How Option Time Value Changes as a Put Moves In the Money

# out of the money time value versus in the money time value


# out of the money time value versus in the money time value












For an out of the money option the time value is entirely positive, then if it moves into the money the time value has a negative impact on the new intrinsic value, ok, but it looks like the negative impact is disproportionate to the positive value there was when the option was out of the money... what is this effect?

So for example EURUSD is @ 1.0950 and the 1.0900 1 week put option is 50 / 55. A few hours later that day EURUSD moves to 1.0850 but the 1.0900 1 week put option price only moves to 70 / 75

In other words the put option price isn't the 50 pips of intrinsic value plus the earlier 50 / 55 pips of time value, or a value more like 100 / 105 (or for a small adjustment for time something like 98 / 103) instead it's often quite a lot less: like 70 / 75... what is that effect and why?

Something in the time value has changed from positive to negative.

If we break down the time value in terms of greeks, in this example the theta and rho are negligible because the underlying market price moves take place over a matter of hours and the option has 1 week more to run... We can see the option delta is clearly less than 1, but the delta doesn't change sign, right? I mean in this example the market moved 100 pips which took the option 50 pips into the money. Even with a delta effect you'd expect the 50 pips intrinsic value to be reflected in the price... correct me if I am wrong. The gamma peaked at the money and then decreased as the option's intrinsic value moved into the money.

What am I missing here? Does the gamma change sign? Is this some positive / negative vega effect?

Apologies if this is a newbie question :)

## Answer by mxzzzzz (score 2)

https://quant.stackexchange.com/a/22927

it is not a "newbie question". actually it is very deep question, especially if you are trying to trade options in some way. all Greeks are about change in premium of the option. Premium consists of two components: time value + intrinsic. Greeks cannot tell you anything about this decomposition, they deal only with total sum (i.e. with overall premium). So The effect that you observe can be explained as follows: when you move into the money zone your premium rises AND at the same time the composition of premium changes - the farther you go in the money the more time value "converts" into intrinsic. This means if you, for example, want to sell an option and collect premium then any movement out of ATM strike (up or down) is negative for you (i assume you are delta-hedged). Time value is a result of convexity, convexity is at maximum at ATM strike.

## Answer by Grégoire Courtois (score 0)

https://quant.stackexchange.com/a/66450

Very clear answer by @mxzzzzz! You can visit https://demonstrations.wolfram.com/OptionsTimeValue/ to have a feel for how time value is affected around the strike, along with the effect of volatility and time to maturity. It also shows you that binary options have negative time value when ITM!