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# Payoff vs Prrobability

Discussion in 'Options' started by panzerman, Aug 25, 2006.

1. ### panzerman

A lot of people calculate probabilities when deciding which strike to consider, but has anyone here traded options based on payoff instead?

Payoff = probability*(reward/risk)

In essence, trading at strikes with the highest payoff instead of highest probability. I'm wondering if over time, that trading based on payoff is the smarter choice. I've tended to notice that ATM or slightly OTM strikes generally have the highest payoffs.

Why not consider expectancy of the bet ?

expectancy = ((win% * winsize) - (loss% * losssize)) / losssize

So if its a 70% winresult with wins 2x the loss size

e = ((0.7 * 2) - (0.3 * 1)) / 1
= 1.1

So for every \$1 you bet you expect a return of \$1.10 (on top of the original dollar).

3. ### panzerman

I doubt that you will get 2:1 returns except for outright long positions (no spreads.) The problem then is that strikes with a 70% (delta 0.3) chance of finishing OTM have a low payoff compared to ATM strikes.

4. ### xtrhvydty

panzer, I know what you're saying, you're looking for the "optimal" strike price, considering the product of return * probability. However, the inherent pricing of the options themselves is based on the assumption that all options will have exactly the same expectancy. In other words there is no optimal strike from a theoretical standpoint. The probability/price ratio should be constant, so a higher probability of ending ITM means a higher price. Plot the strike prices as a function of distance from the stock price to see. This is of course is based on an option pricing model, whose distribution model is not exact. Also the inputs, such as implied future volatility, are just inputs and are really unknown. In addition, probability calculators assume constant volatility, so your own probability calculator is a gross assumption anyway. In reality, if you want to fool the option model you should construct a histogram of volatility and a histogram of returns based on the actual stock itself. Then use the histogram returns over the time period in question (instead of the probability calculator) and the histogram average volatility. The GARCH model (look it up) tries to do this.

Many people argue over the GARCH mathematics but miss an obvious point -GARCH simply demonstrates that the stock itself is the best predictor of its own behavior.

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