Saturday, October 18, 2008

The Frog and the Roo

Recently the CBOE Volatility Index hit a record high of 80. Most of the experts have commented that they never see such a high value before. When volatility becomes high, the price of the options increases as well. I did some searching and found this the Frog and the Roo illustration in a option book easy to digest.

To understand the role of volatility and options prices, just imagine you are at carnival with a unusual game called a frog jumping game. A frog starts in the middle of a floor and it can only jump left or right. The frog jumps randomly to left or right with equal probability. At the end of one minute, the frog’s final destination is marked and you are paid $1 for every foot the frog is to the right of the starting point. If the frog happens to land on the left, you get nothing.

How much would you pay to play this game? There is no right or wrong answer but just pick a number that you think it is reasonable. Now, let’s change the game with the same set of rules except now it’s a kangaroo.

How much would you pay to play this game now? There is no right or wrong answer but just estimate how much wills this game worth to you. It should be obvious that no matter how much you choose for the previous frog game, you are willing to spend more for this kangaroo game. Why is it so? That’s because the kangaroo has the ability to jump further, and that means you could win more money and so this game worth more to you.

Notice that although the reward for both games are different, both have the same negative downside of risk. That is because for both games, you are limited to the risk of losing your $1 bet for every foot to the left of the starting point. In the other hand, your upside is the one that worth the most. Looking at the payoffs of both games, it is obvious that the kangaroo game is more valuable.

To understand how volatility affects option prices, just replace the frog and kangaroo with ATM calls on two different stocks. Which call is more valuable to you? It is the one which has the higher ability to move or in other words it is the stock with higher volatility.

Of course, there are still many reasons that affecting option prices but at least for now, I get a better understand of this unique relationship between the ‘V’ word and option pricing.

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