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This is the 12th in an ongoing series on Basic Options. In this video, we will look closer at Delta
In the last video, I mentioned that the Delta is the rate of change in an option's value when there is a change in the price of the underlying stock. More formally, it is the rate of change in an option's value with respect to changes in price of the underlying stock.
This is a little bit of an over simplification, but a simple way of thinking of it is- when the price of the stock changes one dollar, the Delta is the percent of $1 that the option will change in value.
For instance, if a Call Option has a delta of 0.6, and the stock increases $1 in value, then the Option will increase 60 cents in value. If a Call Option has a Delta of 0.4, and the stock increases $1 in value, then the option will increase 40 cents in value.
If a Put Option has a Delta of -0.3, and the stock decreases $1 in value, then the Put Option will increase 30 cents in value. If a Put Option has a Delta of -0.7, and the stock decreases $1 in value, then the Put Option will increase 70 cents in value.
I also mentioned in the last video, that the Delta is the Hedge ratio.
Let's look at an example. Let's say that a trader has 300 shares of stock, and he is worried that the price of the stock may drop. Therefore, the trader buys 5 Put Options that have a delta of -0.6. At this point, he is Delta Hedged. In other words, if the price of the stock drops $1, his 300 shares of stock drop a total of $300 in value. However, the Delta of -0.6 means that, for each $1 drop in the price of the stock, each Put Option Contract increases 60% of $100 or $60. The trader owns 5 Puts, so his stock decreased in value $300, but his Put Options increased $300 total.
In other words, the option contracts increased in value the exact same amount that the stock decreased in value, so the trader was hedged against loss.
If you remember from my last video, once the price of the stock does change, the Delta changes as well. As a stock goes up and down in value, the Delta increases and decreases.
This means that once the stock price moves, a once hedged position is no longer completely hedged. To maintain a hedge, the ratio of option contracts to shares of stock must be readjusted by increasing or decreasing the amount of shares of stock or option contracts so that the hedge ratio is once again balanced.
Delta Hedging was one of the keys to the Black Scholes formula. The theory was that if one could theoretically continue to keep readjusting the ratio of option contracts to shares of stock on a continuous basis, then one could be constantly hedged and theoretically remove all risk of loss. Therefore, if that is true, then a bunch of theories must apply, or one can place offsetting trades and make more money than one can make on a risk free investment such as a US Government Bond without risk of loss.
Delta Hedging must be adjusted for more than just the changes in the price of the stock as the Delta also changes when there is a change in volatility, Interest Rates, or the time left until the option expires.
Trading a hedged position is called Delta Neutral trading, and will be the subject of a later video.
An option's Delta is derived using probability. I mentioned in the first video that one can create a probability or odds curve of what the future value of the stock will be. For a Call Option, the Delta is derived from the a probability distribution of what the future value of the stock will be, multiplied by the probability that the stock will be above the option strike price. Put another way- If and only if the Option expires in the money, the Delta is a probability distribution of how far into the money the option will be.
So that a bit more on an option's Delta. In the next video, we will compare buying a call option to selling a put option. I hope you enjoyed this video. Thanks for watching.