This game tests your understanding of how straddles and outright options are related. The value of puts and calls in this game is linked by put-call parity and the simple definition of a straddle (i.e. the addition of a call and put of the same strike and expiration). Let’s go through an example from a game.

Spot:                   79.35
Strike:                 78
Put value:            ???

Here we need to calculate the Put value. We reason as follows:

i) The 78 strike put is out-of-the-money. The 78 strike call is in-the-money. This is because of the current Spot price.

ii) Because of i) the call has \$1.35 of intrinsic value (the difference between the strike and the spot); the put has zero intrinsic value.

iii) The extrinsic value of the put and the call are the same (due to put-call parity).

iv) We know that:

Straddle value = Put value + Call value       (1)   (from the definition of a straddle)

So, Put value = Straddle value – Call value   (1)’

We also know that:

Put extrinsic value = Call extrinsic value        (2)  (from put-call parity)

and that:

Call value = Call extrinsic value + Call intrinsic value (3)

So, substituting (2) and (3) into (1)’, we can say that

Put value = Straddle value – (Call intrinsic + Put extrinsic) (4)

Since the put value is entirely extrinsic, we can re-arrange (4)

2 * Put value = Straddle value – Call intrinsic (5)

Sub in the actual numbers:

Put value = ½ * (7.57 – 1.35)

Put value = \$3.11

This is the very long-winded way of arriving at the answer. It should be easy enough with practice to calculate the answer in your head.

### All you need to remember is that the straddle value is equal to the intrinsic value plus twice the extrinsic value.

So here, we could have just taken the straddle price, deducted the intrinsic value and halved the answer to give us the value of the out-of-the-money put. Be sure to check whether the call or the put is the in-the-money option in the question you are answering. Good luck!

## How this straddle calculation is used in the real options market

Traders will often need to make the conversion between an outright and the corresponding straddle. This is because often the at-the-money straddle is a measure of volatility in the market and there will be resting bids and offers in the straddle. The straddle’s last traded price will often be an important price which traders will track.

So being able to move between an outright and the straddle is very important. If a broker shows a \$3.09 bid in the 78 puts in the above example, would you know what bid that is equal to in the 78 straddle?

The answer is 7.53. (Twice \$3.09 plus \$1.35 of intrinsic). There is an even quicker way to make this comparison but many senior traders will prefer junior traders to learn this method first as it shows correct understanding! If you want to know the super short-cut, email [email protected] for details!

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