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A binary call option is, at long expirations, similar to a tight call spread using two vanilla options. One can model the value of a binary cash-or-nothing option, C, at strike K, as an infinitesimally tight spread, where is a vanilla European call: [1] [2]
The value computed at each stage is the value of the option at that point in time. Option valuation using this method is, as described, a three-step process: Price tree generation, Calculation of option value at each final node, Sequential calculation of the option value at each preceding node.
A binary call option is, at long expirations, similar to a tight call spread using two vanilla options. One can model the value of a binary cash-or-nothing option, C, at strike K, as an infinitesimally tight spread, where is a vanilla European call: [35] [36]
N(d −) is the (Future Value) price of a binary call option, or the risk-neutral likelihood that the option will expire ITM, with numéraire cash (the risk-free asset); N(m) is the percentage corresponding to standardized moneyness; N(d +) is the Delta, or the risk-neutral likelihood that the option will expire ITM, with numéraire asset.
Option values vary with the value of the underlying instrument over time. The price of the call contract must act as a proxy response for the valuation of: the expected intrinsic value of the option, defined as the expected value of the difference between the strike price and the market value, i.e., max[S−X, 0]. [3]
Otherwise the intrinsic value is zero. For example, when a DJI call (bullish/long) option is 18,000 and the underlying DJI Index is priced at $18,050 then there is a $50 advantage even if the option were to expire today. This $50 is the intrinsic value of the option. In summary, intrinsic value: = current stock price − strike price (call option)
In the binary system, each bit represents an increasing power of 2, with the rightmost bit representing 2 0, the next representing 2 1, then 2 2, and so on. The value of a binary number is the sum of the powers of 2 represented by each "1" bit. For example, the binary number 100101 is converted to decimal form as follows:
The value is defined as the least squares regression against market price of the option value at that state and time (-step). Option value for this regression is defined as the value of exercise possibilities (dependent on market price) plus the value of the timestep value which that exercise would result in (defined in the previous step of the ...