# Value of Short Call Option

*EDIT* Short call is at the money. Theta increases - does the value change at all? This question confused the sh1t out of me… If I remember correctly, this was the scenario and I said the short call increased in value. Took me a while to choose between that and the no-change b/c of premium.

value goes down over time, for the short position its a gain for the long position its a loss

It was an ATM option. He was short. So he was long theta. So he gained money because everything except the passing of time remained the same.

Lurky Wrote: ------------------------------------------------------- > It was an ATM option. He was short. So he was long > theta. So he gained money because everything > except the passing of time remained the same. Ah ok, I remember now. Good call. Whew, got lucky on that one.

I said no change in value… since he got sold it, his position shouldn’t change unless it moves at or in the money right??

The change in value of his position is negative the change in the option price. Option price goes down over time given all else equal, which means his position value goes up.

Right. The very next question was also tricky.

That question was confusing. I thought if you sold calls, all you care about is the initial call premium? At first I picked no change, but then I realized what they probably wanted me to answer. Gain on the theta question, and loss on the volatility question.

I thought the volatility question said that it went o 15% but the model said 20% so it went down which would also be a gain for a short call no?

If I recall, it was an INCREASE in volatility by X%.

i guess i don’t understand options very well… say i sell an at-the-money call to my neighbor for \$5 If somehow the underlying doesn’t change in price over the next few weeks, I still have his \$5. If the underlying drops way out of the money, I still have his \$5. Only if the option moves in the money does my position change. For him, since he owns the option, the value should change no matter which way it goes, since he can later sell this option… where I am wrong here?

The issue is, being short an option, does your value change? I really don’t know. I know you gain the initial premium, and thus would be locked in at a “gain”. But I feel that the options still have value in the market, so technically you can recognize a gain/loss relative to the initial premium. I did not put ‘no change in value’ for either of the questions. So, I either got 2/2 or 0/2 on those :-/

Pretty sure that was the case. 20% -> 15%. So the value of the call goes down and since he was selling the call, he sees a gain.

Nope Vol decreased so you gain for selling the options. And Florida Gator, I know exactly what you’re talking about and I thought about it during the test but I figured that they must have been looking to test your option greeks and not deal-logic so to speak. In any case, it might actually make sense because when you sell those options you have a future liability for the value of those options, so theoretically should decrease your total position value.

No change in cash doesn’t mean no change in value. Just because you still have the original premium doesn’t mean the value hasn’t changed. Think of a swap or futures contract where there is no initial cash flow but the value can change any time.

A short position is a liability. It isn’t free money… It could cost you a lot if the price shoots to 100000 (although it was covered). So if you are less short (as they were) you gain, simple as. And vice versa.

Just remember, options are a zero sum game. If volatility decreases, value of long call decreases, so value of short call must increase.

To put an end to this discussion, being a fixed income trader, he sold the call, so as time decreases, he gets theta back, i.e value increases. Its the opposite position being long the call, as we like to say it in the real world, you bleed your theta as time decreases.

just think of it this way: if at time zero the short call in out of the money by 5. You then add “X” amount for the time value so lets just say it’s now worth -10. Assuming the spread from from the strike and stock price remain the same (5 in this case), as you get closer to maturity, the “X” portion of the value gets smaller so at expiration it’s only worth 5…so you would gain value

so the short in this case will lose money if the value of the underlying drops significantly correct? i believe that was another question in this vignette