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## Option Valuation

Options delta or Hedge ratio

Hedging measures are often referred to as delta options. The ratio is a tool that enables us to summarize the overall exposure of option portfolios at different exercise rates and maturity periods. Option weight is the change in option value for a $1 increase in share price. A call option has a positive hedge ratio and a put option has a negative hedge ratio.

Under the black scales option formula, the hedge ratio of the call option is N(d1) and the hedge ratio of the put is N(d1)-1. Remember that N (d) represents the area under the normal curve up to d. Therefore, the call option hedge ratio must be positive and the put option hedge ratio is negative and has a value less than 1.0.

Defined variables

The value of selecting black scales assumes that the variable is given. We can ask a different question. What is the variance (or standard deviation) of the observed selection value to fit the black scale formula? This means stock volatility. A defined variable is a variable defined by the value of the option. An investor can compare actual and implied volatility.

If the actual volatility is higher than the implied volatility, the investor may conclude that the option’s fair value is higher than the perceived value. Hence, you can choose the option as a good investment. You can use an excel spreadsheet to calculate the value of selecting black scales with the specified variable.

Dividend option

Share prices decrease by the amount that reflects the payment of the dividend. As a result, the value of the call option will decrease and the value of the put option will increase. The share price is considered to have low risk and risky sector. The black scale model includes the risky part of the share price. The current share price (from the previous dividend date to the present) can be considered as part of the share price risk. So, to value a call option, we need to adjust down the share price to the present value of the dividend payment during the life of the option, and then use the black scale model. We also need to adjust for volatility in the dividend payout ratio because in the dark scale model it is the volatility of the risky part of the share price. This is generally ignored in practice.

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