Implied Volatility Calculator

      4 Comments on Implied Volatility Calculator

Implied volatility is a term which is very commonly used in the context of options trading. This is a very important metric to consider for your trading strategies. If you trade options, IV can help you get the market’s best guess for volatility. This post walks you through in building Implied Volatility Calculator model in Excel.

The Black-Scholes model can be used to estimate implied volatility.Implied Volatility can be estimated using  spot price, strike price, asset price, risk-free rate, time to maturity, and dividend yield. To achieve this, given an actual option value, you have to iterate to find the volatility solution. There are various techniques available; we will use the Newton-Raphson bisection method for calculating Implied Volatility in Excel.

6 Ways Implied Volatility Helps You Make The Right Trading Decisions

  • When to Buy or Sell – Timing is key. When IV is high, you should consider selling an option. Buy, when IV is low
  • Bullish or Bearish – IV decreases on bullish market conditions, rises on bearish market conditions
  • Future Pricing – You can have a good directional idea of the future price of an option by computing its IV
  • Highs and Lows – By the time an option expires, you may be able to estimate the stock’s high and low through IV
  • Calls and Puts – Before you trade a call or a put option, it is always better to check the IV for any pitfalls
  • Track Fluctuations – IV can help you trace irregular movements in the price of the underlying asset

Newton-Raphson Method and Implied Volatility

Implied Volatility is distinctively different from historical volatility measures. The term implied volatility comes from the fact that the volatility is removed from the market prices of options. Using Black-Scholes option pricing model, we can calculate Implied Volatility using trial and error. A great benefit of Newton-Raphson bisection method is that it gives fast convergences and the error approximation reduces rapidly with each additional iteration. The equation to calculate Implied Volatility of an option:

\sigma_{n+1} = \sigma_{n} - \frac{P_{m} - P_{t}(\sigma_{n})}{dP_{t}(\sigma_{n}/d\sigma)}

Pm is the market price of the option which we are trying to solve a fit for,

Pt is the option price given by Black-Scholes equation,

σ is the implied volatility

Once Black-Scholes is structured, we use an iterative technique to solve for σ. This method works for options where Black-Scholes model has a closed form solution.

How does IV work

An ITM (In the money) option has 10 days for expiration. The strike price is 55 and the current stock price is 50. The stock has daily volatility of 0.03. The risk free interest rate is assumed to be 0.02.

European-Call-Option

d_{2} = \frac{ln(50/55) + (0.22/365 - 0.03^{2}/2)10}{0.03\sqrt{10}}

Alternatively, d2 can be calculated as

Implied-Volatility-Calculator

So, the European Call value can be calculated as:

C = S*Norm(d_{1}) - K*e^{(-rt/365)}*Norm(d_{2})

where,

C = call value,

S = spot price of 50,

t = expiry period which is 10 days,

Norm = Normal probability distribution with mu=0 and sigma = 1,

K = option strike price of 55,

r = risk free rate of interest – we have assumed to be 0.02 in this example,

σ = daily stock volatility of 3% or 0.03

In Excel speak,

50 * NORM.S.DIST(-0.95145,TRUE)-55 * EXP((-0.02) * 10/365) * NORM.S.DIST(-1.04632,TRUE)

How to Perform an Implied Volatility Calculation in Excel

The model spreadsheet is easy to use. Just key in current stock price, strike price, risk free rate, days to maturity, dividend yield (if any) and option price. The VBA computes implied volatility and back solves the option price which you have entered. As a cross check, option price calculated using Black-Scholes equation must equal to the option price in the input values.

Implied Volatility Calculator

The following VBA snippet calculates price of an European option using Black-Scholes equation:

Implied Volatility Calculator-VBA1

As you can see, lines 19 through 47 calculate implied volatility for the input values that you have entered. The method iterates till it finds a solution. Precision is defined by constant DELTA_VOL, which is the acceptable error of the function’s result. Since the function iterates to find the correct volatility, setting a higher value can speed execution in a worksheet containing 100 and above instances of this function. Lower values increases the precision. Example:  If the exact implied volatility is 16%, setting “Precision” to .05 will cause the function to return a value between 15.95% and 16.05%.

Implied Volatility Calculator

Closing Notes:

  • “European” call options have the same theoretical value as “American” calls.  American puts are difficult to value than European puts.
  • Black-Scholes formula gives you a good approximation of volatility.
  • Since Black-Scholes cannot be deconstructed to solve for volatility, this model iteratively finds the implied volatility.  It is very similar to Excel’s “Goal-Seek” function.
  • Dividend Yield – The annualized dividend yield of the underlying stock expressed in continuous compounding terms.

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4 thoughts on “Implied Volatility Calculator

  1. B Chan

    I feel that the host of this web-site is a dedicated person who have passion to develop & to share.
    Thank you for your kindness in sharing your work.

    Reply
  2. Pingback: Calculating Implied Volatility – Stock Trading NTS

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