InvestorQ : What is the impact on option Greeks of a put option when the volatility of the stock increases or it reduces?

# What is the impact on option Greeks of a put option when the volatility of the stock increases or it reduces?

1 year ago

To understand the impact of volatility on option Greeks, let us start off with a base case scenario wherein the put option is an ATM option. Consider the table below:

 Underlying Price 180 The current market price of the stock, for example, the closing price of Tata Motors on the last traded day Exercise Price 180 The price at which the underlying instrument will be exchanged. Also called Strike Price or the contract price Today's Date 21-02-2019 Current Date or the date of the trade and this forms the base point for time to expiry Expiry Date 28-03-2019 The Date on which the options contract expires which is routinely the last Thursday of the month Historical Volatility 20% The Historical Volatility of the asset's returns measured by the Variance of returns Risk Free Rate 5.00% The current risk free interest rate i.e. your return on cash held in the bank or the bare minimum returns expected Dividend Yield 0.00% The Annualized Dividend Yield which is measured by the quotient of the dividend per share and the stock price DTE (Years) 0.10 The time left to expiry of the option expressed in terms of fractional years Call Option Theoretical Price 4.0188 Theoretical Value of the Put Option Delta -0.4568 The amount that the theoretical price will change if the market moves up/down 1 point Gamma 0.0356 The amount that the Delta will change if the market moves up/down 1 point Theta -0.0513 The amount that the theoretical price will change when 1 day passes or the time decay Vega 0.2211 The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage point Rho -0.0827 The amount that the theoretical price will change if interest rates move up/down by 1 percentage point # 35 Days Expiry to the last Thursday of March 2019 series is assumed here.

Now let us look at a scenario wherein the volatility goes up higher from 20% to 30%. What is the impact on the value of the put option and the Option Greeks in this case?

 Underlying Price 180 The current market price of the stock, for example, the closing price of Tata Motors on the last traded day Exercise Price 180 The price at which the underlying instrument will be exchanged. Also called Strike Price or the contract price Today's Date 21-02-2019 Current Date or the date of the trade and this forms the base point for time to expiry Expiry Date 28-03-2019 The Date on which the options contract expires which is routinely the last Thursday of the month Historical Volatility 30% The Historical Volatility of the asset's returns measured by the Variance of returns Risk Free Rate 5.00% The current risk free interest rate i.e. your return on cash held in the bank or the bare minimum returns expected Dividend Yield 0.00% The Annualized Dividend Yield which is measured by the quotient of the dividend per share and the stock price DTE (Years) 0.10 The time left to expiry of the option expressed in terms of fractional years Call Option Theoretical Price 6.2310 Theoretical Value of the Put Option Delta -0.4609 The amount that the theoretical price will change if the market moves up/down 1 point Gamma 0.0237 The amount that the Delta will change if the market moves up/down 1 point Theta -0.0826 The amount that the theoretical price will change when 1 day passes or the time decay Vega 0.2213 The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage point Rho -0.0855 The amount that the theoretical price will change if interest rates move up/down by 1 percentage point # 35 Days Expiry to the last Thursday of March 2019 series is assumed here.

What exactly happens to all the option Greeks in this case? Let us go one by one. When the volatility goes up you get to see the theoretical value of the option go up which is obvious because the price of the put option is positively correlated to volatility. However, the change in volatility has not impacted the Delta sensitivity in a big way. However, the Theta of the call option has gone up sharply due to the increase in volatility. That is because the volatility favours the buyer of the option and while it is the Theta that favours the seller of the option. Therefore an increase in volatility means that the put option loses value faster. What about Vega? The Vega of the put option has been not really impacted as the sensitivity of the option price to the volatility is not impacted. What could happen to the option Greeks of the call option if the volatility came down to 10%? Check the table below:

 Underlying Price 180 The current market price of the stock, for example, the closing price of Tata Motors on the last traded day Exercise Price 180 The price at which the underlying instrument will be exchanged. Also called Strike Price or the contract price Today's Date 21-02-2019 Current Date or the date of the trade and this forms the base point for time to expiry Expiry Date 28-03-2019 The Date on which the options contract expires which is routinely the last Thursday of the month Historical Volatility 10% The Historical Volatility of the asset's returns measured by the Variance of returns Risk Free Rate 5.00% The current risk free interest rate i.e. your return on cash held in the bank or the bare minimum returns expected Dividend Yield 0.00% The Annualized Dividend Yield which is measured by the quotient of the dividend per share and the stock price DTE (Years) 0.10 The time left to expiry of the option expressed in terms of fractional years Call Option Theoretical Price 1.8143 Theoretical Value of the Put Option Delta -0.4324 The amount that the theoretical price will change if the market moves up/down 1 point Gamma 0.0705 The amount that the Delta will change if the market moves up/down 1 point Theta -0.0204 The amount that the theoretical price will change when 1 day passes or the time decay Vega 0.2192 The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage point Rho -0.0764 The amount that the theoretical price will change if interest rates move up/down by 1 percentage point # 35 Days Expiry to the last Thursday of March 2019 series is assumed here.

Now how does the fall in volatility impact the value of the put option? Obviously, the value of the put option has come down which is natural with a fall in volatility. What about Delta? Delta has actually fallen because the fall in volatility makes the intrinsic value of the option more important than the time value. What about the Theta or the time decay. Just as rise in volatility works against the option seller (both in the case of calls and puts), the fall in volatility works in favour of the option seller and this is apparent in the fall in Theta or the time decay. The Vega has however fallen very marginally despite the sharp fall in the volatility of the call option.

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