# Straddle and outright option values

## Options trading skills tested :

*Practical understanding of relationship between straddles and outrights.
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## How to set up the training exercise

*Load a Custom Play Volcube simulation with moving spot. Play through some quotes to allow the spot to move a little.*

The purpose of this exercise is make you fully comfortable with the relationship between straddles and outright options. It is something you can practise in the Volcube Mini-game called Straddles, but this exercise brings it into your Volcube trading environment. You can learn about option straddles in this article.

At-the-money straddles are amongst the most important of all option strategies because of their particular characteristic of having low or zero delta but relatively high vega. Straddles are therefore especially important to option and volatility traders as they are most sensitive to changes in implied volatility. Now since a straddle is simply a call and a put of the same strike and expiration traded in the same direction and quantity AND because put-call parity tells us that in many cases puts and calls of the same strike and expiration are, in many important respects, the same instrument, there is a reliable equation that allows us to compute the value of an outright option, given the straddle value, the other outright in the straddle and the spot price. This can be useful to traders in markets where the straddle value is taken as the primary measure of the level of implied volatility. So if the 100 straddle is trading at $6.30, this may equate to a certain level of implied volatility; let’s suppose 25%. Now if the 100 calls are trading at say $3.20 with the spot trading at 100.02, can we calculate what this is equivalent to in the 100 straddle? If put-call parity holds, the answer is yes and this is a useful thing to know. (In this case, the calls are trading at an equivalent straddle value of $6.38, which is rich compared to the actual straddle price).

Now for the exercise where you will learn how to make this calculation. Look at the value of the 100 calls, on the left hand side of the Pricing Sheet. They are worth 3.196. Now imagine these calls are 3.22 bid. **What is this bid equivalent to in the 100 straddle?**

There are several ways to calculate the answer. One is to work out the value of the 100 puts and then add this to 3.22. Notice that the last traded price in the spot market is 100.08 (top right of the Pricing Sheet), so this is where our theoretical values are pinned against. If the 100 calls had a *value *of 3.22 this would be made up of 8 cents of intrinsic value (because the calls are 8 cents in-the-money) and $3.14 of extrinsic value. So, by put-call parity, a bid of 3.22 in the 100 calls is equivalent to a bid of 3.14 in the puts. This implies a synthetic bid in the 100 straddle of **6.36**.

There is a faster method to reach the same answer. Double the number and subtract the intrinsic (if the option is in-the-money) or add it if the option is out-of-the-money. So, for the 100 calls, a 3.22 bid is equivalent to a 3.22 * 2 – 0.08 = 6.36 bid in the straddle. Or a 3.14 bid in the 100 puts, is equivalent to a 3.14 * 2 +0.08 = 6.36 bid.

In markets where the straddle is an important strategy used to measure volatility, the importance of this calculation cannot be underestimated. Its rapid computation (mentally of course) is a fundamental skill for traders to acquire.

Now play through another few steps in Volcube until the spot moves away from 100.08 or wherever it is in your game. Take a look this time at the 101 puts. Imagine an offer in these puts a tick or two below your theoretical value. What offer is that equivalent to in the 101 straddle?

Repeat until you can convert a price in an outright into the equivalent straddle value in a matter of a second or two. You can of course also go the other way; working from a straddle price to the equivalent in an outright, just be reversing the equation.

One final thing to remember. The quantities halve. A bid for 200 lots of the 101 calls is synthetically equivalent to a bid for 100 lots of the 101 straddle. This should be obvious, but in case it isn’t, just imagine that 100 lots of the 101 calls are considered calls but, via put-call parity, the other 100 lots (out of the total of 200) are considered puts. That gives a bid for 100 calls and a synthetic bid for 100 of the same strike puts i.e. a synthetic straddle.

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*These articles are for informational purposes only. They should not be regarded as an offer to sell or as a solicitation or an offer to buy any financial or derivative products.*

## Volcube : options training technology

The world's most advanced option market simulator and training tool, used by leading derivatives trading firms to train their option traders.