# Option Value Calculator

### Larger investments with small capital

### Higher returns on capital through leverage

### Option to trade in indices and stocks

### Suitable across market conditions

## What is an Options Value Calculator?

An Options value calculator is an online tool to calculate the fair value of a given call or put option based on factors like price, time, and volatility. It calculates the value of options by considering the asset's current price, time left, and volatility, guiding traders on whether an option is currently undervalued or overvalued.

One of the primary functions of the options valuation calculators is to determine the theoretical price of an option. This is often achieved through the utilisation of the Black-Scholes model, one of the most widely accepted and used formulas for pricing options. The calculator takes into account several critical factors: the current asset price, strike price, time to expiration, and implied volatility. Some calculators can also accommodate additional user inputs, making them adaptable to a variety of trading scenarios. .

The benefit of an estimation of an option's theoretical price lies in its ability to offer traders and investors a clear understanding of the option's potential worth at the specific moment of valuation.

For traders, options calculators are more than just tools for pricing options. They play a crucial role in risk management. The calculated option value serves as a benchmark for evaluating trading strategies and their associated risks. By knowing the theoretical price of an option, traders can evaluate whether an option is overvalued or undervalued in the current market. This insight can guide them in constructing trading strategies that are not only profitable but also well-protected against potential losses.

## How do Options Value Calculators online work?

Online Options Time Value Calculators use inputs such as asset price, time to expiry, implied volatility, and other parameters to estimate the fair value of options. Online Options Value Calculators are powerful tools that assist traders in making informed trading decisions by returning the fair value of an option in no time without the need for manual calculations.

Online Options Value Calculators are modeled on the Black-Scholes model which was introduced in 1973 by Fischer Black and Myron Scholes. The options value calculator requires the users to input the basic parameters such as the current price of the underlying, interest rate, time left to expiry, and implied volatility of the asset to calculate the fair value of the given option.

The significance of each input parameter in the Black Scholes model - and in the option value calculator - is explained below:

- Underlying Price: The current price of the underlying asset plays a crucial role in determining the value of an option. Depending on whether you hold a call option (which gives you the right to buy the asset) or a put option (which gives you the right to sell the asset), the relationship between the asset's current price and the option's strike price is vital. The nearer the strike price to the underlying price, the higher your chances of your option turning in the money and you being profitable.
- Time to Expiration: Options contracts have a set expiration date. As this date approaches, the value of the option can change and hence the options value calculator considers the time remaining until the option expires. The closer an option is to expiration, the riskier it becomes, and this is factored into the calculation. The rationale is that as time diminishes, there is less time for the asset price to move in a favourable direction, making the option less valuable.
- Implied Volatility: Volatility refers to how much the price of the underlying asset is expected to fluctuate over time. High volatility typically leads to higher option prices because there is a greater likelihood that the asset's price will move significantly, potentially increasing the option's value. Implied volatility is a measure of how much the market anticipates the asset's price will fluctuate in the future. Online options calculators take this into account, allowing users to input their estimates or use historical data to get a fair idea of implied volatility. It is extremely important to enter the implied volatility correctly as it has a huge impact on the fair value of the option. Overestimating the implied volatility can result in justifying higher prices for options while underestimating it can result in arriving at unfairly low prices - both of which can impact your trading decision negatively.
- Interest Rate: In the Black-Scholes model, a risk-free interest rate is used to calculate the prices of call and put options. For Indian scenarios, one can use the interest rate on a treasury bill which varies between 7%-7.5% as a risk-free interest rate. The price of a call option and interest rate are directly correlated which means that an increase in the interest rate results in an increase in the price of a call option. Alternately, the price of a put option and interest rate are inversely correlated which means that an increase in the interest rate results in a decrease in the price of a put option.

## How do you calculate options value?

The Black Scholes model is the most widely accepted model to calculate the theoretical price of options. Below is the formula, as proposed by the Black Scholes model to calculate the value of an option using factors like underlying price, strike price, time to expiry, implied volatility, and risk-free interest rate.

The basic Black Scholes model formula for calculating the value of a European call option in India would be:

C = S * N(d1) - X * e^(-rt) * N(d2)

Where:

C is the call option price.

S is the current stock price.

N(d1) and N(d2) are cumulative standard normal distribution functions of d1 and d2, respectively.

X is the option's strike price.

e is the base of the natural logarithm.

r is the risk-free interest rate specific to the Indian market.

t is the time until option expiration.

For a European put option, the formula is similar:

P = X * e^(-rt) * N(-d2) - S * N(-d1)

The variables d1 and d2 are calculated as follows, just as in the standard BSM formula:

d1 = (ln(S / X) + (r + (σ^2) / 2) * t) / (σ * √t) d2 = d1 - σ * √t

- σ is the volatility of the stock's returns.
- The interest rate, r, should be taken as the risk-free interest rate on a government bond or a treasury bill.

Since the calculations mentioned above are complex and require a lot of computation, options traders rely on online options value calculators to calculate the fair price of options in real time to assist them with their trading decisions.

## Benefits of using Motilal Oswal Options Value Calculator

Online options value calculators help traders make informed decisions, calculate risk management, precise valuations, and improve trading strategies. The Options Value calculator saves time, enhances profitability, and reduces the likelihood of making costly errors in options trading.

Here are the benefits of the Options valuation calculator-

- Informed Decision-Making: One of the primary advantages of using an online Options time Value Calculator is the ability to make well-informed decisions. These calculators provide accurate estimations of an option's current value based on real-time market data and the specific parameters of the option contract. Equipped with this information, traders can decide whether to buy, sell, or hold their options, thus reducing the element of guesswork and making direct decisions in real time before the opportunity runs out.
- Improved Trading Strategies: Options traders often use complex strategies that involve multiple options contracts. An online calculator can analyze and evaluate these strategies, giving traders insights into their potential performance. It helps traders optimize their strategies by understanding how changes in one leg of the trade can affect the overall position. By experimenting with different scenarios using the calculator, traders can refine and fine-tune their strategies for maximum efficiency.
- Precise Valuations: Options Value Calculators employ advanced mathematical models to precisely determine the fair value of options. These models consider not only the current asset price and strike price but also other factors like time to expiration and implied volatility. This precision is important when dealing with complex options strategies, such as spreads or combinations of calls and puts. It ensures that traders have accurate valuations for each component of their strategy.
- Time Efficiency: Manually calculating the value of options can be a time-consuming process, especially when dealing with multiple options or complex strategies. Online Options Value Calculators automate this task, providing quick and accurate results. This time-saving benefit is especially valuable for active traders who need to make rapid decisions in fast-moving markets.
Using Motilal Oswal Options Value Calculator can not only significantly enhance your overall understanding of options but also impact your trading success by performing complex calculations for you in real time and enabling you to grab all options trading opportunities.