Option Greeks in Python

 How to apply Option Greeks in Python?

Options Greeks are a set of risk measures that help traders and investors understand the various factors influencing the price and behavior of options contracts. These Greeks are calculated using mathematical models and are used to assess and manage the risk associated with options trading. There are several Greek letters used to represent these measures, each corresponding to a different aspect of an option's pricing and sensitivity to market changes.

Five Greeks Delta, Gamma, Theta, Vega, and Rho

Delta (Δ): Measures the rate of change in the option’s price for a one-point move in the price of the underlying asset. For example, a delta of 0.5 suggests the option price will move $0.50 for every $1 move in the underlying asset.

Delta is the most commonly referred to in Greek and probably the easiest to understand. Delta measures the sensitivity of an option's price to changes in the price of the underlying asset. It quantifies how much an option's price is expected to change for a one-point move in the underlying asset's price. A call option typically has a positive delta (between 0 and 1), indicating that its price rises as the underlying asset's price goes up. A put option has a negative delta (between -1 and 0), meaning its price moves inversely to the underlying asset's price. The delta of an option indicates how much the price of an option should change in response to the $1 change in the underlying security. Since a call option benefits when the underlying rises in price, The delta for the call is positive. similarly since of put option loses value when the underlying arises in price, The delta for put options is -ve.

Gamma (Γ): Represents the rate of change in the delta with respect to changes in the underlying price. This is important as it shows how stable or unstable the delta is; higher gamma means delta changes more rapidly.

Gamma measures the rate of change of an option's delta with respect to changes in the underlying asset's price. It helps traders assess how the delta might change as the underlying asset's price moves. High gamma indicates that the delta is more sensitive to small price changes in the underlying asset, while low gamma suggests that the delta is less responsive. .Gama is directly related to the delta. Major stops around The delta will move higher or lower. Gama indicates how much delta changes with a $1 change in the underlying security. Unlikely Delta Gamma is positive for both the call option and the put option. this is a function of rage in the underlying forcing The delta of both calls is higher and puts a decrease in the underlying to post delta lower for both calls and put option. when a put option delta is pushed higher it becomes less negative and when it goes lower it is more negative therefore the sign of Gamma is always positive.

Theta (Θ): Measures the rate of time decay of an option. It indicates how much the price of an option will decrease as one day passes, all else being equal.

Theta relates to the effect that the passage of time will have on the value of an option. Theta has a negative impact on both call and put options due to the passage of time decreasing the value of an option be it a call or put. the value of theta indicates how much value an option will lose from day to day or sometimes over the number of days. in the case of theta, the unit of change could be based on something other than one day. Theta measures the rate of time decay of an option's value. It quantifies how much an option's price is expected to decrease as time passes, assuming all other factors remain constant. Theta is particularly important for option sellers (writers) because it represents their potential profit as the option's time to expiration decreases.

Vega (ν):Indicates the sensitivity of the price of an option to changes in the volatility of the underlying asset. A higher vega means the option price is more sensitive to volatility. 

Vega indicates how much the price of an option will increase or decrease with a 1% increase or 1% decrease in the implied volatility of the option works the same for both call option and put option with an increase in implied volatility hits the same for both call option and put option with an increase in implied volatility increases the value of the call or put option for a decrease in implied volatility has a negative impact on the value of calls and puts. Vega measures an option's sensitivity to changes in implied volatility, which is a measure of the market's expectations for future price volatility of the underlying asset. A higher vega indicates that the option's price is more responsive to changes in implied volatility, while a lower vega suggests the opposite.

Rho (ρ): Measures the sensitivity of an option’s price to a change in interest rates. It indicates how much the price of an option should rise or fall as the risk-free interest rate increases or decreases. 

Rho measures the sensitivity of an option's price to changes in interest rates. It's particularly relevant for traders of options on interest rate-sensitive assets. An increase in interest rates generally benefits call options and hurts put options. Rho indicates how much an option will increase or decrease in value based on a 1% change in the risk-free interest rate.

Lambda (Λ): Lambda is not as commonly used as the other Greeks, but it represents the percentage change in the option's price for a 1% change in the implied volatility.

These Greeks are essential tools for options traders and investors to assess and manage their positions effectively. By understanding how options are influenced by changes in underlying price, time decay, volatility, interest rates, and more, market participants can make informed decisions and develop strategies to meet their financial objectives while managing risk.These Greeks are also essential tools for traders to manage risk, construct hedging strategies, and understand the potential price changes in their options with respect to various market factors. Understanding and effectively using the Greeks can be crucial for the profitability and risk management of options trading.

Greeks

Real Life Condor Setups Real iron condor setups involves a complex interplay of market analysis, options pricing, and strategic planning. Below are 10 common setups we will explore in further detail. 

Iron Condor Setup 

#1: The Market Stabilizer Identify an underlying asset with low volatility and a narrow trading range. Sell an out-of-the-money (OTM) call and an OTM put. Buy a further OTM call and put to limit risk. Monitor for minimal market movement and manage the trade by adjusting the wings as needed. 

#2: The Earnings Play Prior to an earnings announcement, select a stock with historically muted post-earnings moves. Establish the iron condor just before the earnings report to capture high implied volatility. Position the strikes outside of the expected move calculated from the options market. After the earnings report, look to close the position to capture the volatility crush. 

#3: The Index Balancer Choose a broad market index ETF that tends to have less dramatic swings. Set up the iron condor during a period of market equilibrium. Use a balanced distance between the call spread and put spread relative to the current price. Aim for a 1:1 risk-reward ratio and manage the trade by rolling the untested side if the market trends. 

#4: The Monthly Income Use a consistent monthly cycle, selling iron condors on a chosen index with 30–45 days to expiration. Select strikes based on a probability of success, typically choosing deltas around 15 for both the call and put side. Plan to close or adjust the position if it reaches a certain percentage of max profit or loss. 

#5: The High Volatility Harness During a period of elevated market volatility, select a stock or index with high option premiums. Sell the iron condor, collecting more premium due to the increased implied volatility. Choose wider strike widths to accommodate the larger expected range. Adjust the trade more actively to manage risk as the market moves. 

#6: The Sector Speculator Focus on a sector ETF that is experiencing a temporary period of stability. Sell the iron condor with the intention to profit from the sector’s short-term stagnation. Select strikes that are beyond the support and resistance levels of the ETF. Close the position early for a profit or roll the spreads to the next month if untouched. 

#7: The Diversified Approach Build iron condors across multiple non-correlated assets to spread risk. Allocate a small percentage of the portfolio to each setup to maintain diversification. Choose varying expiration dates and strike widths to avoid systemic risk. Adjust individual positions based on asset-specific movements.

#8: The Gamma Guard In a low-volatility environment, construct an iron condor with a shorter time frame to expiration (10–20 days). Place the strikes closer to the current price to profit from gamma decay as expiration approaches. Be ready to close or adjust the position quickly in case of adverse price movements. 

#9: The Trend Follower Identify an underlying that is starting to settle into a range after a trend. Sell the iron condor with strikes that align with the new support and resistance levels formed by the range. Use technical analysis to adjust the position if the previous trend appears to resume. 

#10: The Patient Player Choose an underlying with a longer-term neutral outlook. Sell an iron condor with a longer duration to expiration (60–90 days). Plan to manage the trade slowly, making adjustments only when necessary, and focus on theta decay over time.

Code python

!pip install mibian

import mibian

from tabulate import tabulate

Put price calculation python

stock_price=18141

strick_price=18050

interest_rate=10

day_to_expiry=1

volatility=14

print(tabulate([['Delta',greeks.putDelta],

               ['Gamma',greeks.gamma],

               ['Vega',greeks.vega],

               ['Theta',greeks.putTheta],

               ['Rho',greeks.putRho]

               ],headers=['Greeks','Value'],

tablefmt='orgtbl'))

print("")

print('The put price is',greeks.putPrice)

| Greeks | Value | |----------+--------------| | Delta | -0.271958 | | Gamma | 0.00249844 | | Vega | 3.14818 | | Theta | -20.6807 | | Rho | -0.135657 | The put price is 22.23591721073535

Call price calculation python

greeks=

mibian.BS([stock_price,strick_price,interest_rate,day_to_expiry],

volatility=volatility)

print(tabulate([['Delta',greeks.callDelta],

               ['Gamma',greeks.gamma],

               ['Vega',greeks.vega],

               ['Theta',greeks.callTheta],

               ['Rho',greeks.callRho]

               ],headers=['Greeks','Value'],tablefmt='orgtbl'))

print("")

print('The call price is',greeks.callPrice)

| Greeks | Value | |----------+--------------| | Delta | 0.766483 | | Gamma | 0.00230356 | | Vega | 2.90775 | | Theta | -24.1325 | | Rho | 0.377825 | The call price is 114.14080597325301

BANKNIFTY 14 NOV

| Greeks | Value |

|----------+---------------| | Delta | -0.287968 | | Gamma | 0.000439314 | | Vega | 11.8443 | | Theta | -41.0996 | | Rho | -0.917959 | The put 37900 price is 141.35753092334926

| Greeks | Value | |----------+---------------| | Delta | 0.395048 | | Gamma | 0.000604113 | | Vega | 13.3677 | | Theta | -45.0014 | | Rho | 1.22884 | The call 38500 price is 176.7195478090489

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