**Time value**

Speculators familiar with buying options know it too well: the option value erodes over time if the stock stays level. The option value is composed of two components:

· Intrinsic value (for a call option above strike or a put option below strike)

· Time value

While the intrinsic value only depends on the option strike and the share price, time value is a different animal. It is larger for a stock that is most likely to end up ‘in the money’. Hence the time premium is higher the more of the following clauses are fulfilled:

· the stock price is pretty close to the strike (the option is ‘near the money’),

· the option has some time left for the stock to pass the strike price,

· the underlying exhibits a high volatility, making it more likely for the stock to bridge the gap to the strike price.

Option writers generally take advantage of the time value of their written positions quickly eroding. The rate by which the option value is eroding is defined by the Greek Theta (q). It is expressed in currency per trading day, usually in USD per day, sometimes expressed in cts/day.

The amount by which an option price changes relative to the change of the underlying stock is represented by the Greek delta (δ or Δ, the latter is capital delta). If δ = 0.30, the option is to appreciate by $0.30 for a $1 rise of the stock. For put options, δ is negative. The nice thing about the Greeks δ and q is additivity. Two call options with different strikes have different δ and q. If you’re long one contract of two options (labelled 1 and 2), the combined (δ, q) = (δ

_{1}+ δ_{2}, q_{1}+ q_{2}).**Help the stock is up and my call option fails to mirror it…**

Can happen: especially with a call option ‘near the money’. With

(δ + q) £ 0

the per day loss of time value of the call option would equal or exceed its gain of approaching the strike. Something you like to avoid, therefore consider an option spread.

**Option spreads quenching theta**

A bullish call spread consists in buying an ‘in the money’ call option and selling simultaneously an ‘out the money’ call option with the same expiry date. You would preferably choose a quarterly option (or a yearly leap) which has plenty of time left before expiry. Your investment equals the price difference between the bought call and the written call. It also is the total ‘value at risk’.

For the two Greeks of that spread we obtain: (δ, q) = (δ

_{1}- δ_{2}, q_{1}- q_{2}). The expensive ITM call has an intrinsic value equal to (share price – strike). Its time value is (option price – intrinsic value). The out-the-money written call is pure time value. You notice that the combined q is the difference of the two q’s of the components: the long (bought) and short (written) call. Depending on how you choose the strike levels relative to the current stock price, the combined q is usually near 0, both a slightly negative or a even slightly positive theta value is possible:*an option spread has a weak time dependency*. The time value loss of the ITM bought call is offset by that of the OTM written call.**Parameters, not constants!**

All novice option investors tend to overlook this! The parameters δ and q aren’t constants (neither are the other Greeks). Whereas it is acknowledged that δ depends on the share price, it also varies over time. With an ITM call option, a $1 rise of the underlying share price makes the intrinsic value of the option go up $1. Since the option price rises less than $1, this implies that the time value has dropped.

The option being ITM, δ > 0.5. For an OTM call option, δ will typically be lower than 0.5. It may still be slightly higher than 0.5 for a NTM option of a stock paying a dividend prior to option expiration. Non-zero FED rates also tend to raise δ. The interest rate sensitivity is represented by the Greek r (rho).

A leap (with a far away expiry date) still has value when the stock price of the underlying is far below the option strike. The share price has time left to rise and the option may very well end up in the money. Although below 0.5, the option delta is meaningful and for a $1 rise of the underlying, the option is to rise a few dimes.

As time goes by, the stock price sensitivity of an OTM call is fading: shortly before expiry it doesn’t really matter whether the stock price is 10% or 20% below the call option strike. It’s going to expire worthless anyhow. The ITM call is going to behave almost in lockstep with the underlying share shortly before expiry. The δ is almost equal to 1, meaning time value has dwindled.

The stock price dependency of delta gets steeper as the expiry date approaches. |

In this example the option with one month left is reacting noticeably to the stock price rising only if it gets to about 90% of the strike value. At 10% above the strike value, the option starts behaving almost like the underlying stock. A “real life” example is given in an earlier post: Buying an option ‘in the money’

**Delta evolution and bullish spreads**

Delta variation over time favourably affects a bullish call spread: with the stock having moved sideways the value of the option written OTM has dwindled. Moreover its stock price sensitivity has dropped to near zero as it is likely to expire worthless. On the other hand, the ITM option now has a delta almost equal to 1.

Depending on how you have chosen the strike levels of a bullish spread, the break-even price may be near or even below the stock price level at which the position was opened.

**How does it all work out?**

I’ve revealed the mechanisms here, but how does it all work out? You can find this in any elementary option course, but for the sake of completeness:

- With a bullish spread you have bought an ITM call. To offset the investment cost, you have written an OTM call with the same expiry date. Your net investment is the difference between the option premiums, which is also what you may lose in the worst case.
- The maximum profit is capped to the difference between the two strike prices. The maximum profit is reached as the stock hits the strike price of the written option.
- The combination ends worthless if the stock price drops below the strike level of the option bought ITM. The loss is smaller than what you lose buying a call that expires worthless (you had an incoming option premium, remember.)
- Since you have sold far more ‘time value’ than what you have paid, the break even price most likely is close to where you got in that bullish call spread combination.
- A bullish call spread leverages a limited increase of the underlying stock and easily allows a double of the money invested.
- It’s however clear that you ‘re never going to ‘shoot the moon’ with this strategy.

**Help?**
You ‘re not sure what all those acronyms really mean? Check out in the e-learning section of the 888options site.

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