-
Notifications
You must be signed in to change notification settings - Fork 0
/
OptionDash.py
257 lines (205 loc) · 10.5 KB
/
OptionDash.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
import streamlit as st
import yfinance as yf
import pandas as pd
import numpy as np
import datetime as dt
import altair as alt
from scipy.stats import norm
def create_bar_chart(data, x_column, y_column, color_column=None, title=None):
"""
Create a bar chart using Altair.
Parameters:
- data (DataFrame): Input data for the chart.
- x_column (str): Name of the column for the x-axis.
- y_column (str): Name of the column for the y-axis.
- color_column (str, optional): Name of the column for coloring bars (default None).
- title (str, optional): Title of the chart (default None).
Returns:
- alt.Chart: The Altair bar chart object.
"""
chart = alt.Chart(data).mark_bar().encode(
x=alt.X(x_column, title=x_column),
y=alt.Y(y_column, title=y_column),
).properties(
width=600,
height=400,
)
return chart
def create_grouped_bar_chart(data, x, y1, y2, title):
df = pd.DataFrame(data)
# Melt the DataFrame to long format for Altair visualization
df_melted = df.melt(id_vars=[x], value_vars=[y1, y2], var_name='Variable', value_name='Value')
# Create the bar chart using Altair
chart = alt.Chart(df_melted).mark_bar().encode(
x=f'{x}:O', # Use Ordinal scale for categorical x-axis
y=alt.Y('Value', title='Value'), # Quantitative scale for y-axis
color='Variable:N', # Color bars based on the variable
#column='Variable:N' # Separate bars for Value1 and Value2
xOffset ='Variable:N'
).properties(
width=600,
height=400,
title=title
).configure_view(
stroke = None,
)
return chart
def black_scholes(S, K, T, r, sigma, option_type='call'):
"""
Calculate the fair price of a European call or put option using the Black-Scholes formula.
Parameters:
S (float): Current price of the underlying asset
K (float): Strike price of the option
T (float): Time to expiration (in years)
r (float): Risk-free interest rate (annualized, expressed as a decimal)
sigma (float): Volatility of the underlying asset (annualized, expressed as a decimal)
option_type (str): Type of option, either 'call' or 'put'
Returns:
float: Fair price of the option
"""
d1 = (np.log(S / K) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))
d2 = d1 - sigma * np.sqrt(T)
if option_type == 'call':
option_price = S * norm.cdf(d1) - K * np.exp(-r * T) * norm.cdf(d2)
elif option_type == 'put':
option_price = K * np.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)
else:
raise ValueError("Option type must be 'call' or 'put'.")
return option_price
def American_Binomial(S, K_list, T, r, sigma, steps, option_type='call'):
"""
Calculate the fair prices of American options for multiple strike prices using the binomial tree method.
Parameters:
S (float): Current price of the underlying asset
K_list (list or array): List of strike prices for which option valuations are needed
T (float): Time to expiration (in years)
r (float): Risk-free interest rate (annualized, expressed as a decimal)
sigma (float): Volatility of the underlying asset (annualized, expressed as a decimal)
steps (int): Number of time steps in the binomial tree
option_type (str): Type of option, either 'call' or 'put'
Returns:
list: Fair prices of the options corresponding to each strike price in K_list
"""
dt = T / steps
u = np.exp(sigma * np.sqrt(dt))
d = 1 / u
p = (np.exp(r * dt) - d) / (u - d)
option_values_list = [] # List to store option values for each strike price
for K in K_list:
# Initialize option values at maturity
prices = np.zeros(steps + 1)
option_values = np.zeros(steps + 1)
for i in range(steps + 1):
prices[i] = S * (u ** (steps - i)) * (d ** i)
option_values[i] = call_payoff(prices[i], K) if option_type == 'call' else put_payoff(prices[i], K)
# Calculate option values at earlier nodes
for j in range(steps - 1, -1, -1):
prices = prices[:-1] / u
option_values = (p * option_values[:-1] + (1 - p) * option_values[1:]) * np.exp(-r * dt)
if option_type == 'call':
option_values = np.maximum(option_values, call_payoff(prices, K))
else:
option_values = np.maximum(option_values, put_payoff(prices, K))
option_values_list.append(option_values[0]) # Store the option value for this strike price
return option_values_list
def call_payoff(S, K):
return np.maximum(0, S - K)
def put_payoff(S, K):
return np.maximum(0, K - S)
def get_current_price(Symbol):
# Fetch today's data
todays_data = Symbol.history(period='1d')
# Check if the closing price is available (not 0)
if todays_data['Close'][0] != 0:
return todays_data['Close'][0]
else:
# Fetch data for the previous day if today's close is 0
yesterdays_data = Symbol.history(period='2d')
# Return the first entry, assuming it's the most recent one after today
return yesterdays_data['Close'][0]
st.title("Options Analysis Dashboard")
st.write("A Basic Dashboard that when given a Ticker and American Option Expiry will calculate the Black-Scholes-Merton price of the option as well as the binomial tree price.")
with st.expander("**How To Use** :rocket:"):
st.markdown("""
1. Ensure a valid ticker symbol is selected, and is the same as used on yahoo finance.
2. Enter an expiry (0dte expiry not supported)
3. Select Put / Call
4. Select modelling option
5. Enter risk free interest rate (annual %)
6. Enter binomial tree steps (normally converges after 250)
7. View the analysis!
""")
st.warning("Dashboard uses yFinance to fetch live data, and therefore cannot generate data outside of market hours.")
ticker = st.text_input("ticker", value = "SPY")
Symbol = yf.Ticker(ticker)
# Download historical data in order to find volatility
historicals_5y = Symbol.history(period="5y")
historicals_1y = Symbol.history(period="1y")
st.write("Stock Price over 5 Years")
st.line_chart(historicals_5y['Close'])
expiry_data = Symbol.options
expiry = st.selectbox("Select an expiry ", expiry_data)
opt = Symbol.option_chain(expiry)
# Initialise dataset
calls = pd.DataFrame(opt.calls)[["strike", "bid", "ask", "openInterest", "impliedVolatility", "inTheMoney"]]
puts = pd.DataFrame(opt.puts)[["strike", "bid", "ask", "openInterest", "impliedVolatility", "inTheMoney"]]
calls = calls.rename(columns = {"bid" : "Bid", "ask": "Ask", "impliedVolatility" : "IV", "inTheMoney" : "ITM", "openInterest" : "Open Interest"})
puts = puts.rename(columns = {"bid" : "Bid", "ask": "Ask", "impliedVolatility" : "IV", "inTheMoney" : "ITM", "openInterest" : "Open Interest"})
st.write(f'## Option Chain for {ticker} - Expiry: {expiry}')
# Displays Option Chains
col1,col2 = st.columns(2)
col1.write("Call Option Chain")
col1.write(calls)
col2.write("Put Option Chain")
col2.write(puts)
# Derivative Pricing
st.write("## Derivative Pricing Basic Models")
#Decision1 = st.selectbox("Put or Call? ", ["Put", "Call"])
Decision1 = st.radio("Put or Call?", ('Put', 'Call'), horizontal=True)
Decision2 = st.radio("Analyse against Black-Scholes-Merton or Binomial Tree", ('Black-Scholes-Merton', 'Binomial Tree'))
# Calculate daily returns
historicals_1y['Daily Return'] = historicals_1y['Close'].pct_change()
# Calculate annualized volatility
volatility = historicals_1y['Daily Return'].std() * np.sqrt(252) # 252 trading days in a year
#st.write(volatility)
if Decision1 == "Put":
option_type = "put"
K = puts['strike']
actual_ask = puts['Ask']
elif Decision1 == "Call":
option_type = "call"
K = calls['strike']
actual_ask = calls['Ask']
# American Options Price Calculations
T = (pd.to_datetime(expiry) - pd.to_datetime('today')).days / 365
r = st.slider('Select an annualised risk free interest rate (%)', min_value=0.0, max_value=20.0, value=8.0, step=0.25)/100
Bin_Steps = st.slider('Select the amount of binomial tree steps', min_value=50, max_value=1000, value=150, step=1)
S = get_current_price(Symbol)
Am_BSM = black_scholes(S, K, T, r, volatility, option_type)
#Am_BSM = pd.concat([K, Am_BSM], axis = 1)
Am_Bin = American_Binomial(S, K, T, r, volatility, Bin_Steps, option_type)
Options_Analysis = pd.DataFrame()
Options_Analysis['Strike'] = K
Options_Analysis['BSM'] = Am_BSM
Options_Analysis['Binomial Model'] = Am_Bin
Options_Analysis['Actual Price'] = actual_ask
Options_Analysis['Absolute BSM Error Percentage'] = 100 * abs(Options_Analysis['BSM'] - Options_Analysis['Actual Price']) / Options_Analysis['Actual Price']
Options_Analysis['Absolute Binomial Error Percentage'] = 100 * abs(Options_Analysis['Binomial Model'] - Options_Analysis['Actual Price']) / Options_Analysis['Actual Price']
#st.write(Am_BSM)
#st.write(S)
#st.write(K)
#st.write(Options_Analysis)
if Decision2 == 'Black-Scholes-Merton':
Options_Analysis = Options_Analysis.query('`Absolute BSM Error Percentage` < 25')
bar_chart = create_grouped_bar_chart(Options_Analysis, 'Strike', 'Actual Price', 'BSM', 'BSM vs Actual Price')
bar_chart2 = create_bar_chart(Options_Analysis, 'Strike', 'Absolute BSM Error Percentage')
MSE = np.square(np.subtract(Options_Analysis['Actual Price'],Options_Analysis['BSM'])).mean()
else:
Options_Analysis = Options_Analysis.query('`Absolute Binomial Error Percentage` < 25')
bar_chart = create_grouped_bar_chart(Options_Analysis, 'Strike', 'Actual Price', 'Binomial Model', 'Binomial Model vs Actual Price')
bar_chart2 = create_bar_chart(Options_Analysis, 'Strike', 'Absolute Binomial Error Percentage')
MSE = np.square(np.subtract(Options_Analysis['Actual Price'],Options_Analysis['Binomial Model'])).mean()
st.altair_chart(bar_chart, use_container_width=True)
st.altair_chart(bar_chart2, use_container_width=True)
st.write(f"The Mean-Square Error of this Option Modelling is {MSE}")
st.write("This dashboard demonstrates how options pricing occurs, and provides a very limited example for both Binomial and Black-Scholes derivative modelling. Further ways the model could be improved would be to create a bespoke volatility model, allowing greater accuracy in the BSM. The model does not currently factor in any Dividends, and assumes constant volatility. If you wish to explore further projects of mine, [please visit my Github page.](https://harryrogers0.github.io)")