Binary options (also called “Fixed Return Options,” “FRO,” or digital) are popular in the OTC market for hedging. They are also useful for speculators and for other traders to construct complex derivatives portfolios.
The payoff for these kinds of options is fixed. Buyers can get a fixed amount of cash or assets in case the option will be in-the-money or get nothing if options will be out-of-money on expiration date. That is the reason why these options are called “binary” – because only two outcomes exist for the buyer:
- Get nothing ($0)
- Get a fixed payoff (for example $1,000)
In addition to the OTC market, binary options are traded at AMEX and CBOE.
The payout amount for CBOE binary options is $100. CBOE lists both put and call binary options. If (at expiration date) the underlying price will be above the strike price, the buyer of call will receive $100 per contract; but if the price will be below the strike price, he will receive nothing.
Interesting point – the price of binary options with a $100 payout will reflect the probability that the underlying security price will reach the selected price at expiration. Example: price $0.25 means 25% probability.
Let’s take a look at the example – in Aug 2012, a trader bought a “cash-or-nothing” binary option contract with following terms:
- Expiration – March 2013 (nine months to expiration)
- Underlying price – $100
- Strike price – $80
- Cash payout – $10 ($1,000 for one option contract)
Market conditions are as follows:
- Interest rate – 1.5%
- Volatility – 35%
In this case, option will be quoted approximately $2.13 and P/L chart at expiration date will look like:
How do you calculate fair value and Greeks for binary option? According to the Black-Scholes model, a binary option is derivative of an European option (for example, the June 15th-strike call binary will be the mathematical derivative from the June 15th-strike vanilla option).
So, binary’s fair value has the same curve as vanilla’s Delta; and binary’s Delta has the same curve as vanilla’s Gamma.
Let’s take a look at the portfolio of binary and vanilla options with the following parameters:
- Strike – $15
- Expirations – Aug. 2012, Sept. 2012, Dec. 2012, Mar. 2013
Suppose volatility is 125% and interest rate is 1.5%. In regards to the Black-Scholes model, P/L and Delta charts will be the following:
Binary options have been introduced in two of ETNA’s solutions for option trading:
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