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This Demonstration shows the price and "Greeks" for binary call and put options together with the corresponding vanilla European option as a function of underlying spot price (the option strike price is …

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CHAPTER 5 OPTION PRICING THEORY AND MODELS In general, Strike Price Net Payoff on call option Figure 5.1: Payoff on Call Option Price of Underlying Asset

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A binary option (also called a if the option expires with the underlier above the strike price. vanilla call with that of a European cash-or-nothing binary call:

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This MATLAB function computes cash-or-nothing option prices using the Black-Scholes option pricing model.

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For the common high-low binary option, the trader buys a binary call option if he thinks the price of the underlying asset will go up above the current market price or if he thinks the underlying asset price will go down, then he will buy a binary put option. If his assessment is correct, he will receive a payout.

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The value of a European binary call option, paying $1 if the underlying asset is above the strike at expiration, in the Black-Scholes world is. e−r(T−t)N(d2) where the asset price is S, time is t, strike K, expiration T, asset volatility σ, dividend yield D and risk-free interest rate r and.

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Thus, we know that the investment, $50 minus the call option price, has to be equal to the present value USING THE BINOMIAL OPTION-PRICING MODEL FOR MORE THAN ONE

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For example if a binary call with a strike of $1,000 (the strike is the underlying price at wish he starts to win) was bought for $50 and has a 50% delta. This means that if the underlying price move from $1,000 to $1,005 i.e. up $5 then its option price moves by $5 times %50 = $2.5.