 The same holds in the case of a binary put. Of course, this option only generates a payoff Q , if the stock price S T , is smaller than the strike price K. Notice that binary option trading is strongly seen as pure speculation and even gambling. Due to the resemblance of the binary option payoff with sports betting, it is hard to justify its hedging value in any risk management exercise.

19. Black-Scholes Formula, Risk-neutral Valuation

The most straightforward way in pricing a binary option is done through a simulation experiment. In many simulation exercises, the geometric Brownian motion, as shown below, can be used to model the underlying stock behaviour.

Another possibility to value binary options is the construction of a multi-step binomial model. In order to implement the stock price evolution in Excel this has to be restated as follows:. The value of a Binary option can be calculated based on the following method:. Step 3: Calculate the payoff of the binary call and, or put and store it.

## Black–Scholes model - Wikipedia

Binary options either generate in the future a certain payoff as specified by the contract or none at all. Can you think of why this is? Does the type of call option change how the underlying changes? Take a look at dirichlet also known as zero gamma condition and other types of boundary conditions. That is the right start, but what is the expectation? Plug this into your formula.

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• Binary Option | Payoff Formula | Example.

The problem is that this expectation is in real probability space and you want it in your risk neutral space. You can use girsanov's theorem.

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