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FINCAD offers the most transparent solutions in the industry, providing extensive documentation with every product. This is complemented by an extensive library of white papers, articles and case studies. A Binary Barrier Option is a type of digital option for which an option's payout depends on whether or not the asset touched a barrier level at some time during the life of the option. The value of the payoff is not affected by the size of the difference between the underlying and the strike price, and can be in the form of a cash payment or delivery of the underlying.

The options described here are path dependent, which american digital option pricing that the payout profile depends on the asset value during the life of the option and the value of the underlying asset when american digital option pricing barrier is hit or on the expiry date of the option.

For a call, the payout is received if the underlying asset price is greater than the strike price, and for a put, the payout is received if the strike is greater than the underlying asset price. There are two classes of binary barrier options. The first are options where a payout of cash or the asset is made if the barrier is hit or not hit during the life of the option. The payout is made either when the barrier is hit, or at option expiry.

For cash payouts, this distinction will only affect the period of time over which the payment is discounted. For asset payouts, however, the distinction is more subtle.

If the payout is made when the barrier is touched, then the present value of the payout is equal to the discounted barrier value — since this is the asset value when the barrier is touched. On the other hand, if the payout is made american digital option pricing option expiry, then the present value of the american digital option pricing is equal to whatever the asset value happens to be at the expiry date, discounted back to the valuation date.

The second class includes options where a payout of cash or the asset is made if the barrier is hit or not hit during the life of the option and if the option is in-the-money at expiry. These are types of knock-in and knock-out binary barrier options. There are other types of digital options available within the FINCAD library, including various flavors of double barrier binary options. Introduction A Binary Barrier Option is a type of digital option for which an option's payout depends on whether or not the asset touched a american digital option pricing level at some time during the life of the option.

Technical Details There are two classes of binary barrier options. Calculate the fair value, risk statistics and probability of hitting the barrier for a binary barrier option with a payoff equal to the asset value if the barrier is touched, or nothing if the barrier is never touched.

Calculate the fair value, risk statistics and probability of hitting the barrier for a binary barrier option with a payoff of a fixed amount of cash if the barrier is touched, or nothing if the barrier is never touched.

Calculate the fair value, risk statistics and probability of hitting the barrier for a knock-in binary barrier call or put option with a payoff equal to the value of the asset if the barrier is touched and the option is in the money. Calculate the fair value, risk statistics and american digital option pricing of hitting the barrier for a knock-in binary barrier call or put option with a payoff of a fixed amount of cash if the barrier is touched and the option is in-the-money. Calculate the fair value, american digital option pricing statistics and probability of hitting the barrier for a binary barrier option with a payoff equal to american digital option pricing value of the asset if the barrier is not touched, or nothing if the barrier is touched.

Calculate the fair value, risk statistics and probability of hitting the barrier for a binary barrier option with a payoff of a fixed amount of cash if the barrier is not touched, or nothing if the barrier is touched. Calculate the fair value, risk statistics and probability of hitting the barrier for a knock-out binary barrier call or put american digital option pricing with a payoff equal to the value of the asset if the barrier is not touched and the option is in the money at expiry, or nothing if the barrier is touched.

Calculate the fair value, risk statistics and probability of hitting the barrier for a knock-out binary barrier call or put option with a payoff of american digital option pricing fixed amount of cash if the barrier is not touched and the option is in the money at expiry, or nothing if the american digital option pricing is touched.

Calculate the fair value, delta, and probability of hitting the barrier for a path dependent digital option where the payoff is on the expiration date.

Calculate the fair value, delta, and probability of hitting the barrier for a path dependent digital option where the payoff is made at the time the barrier is touched. The next generation of powerful valuation and risk solutions is here. Portfolio valuation and risk analytics for multi-asset derivatives and fixed income.

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This post is based on problems 2. I was asked how to price a digital option in a job interview - and had no idea what to do! A call is only worth exercising using if the underlying price, , is greater than at , as the payoff from exercising is. A digital call option with is similar - it pays off one dollar if at expiration, and pays off zero otherwise:.

Suppose you have a model for pricing regular call options. How can you use to price the digital option? As a starting point, consider buying a call with and selling a call with:. This is close to the digital option, but not exactly right.

We want to make the slope at steeper, so we need to buy more options. Consider buying two calls with and selling two calls at:. As opposed to a slope of 1 between and , now we have a slope of two between and Generalizing this idea - consider a number. To get a slope of , you buy calls at and you sell calls at. How much will the above portfolio cost? You earn from selling the calls, and pay for the calls.

The net cost is: Many complicated payoffs can be re-created as combinations of vanilla puts and calls. Digital Call Options A digital call option with is similar - it pays off one dollar if at expiration, and pays off zero otherwise: As a starting point, consider buying a call with and selling a call with: Consider buying two calls with and selling two calls at: Given that the slope is , to get an infinite slope, we take the limit as goes to zero.

It might look more familiar if I re-wrote it as: Conclusion Many complicated payoffs can be re-created as combinations of vanilla puts and calls.