$\text{X = Strike Price of Call Of -$3 instead of -$5).

import pandas as pd

#Example of profit and payoff of
df = pd.DataFrame(list(range(101)), columns = ['Stock Price'])
df['$50 Call Payoff'] = df['Stock Price'].apply(lambda x: max(x-50, 0))
df['$50 Call Profit'] = df['$50 Call Payoff'] - 5
df = df.set_index('Stock Price')
print(df)

import matplotlib.pyplot as plt
#Graph the payoff
ax = df['$50 Call Payoff'].plot(kind='line')
ax.axhline(0, linestyle='--', color='grey')
plt.xlabel('Stock Price')
plt.ylabel('Payoff')
plt.title("$50 Call Option Payoff")
plt.show()

import matplotlib.pyplot as plt
#The cost is just a linear shift downwards
ax = df['$50 Call Profit'].plot(kind='line')
ax.axhline(0, linestyle='--', color='grey')
plt.xlabel('Stock Price')
plt.ylabel('Profit')
plt.title("$50 Call Option Profit")
plt.show()

There are different strike prices on options as well. For example, if you plot a call option with a strike price of $60, you can see that it is a horizontal shift to the right of $10 for the payoff profile.

#Compare with a $60 strike price call
df['$60 Call Payoff'] = [max(x-60, 0) for x in df.index]
ax = df[['$50 Call Payoff', '$60 Call Payoff']].plot(kind='line')
ax.axhline(0, linestyle='--', color='grey')
plt.xlabel('Stock Price')
plt.ylabel('Payoff')
plt.title("Call Option Payoffs")
plt.show()

Put options are the opposite of this. For put options, the buyer is given the option to sell at a given stock price. So, if the stock was only $40 in the market but the put option had a strike price of $50, the buyer could buy a stock for $40 and immediately sell the stock for $50 with the put options realizing a payoff of $10. Quite like call options, you do have to pay for the put option since there is no negative payoff and only positive payoffs anywhere the option doesn’t payoff with 0.

Do the same analysis for put options.

#A put option works in the opposite way
df['$50 Put Payoff'] = [max(50-x, 0) for x in df.index]
ax = df['$50 Put Payoff'].plot(kind='line')
ax.axhline(0, linestyle='--', color='grey')
plt.xlabel('Stock Price')
plt.ylabel('Payoff')
plt.title("$50 Put Option Payoff")
plt.show()

#Profit still is just a linear shift down
df['$50 Put Profit'] = df['$50 Put Payoff'] - 5
ax = df['$50 Put Profit'].plot(kind='line')
ax.axhline(0, linestyle='--', color='grey')
plt.xlabel('Stock Price')
plt.ylabel('Profit')
plt.title("$50 Put Option Profit")
plt.show()

Compare both of these to the payoff and profit if you were to buy a stock for $50 and later sell it given whatever price it was between $0 and $100.

#Notice the obvious payoff/profit that comes from actually owning a stock if it were at $50 right now
df['Stock Payoff'] = df.index
df['Stock Profit'] = df['Stock Payoff']-50
ax = df[['Stock Payoff', 'Stock Profit']].plot(kind='line')
ax.axhline(0, linestyle='--', color='grey')
plt.xlabel('Stock Price')
plt.ylabel('Profit/Payoff')
plt.title("$50 Stock")
plt.show()

Bonds pay off the same no matter what the stock pays off as. If we were to buy a bond at $100 today, and then receive $105 in a year (a 5% coupon on $100 plus $100 face value), we would get the following payoff graphs:

#Now consider a 1 year 5% coupon bond priced at $100. It's payoff is independent of stock price!
df['Bond Payoff'] = 105
df['Bond Profit'] = df['Bond Payoff'] - 100
ax = df[['Bond Payoff', 'Bond Profit']].plot(kind='line')
ax.axhline(0, linestyle='--', color='grey')
plt.xlabel('Stock Price')
plt.ylabel('Profit/Payoff')
plt.title("Par 1 Year 5% Coupon Bond")
plt.show()

ption}$$