Difference in premium between call and put

[Guest Calvin]

I'm having trouble figuring this out. 

 

A stock has a call option with a strike price of $100 and a premium price of $1. 

The same stock has a put option for a $100 strike price and a premium of $2.

Is it not possible for me to write a $100 put for $200 premium, buy a call for $100, and have a guaranteed profit of $100? Am I missing something?

[Kim 8,043]

It is not a guaranteed profit.

For example, if the stock goes down to $98, your call loses $100 and your put is breakeven. If the stock continues going down, you are losing extra $100 for each $1 it moves down, in addition to $100 loss in the calls.

[clems 27]

Selling a put is the same type of bullish play as Buying a call.  So if the markets go down, you lose on both.  

[jason 0]

Generally, call and put prices on the same strike / expiration are governed by put-call parity.  

http://www.investopedia.com/terms/p/putcallparity.asp

Calls / puts are priced in a way such that there is no risk-free money (arbitrage-free) that can be made from simply buying one and selling another.  

[Guest Calvin]

On 8/2/2017 at 1:52 PM, Kim said:

It is not a guaranteed profit.

For example, if the stock goes down to $98, your call loses $100 and your put is breakeven. If the stock continues going down, you are losing extra $100 for each $1 it moves down, in addition to $100 loss in the calls.

I don't understand how the put is losing. I don't execute the call if the stock falls to 98$ and the put expires worthless. 

 

If the the stock falls to $97 the put expires worthless and I don't execute the call?

 

i understand put/call parity. So what if I find a example without it. Wouldn't it be guaranteed?

[Kim 8,043]

If the stock goes to 98, put does not expire worthless - it is $2 ITM and is worth $200 at expiration, so you have to buy it for $200 (or be assigned the stock). The call expires worthless, so you lose $100 on the call anyway.

if the stock goes to say $95, the put is worth $500, so you lose $300 on the put and $100 on the call.

[cuegis 683]

On 8/2/2017 at 0:21 PM, Guest Calvin said:

I'm having trouble figuring this out. 

 

A stock has a call option with a strike price of $100 and a premium price of $1. 

The same stock has a put option for a $100 strike price and a premium of $2.

Is it not possible for me to write a $100 put for $200 premium, buy a call for $100, and have a guaranteed profit of $100? Am I missing something?

Yes. You are missing something.You didn't complete the risk-free arbitrage.

If you sell a put and buy a call (same strike, same expiry) you have just bought 100 shares of synthetic stock and will incur all of the same risks and rewards as if you were long 100 shares.

If such pricing DID exist, the way to "lock in" the profit would be to sell the put for $200, buy the call for $100, then sell 100 shares of the stock at $100.

Now there is zero risk other than the rare "pin" risk which would happen if the everything expired with the stock exactly at $100.

This way you would not know whether you are going to be assigned on your short put, or whether you should excercise your long call, and dump the stock.