By David Ruscelli
Put, Call and Strike Options (part II)
In the previous article (Put, Call and Strike Options) we have shown how to compose the price of an option (time value + intrinsic value) and listed all the variables that can define the value itself. Now we can get into detail, trying to figure out what strategies can be adopted through the combined use of options.
Factors defining the option value:
1) The market price of the underlying asset. The call value depends on the price of the stock. The more the price of the asset reference increases, the more its value increases, while it decreases in the opposite case. Put options work in the opposite way, so they increase in value when the stock price decreases;
2) The strike price. Same considerations of point 1), but in the opposite direction: the more the strike price increases, the less the value of the call is, as the option will always be more out of the money;
3) The expiration or residual life of the option (strike date or expiration date), which is measured in months or weeks. The greater the duration is, the greater the chance of an event that results in an increase of the price volatility is and therefore the option value will be higher;
4) The volatility of the underlying asset. The volatility of a stock is the property of the price to decrease or increase stronger or slower when new financial events occur. The more a stock is volatile, the greater the chance of an useful quotation for the investor over time is; therefore, the option value will increase;
5) The riskfree interest rate (free risk rate). The interest rate has a fundamental importance because it is used to define the forward price of the underlying asset. It affects the value of an option because its increase raises the forward price of the underlying asset and the strike price too, with an increase in the value of the call and a decrease in the put.
Here below a summary table which explains the pricing of an option
If one of these increases:


The value of: 

Call 
Put


The asset price 
Increases 
Decreases 

The strike price 
Decreases 
Increases 

The option duration 
Increases 
Increases 

The volatility of the asset 
Increases 
Decreases 

The interest rates level 
Increases 
Decreases 





If one of these decreases:

Call 
Put 

The asset price 
Decreases 
Increases 

The strike price 
Increases 
Decreases 

The option duration 
Decreases 
Decreases 

The volatility of the asset 
Decreases 
Increases 

The interest rates level 
Decreases 
Increases 
One of the most important factors is the volatility. It can be defined as the measure of the change of the asset price; therefore, it defines the dispersion of the price of the underlying asset and it must not be confused with the tendency of the price. We can find two concepts of volatility:
 The historical volatility
 The intrinsic volatility.
The historical volatility can be estimated on the basis of the previous prices of the asset and can be calculated as the standard deviation of daily changes in price and for a certain period of time. The historical volatility is calculated as a daily logarithmic change, recorded by a title on a given observation period and is expressed on an annual basis as a percentage value. After the daily survey of prices, there is the calculation of the annualized historical volatility and the historical volatility of the period. The value of the option rises when the volatility increases.
The implicit volatility is defined by the market and implicit in the option prices; this is the value that operators are willing to pay because in line with the volatility they were expecting for that period.
In the next article we will see what strategies that can be adopted through the combined use of put and call options.