# Trading in fx option gamma strategies product

Technically, this is not a valid definition because the actual math behind delta is not an advanced probability calculation. However, delta is frequently used synonymously with probability in the options world.

Usually, an at-the-money call option will have a delta of about. As an option gets further in-the-money, the probability it will be in-the-money at expiration increases as well. As an option gets further out-of-the-money, the probability it will be in-the-money at expiration decreases. There is now a higher probability that the option will end up in-the-money at expiration.

So what will happen to delta? So delta has increased from. So delta in this case would have gone down to. This decrease in delta reflects the lower probability the option will end up in-the-money at expiration. Like stock price, time until expiration will affect the probability that options will finish in- or out-of-the-money. Because probabilities are changing as expiration approaches, delta will react differently to changes in the stock price.

If calls are in-the-money just prior to expiration, the delta will approach 1 and the option will move penny-for-penny with the stock. In-the-money puts will approach -1 as expiration nears. If options are out-of-the-money, they will approach 0 more rapidly than they would further out in time and stop reacting altogether to movement in the stock.

Again, the delta should be about. Of course it is. So delta will increase accordingly, making a dramatic move from. So as expiration approaches, changes in the stock value will cause more dramatic changes in delta, due to increased or decreased probability of finishing in-the-money.

But looking at delta as the probability an option will finish in-the-money is a pretty nifty way to think about it. As you can see, the price of at-the-money options will change more significantly than the price of in- or out-of-the-money options with the same expiration.

Also, the price of near-term at-the-money options will change more significantly than the price of longer-term at-the-money options. So what this talk about gamma boils down to is that the price of near-term at-the-money options will exhibit the most explosive response to price changes in the stock. But if your forecast is wrong, it can come back to bite you by rapidly lowering your delta.

But if your forecast is correct, high gamma is your friend since the value of the option you sold will lose value more rapidly. Time decay, or theta, is enemy number one for the option buyer. Theta is the amount the price of calls and puts will decrease at least in theory for a one-day change in the time to expiration.

Notice how time value melts away at an accelerated rate as expiration approaches. In the options market, the passage of time is similar to the effect of the hot summer sun on a block of ice. Check out figure 2. At-the-money options will experience more significant dollar losses over time than in- or out-of-the-money options with the same underlying stock and expiration date.

And the bigger the chunk of time value built into the price, the more there is to lose. Keep in mind that for out-of-the-money options, theta will be lower than it is for at-the-money options. However, the loss may be greater percentage-wise for out-of-the-money options because of the smaller time value.

Obviously, as we go further out in time, there will be more time value built into the option contract. The portfolio would be picking up negative delta which the trader would cover by buying stocks [buying low] in a falling market.

The trader is making a profit in this situation by accumulating negative deltas on the way down. It would start to appear that being long gamma always gives you a profit. Remember that we told that positive gamma is an expensive strategy because of the time decay. To be able to earn profits overall, the stock movements should be able to compensate for the loss in time decay.

So when the trader believes that the market is going to be sluggish [small moves], he would keep a short gamma position and be happy to earn PnL due to theta. But, being short gamma is a risky strategy. The trader will start loosing money in trending markets. The analysis is similar to the discussion above, when the market crashes the portfolio picks up positive delta and the trader will find himself in a situation where he is selling when the market is crashing [selling low].

Similarly when the market rallies, the portfolio would pick up negative delta and the trader would find himself in a situation where he's buying in the peaking market to delta hedge. In a collapsing market the traders sometimes might like to hedge less often in the hope that the market would rebound [after all you dont realize profit or loose unless you book it].

But then the risk manager should know that this strategy runs the risk of realizing even more losses in future by not booking small ones today. Hence short gammas can get the risk managers worried. A physicist thinks reality is an approximation to his equations. A mathematician doesn't care. Gamma exposure and risk management 3. I have my own problems to solve.