# Convert option price to odds

This post is about converting the price of an option to an odds format. The same methods also apply if you want to convert stock option prices to an odds format, or any other option price into any odds format including decimal odds, fractional odds, and moneyline (american) odds. A fun application is also found below (including some free bitcoins for you).

For this example, I’ll use a bitcoin option price from Deribit and convert that option price into decimal odds.

The first thing is to choose an option on Deribit to use for our example. At the time of writing, I’m picking the September 28th, 2018, \$8500 calls currently trading at 0.008 (\$51.25) with an implied volatility of 95% and the underlying trading trading at \$6243. This means we will use an out of the money call with 18 days and 9 hours till expiration. Its also worth noting that the contracts on Deribit are european cash settled options.

Now that I’ve chosen an option to use, cnxt I’ll is convert the price of my chosen option into a binary price format. Binary options are “all or none” prices quoted between 0 and 1. Binary options are associated with many over the counter unregulated “gambling” type sites (that are usually a rip off) but its best to forget about binary trading sites and think about binary option prices for what they are; just another price format.

Converting the price of an option on Deribit to a binary number means plugging in the option’s details into a Black-Scholes model, I do this on excel, and here is a link to my spreadsheet.

I plug my chosen option’s time till expiration expressed as a fraction of the year. This changes 18 days and 9 hours to 19.375 days / 365 days = 0.0530821917808219 years. My risk free rate is 1.35%. The implied volatility of this option is 95% and there are no dividends/interest/cashflow associated with it. The underlying price is \$6243 and the strike price is \$8500.

Drumroll please… after plugging in the variables, the excel spreadsheet calculates the price of this binary call option as 0.064 or 6.24/100. This tells us a few things. We know this call option is out of the money, and we know the implied volatility of this option is high, so it makes sense that this option will have a low chance of being called. So its price of 0.054 makes sense. Based on the option’s binary price, we can infer that this option has maybe a 6.4% chance of being called in the money.

The toughest part of this method is calculating the binary option price (which we just did), the easy part is converting this binary price into an odds format we prefer to use. I like using decimal odds, so next I divide 1 by the binary option price. So a binary option of 0.064 = 1/0.064 = 15.46 decimal odds. A binary option of 0.064 can also be expressed in decimal odds format as 15.46.

If we were to post a betting market on whether the price of bitcoin will be higher than \$8500 in 18 days and 9 hours, we might offer decimal odds of 15. For every dollar wagered on whether the price of bitcoin will be higher than \$8500 in 19 days 9 hours, we might be willing to pay 15 back if so.

For fun, I created a fixed odds bet at CoinRoster expressing the option quoted above in decimal odds for readers of this blog to bet on. Click here to view these odds at CoinRoster. You can also get 0.00007 bitcoins for free when you sign-up for CoinRoster using promo code parimutuelfreeplay1. Good luck!