# 4 ways to understand option delta

You're welcome to use my option pricing spreadsheet - it's a good way to familiarise yourself with the theoretical values by playing around with various scenarios and viewing the changes that take place after changing the inputs to the model. The remaining sensitivities in this list are common enough that they have common names, but this list is by no means exhaustive.

## BREAKING DOWN 'Delta'

Although rho is a primary input into the Black—Scholes model, the overall impact on the value of an option corresponding to changes in the risk-free interest rate is generally insignificant and therefore higher-order derivatives involving the risk-free interest rate are not common.

The most common of the Greeks are the first order derivatives: The remaining sensitivities in this list are common enough that they have common names, but this list is by no means exhaustive. The use of Greek letter names is presumably by extension from the common finance terms alpha and beta , and the use of sigma the standard deviation of logarithmic returns and tau time to expiry in the Black—Scholes option pricing model.

Several names such as 'vega' and 'zomma' are invented, but sound similar to Greek letters. The names 'color' and 'charm' presumably derive from the use of these terms for exotic properties of quarks in particle physics. For a vanilla option, delta will be a number between 0. The difference between the delta of a call and the delta of a put at the same strike is close to but not in general equal to one, but instead is equal to the inverse of the discount factor.

These numbers are commonly presented as a percentage of the total number of shares represented by the option contract s. This is convenient because the option will instantaneously behave like the number of shares indicated by the delta. For example, if a portfolio of American call options on XYZ each have a delta of 0. The sign and percentage are often dropped — the sign is implicit in the option type negative for put, positive for call and the percentage is understood. Delta is always positive for long calls and negative for long puts unless they are zero.

The total delta of a complex portfolio of positions on the same underlying asset can be calculated by simply taking the sum of the deltas for each individual position — delta of a portfolio is linear in the constituents. Since the delta of underlying asset is always 1. This portfolio will then retain its total value regardless of which direction the price of XYZ moves. Albeit for only small movements of the underlying, a short amount of time and not-withstanding changes in other market conditions such as volatility and the rate of return for a risk-free investment.

The absolute value of Delta is close to, but not identical with, the percent moneyness of an option, i. For example, if an out-of-the-money call option has a delta of 0. At-the-money calls and puts have a delta of approximately 0. The actual probability of an option finishing in the money is its dual delta , which is the first derivative of option price with respect to strike. Given a European call and put option for the same underlying, strike price and time to maturity, and with no dividend yield, the sum of the absolute values of the delta of each option will be 1 — more precisely, the delta of the call positive minus the delta of the put negative equals 1.

This is due to put—call parity: If the value of delta for an option is known, one can calculate the value of the delta of the option of the same strike price, underlying and maturity but opposite right by subtracting 1 from a known call delta or adding 1 to a known put delta. For example, if the delta of a call is 0.

Vega [4] measures sensitivity to volatility. Vega is the derivative of the option value with respect to the volatility of the underlying asset. Vega is not the name of any Greek letter. Presumably the name vega was adopted because the Greek letter nu looked like a Latin vee , and vega was derived from vee by analogy with how beta , eta , and theta are pronounced in American English.

All options both calls and puts will gain value with rising volatility. Vega can be an important Greek to monitor for an option trader, especially in volatile markets, since the value of some option strategies can be particularly sensitive to changes in volatility.

The value of an option straddle , for example, is extremely dependent on changes to volatility. The mathematical result of the formula for theta see below is expressed in value per year. By convention, it is usual to divide the result by the number of days in a year, to arrive at the amount an option's price will drop, in relation to the underlying stock's price. Theta is almost always negative for long calls and puts, and positive for short or written calls and puts.

An exception is a deep in-the-money European put. The total theta for a portfolio of options can be determined by summing the thetas for each individual position. The value of an option can be analysed into two parts: The time value is the value of having the option of waiting longer before deciding to exercise. Even a deeply out of the money put will be worth something, as there is some chance the stock price will fall below the strike before the expiry date. However, as time approaches maturity, there is less chance of this happening, so the time value of an option is decreasing with time.

Thus if you are long an option you are short theta: Except under extreme circumstances, the value of an option is less sensitive to changes in the risk free interest rate than to changes in other parameters. For this reason, rho is the least used of the first-order Greeks.

Rho is typically expressed as the amount of money, per share of the underlying, that the value of the option will gain or lose as the risk free interest rate rises or falls by 1. Obviously, this sensitivity can only be applied to derivative instruments of equity products. Gamma is the second derivative of the value function with respect to the underlying price. Most long options have positive gamma and most short options have negative gamma.

I have found out about this method by looking at topics that are discussed here: Calculate strike from Black Scholes delta. Delta - strike relationship regardless of expiry? In FX world, the ATM strike is the delta-neutral strike, that is, the absolute delta values of a call and the corresponding put are the same. Moreover, the delta can be premium adjusted or not depending on the particular currency pair. See the linked paper as mentioned by AntoineConze.

There are specific quotation conventions for specifying ATM and deltas for FX options quotes unadjusted deltas, premium adjusted deltas, etc. These conventions vary across currency pairs. See this paper https: By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. Your data provider should give you strike, also.

At least if you're paying them money. What kind of option is this? I am not familiar with zinc march It's Zinc on the London Metals Exchange: I handle volatility curves where moneyness is quoted in delta by an iterative guess: Use an initial guess for delta of 0. Repeat using Newton-Raphson, until the difference in delta is small enough.

Jesper Harder 59 2. David-Michael Lincke 2. So it's very possible. I don't have any experience with this exchange and it's something that the OP should check out. My answer is really more general about how someone would quote delta on a typical equity option. Thanks for the lesson! OK, I might be confusing "delta quoting convention" with the "sticky delta" model: Rustam 2 Sign up or log in Sign up using Google.

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