Long Straddle Delta: Don’t Just Wait till Expiration

In the previous article about long straddle option trades, we looked at them mainly from the perspective of holding a long straddle position till expiration and explored various scenarios for your P/L. Though the buy and hold approach and never looking at the position prior to expiration is one way to trade straddles, you will often prefer watching and managing the position during the whole time and possibly also closing it sooner.

What-if calculations are not enough

Though they are still very useful for knowing your theoretical risk and reward conditions, the simple static scenario calculations from the previous article are not sufficient when you want to manage a long straddle position in real time. In this case, you will need to measure the position’s exposure to major factors like underlying stock price or passing time at every moment.

Yes, we are now talking about the option Greeks. With today’s option trading platforms you can watch the Greek values in real time summed up for your whole position and see the exposure immediately. Let’s now look at the most important one: the delta.

Opening a long straddle position at the money

Let’s say you have opened a long straddle position by buying a call and a put option on Bank of America, both options with strike price of 20. If Bank of America stock is trading at 20 at the time, both these options are at the money. This is when a long straddle position can be bought for the lowest price and when it makes the most sense to open it if you intend to play it as an unbiased non-directional long volatility trade.

Long straddle delta at the money is zero

An at the money call option has a delta of roughly 0.50 (if stock price goes up 1 dollar, the call option’s price goes up by 0.50), while an at the money put option has a delta of roughly -0.50 (if stock price goes up 1 dollar, the put option’s price goes down by 0.50). If you hold both options simultaneously, the total delta of your position is the sum of the two deltas, which in this case equals zero. This is in line with long straddle being a non-directional trade.

Stock goes up from the strike price: delta turns positive

If Bank of America stock price goes up by several dollars, the call option you hold as part of the straddle is now in the money and its delta increases to somewhere between 0.50 and 1.00. The put option on the contrary is out of the money (if the stock ended up higher than the strike price, the put option would be worthless at expiration). The put option’s delta moves closer to zero and it is now somewhere between -0.50 and zero.

You again calculate the total long straddle delta by summing up the two deltas (a larger positive number for the call and a smaller negative number for the put). You get a positive number. For example the call option’s delta is 0.70, the put option’s delta is -0.30, and the total long straddle delta is 0.40. As a result of the underlying stock price going up, the long straddle position has become directional. It has a positive delta and its value and your profit increases as the stock price goes up.

The higher the stock, the higher the delta

The higher the underlying stock price gets:

When the stock price gets very far from the straddle’s strike and/or very little time remains till the straddle’s expiration, the call option’s delta is almost 1.00, the put option’s delta is almost zero, and the long straddle position behaves almost like a long stock position.

Stock goes down from the strike price: delta turns negative

On the other hand, if Bank of America stock goes down from the strike (e.g. to 15), the call option is out of the money and its delta is closer to zero, while the put option is in the money and its delta is closer to -1.00. The overall delta of the long straddle position is now negative. The long straddle becomes directional, but in this case it is bearish (the total delta is negative). The further the stock falls, the more negative the straddle’s delta gets, and in an extreme case long straddle can behave almost like a short stock position.

Does a long straddle position always win?

A quick recapitulation:

Long straddle as a long volatility trade profits when the stock moves a lot and we don’t care which way it goes. Up or down. Wonderful, isn’t it? But when do you lose?

Time value and cost of a long straddle

In order to open a long straddle position, you must buy the options (that’s why it’s called long). You pay a premium, because both calls and puts you buy have time value at the time you are buying them. The longer the time to expiration (and the greater chance for the stock to move a lot and make you a profit), the more you pay for the time value.

Long straddle worst case scenario

The worst case scenario with a long straddle is when the stock stays exactly at the strike price of your options. Not only you get nothing in terms of intrinsic value, but the option premiums melt with the passage of time. In this case, the trade results in a loss. A good thing with long straddle is that you can’t lose more than what you have paid for the position and your maximum risk is limited and controlled.

Also watch long straddle theta and vega

Time is against you and it is therefore good to keep an eye on it. Passage of time does not only cost you money, but it also influences the deltas and the straddle’s directional exposure. When managing a long straddle position, other Greeks are worth watching besides the delta, especially theta and vega. We’ll talk about them soon in another article.

Related pages

formula of kurtosisstandard deviation without calculatorvega greekshow to write ln in excelaveraging percentages calculatorhistorical volatility formulacoefficient of skewexcel normdist functionhow to calculate stdevhow to calculate mean variance and standard deviationwhat does oversold mean in the stock marketmsft historical pricesfxf trackingblack scholes xlsyahoo finance historical exchange ratesetf vxxthe pricing of options and corporate liabilitieshow to trade using macdaveraging percentages calculatorpro shares ultraoptions trading booksthe black scholes option pricing model13f filings databasefutures roll datesvix realtimehow to calculate daily volatility of a stocksymbol for vixstraddle positionsquaring a negativevariance formula derivationexpiration calendarvix futures term structureweighted average cost inventory formulablack shoelsvix futures expirationstdev sweighted average cost inventory methodhow do you calculate sample variancecalculate coefficient of skewnessproshares short s&p 500vqt etnhow to short the vixskewness in statisticskurtosis coefficientmean median standard deviation calculatorcalculating the sample variancewhat does vix meanskewness and kurtosis calculatorformula for sample covariancescholes mertonweighted standard deviation excelhow to calculate mean variance and standard deviationrsi formulavariance defblack scholes definitionfxb etfcredit suisse nassau branchstdev.squote vixcalculate variance in excelhow to find median with even numbersdefinition of std deviationthe greeks financekurtosis for normal distributionskewness and kurtosis in statisticsvega greek symbolformula for standard deviation in excelsharpe ratio calculatorsample median calculatorbull call spread payoff diagramvix and morecboe delayedprice variance calculatorleveraged etfs listformula to calculate variance in excel