First of all I would like to give credit to Liying Zhao Options Analyst at HyperVolatility for helping me to conceptualize this article and provide the quantitative analysis necessary to develop it.

The present report will be followed by a second one dealing with second order Greeks and how they work. Options are way older than one might imagine. The pricing of options has always attracted academics and mathematicians but the first breakthrough in this field was pioneered at the beginning of the by Bachelier.

He literally discovered a new way to look at option valuation, however, the real shift between academia and business occurred in when Black, Scholes and Merton developed the most popular and used option pricing model. Such a discovery opened an entire new era for both academics and market players.

Being one of the most crucial financial derivatives in the global market, options are now widely adopted as an effective tool to leverage assets or control portfolio risk.

Nowadays, it is easy to find articles, researches and studies on option pricing models but this article will instead focus on options Greeks and in particular first-order Greeks derived in the BSM world. Mathematically, Greeks are the partial derivatives of the option price with respect to different factors such as volatility, interest rate and time decay.

The purpose of this article is to explain, as clearly as possible, how Options Greeks work but we will concentrate only on the most popular ones: Delta, Gamma, Vega or KappaTheta and Rho. It is worth mentioning that all the charts that will be presented have been extrapolated by assuming that the underlying is a WTI futures contract, that the options have a strike price X ofthat the risk-free interest rate r is 0.

The chart displays how the Delta moves in respect to the underlying price S and time to maturity T: The chart clearly shows that in-the-money call options have much higher Delta values than out-of-the-money options while ATM options have a Delta which oscillates around 0.

Call options have a Delta which ranges between 0 and 1 and it gets higher as the underlying approaches the strike price of the option which means that out-of-the-money call options will have a Delta close to 0 while ITM options will have a Delta fluctuating around 1.

Many traders think of Delta as the probability of an select option in jsp examples expiring in-the-money but this interpretation is not correct because the N d term in its formula expresses the probability of intrinsic value of stock options calculator option expiring ITM but only in a risk-neutral world.

In real trading conditions higher Delta calls do have a higher probability to forex scalping strategy system v1.4 ea free ITM than lower Delta ones, however, the number itself does not provide a reliable source of information because everything depends on the underlying.

The Delta simply expresses the exposure of the options premium to the underlying: Put options, instead, have a negative Delta which ranges between -1 and 0 and the below reported chart displays its fluctuation in respect to the underlying asset. The same applies to put options but in this case the ATM Delta will forex dobre ksiazki Gamma reaches its maximum when the underlying price is a little bit smaller, not exactly equal, option trading delta gamma theta vega the strike of the option and the chart shows quite evidently that for ATM option Gamma is significantly higher than trading forex is not easy OTM and ITM options.

The fact that Gamma is higher for ATM options makes sense because it is nothing but the quantification of how fast the Delta is going to change and an ATM option will have a very sensitive Delta because every single oscillation in the underlying asset will alter it.

The interpretation is rather simple: The below reported 3-D chart sistema trading forex Vega as a function of the asset price and time to maturity for a WTI options with strike atinterest rate at 0. The chart clearly highlights the fact that Vega is much higher for ATM options than for ITM and OTM options.

The shape of Vega as a function of the underlying asset price makes sense because ATM options have by far the highest volatility potential but what does Vega really tell us in real trading conditions? Implied volatility is the key factor in options pricing because the price of a single options will vary according to this number and this is precisely why implied volatility and Vega are essential to options trading the HyperVolatility Forecast service provides analytical, easy to understand projections and analysis on volatility and price action for traders and investors.

As time to maturity is always decreasing it is normal to express Theta as negative partial derivatives of the option price with respect to T. Theta represents the time decay of option prices in terms of a 1 year move in time to maturity and to view the value of Theta for a 1 day move we should divide it by or the number of trading days in one year.

The below reported chart shows how Theta moves:. Theta is evidently negative for at-the-money options and the reason behind this phenomenon is that ATM options have the highest volatility potential, therefore, the impact of time decay is higher.

Options Greeks: Delta,Gamma,Vega,Theta,Rho | HyperVolatility

Think of an option like an air balloon which loses a bit of air every day. ITM options are more influenced by changes in interest rates negative Rho because the premium of these options is higher and therefore a fluctuation in the cost of money interest rate would inevitably cause a higher impact on high-premium instruments.

Furthermore, it is rather clear that long dated options are much more affected by changes in interest rates than short-dated derivatives. The below reported chart displays how Rho oscillates when dealing with put options:.

Option Greeks - Delta,Gamma,Theta,Vega,Rho

The Rho graph for put options mirrors what it has been stated for calls: ITM have a larger exposure than ATM and OTM put options to interest rate changes and long term derivatives are much more affected by Rho than in the short term even in this case the 3-D graph displays negative values.

Hence, an increase in interest rates will augment the value of a hypothetical call option and the rise will be equal to Rho. As stated at the beginning of the present report this is only the first part and a second article dealing with second order Greeks will be posted soon. Your email address will not be published. Home Forecast Service About Contacts HyperVolatility Channel Legal Disclaimer Our Partners HyperVol Links HyperVolatility Links Volatile Readings Volatile Forums.

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Option Greeks Explained | The Options & Futures Guide

How do we interpret it? The below reported chart shows how Theta moves: The below reported chart displays how Rho oscillates when dealing with put options: Leave a Reply Cancel reply Your email address will not be published. Support Forum Plugins Themes Documentation Suggest Ideas. HyperVolatility All Rights Reserved.