As with all securities, trading options carry the risk that the value of the option will change over time. However, unlike conventional securities, the return on holding an option is not linear relative to the underlying value and other factors. As a result, the risks associated with with withholding options are more complicated to understand and predict. An alternative approach, though related, is to use a local volatility model that deals with volatility as a deterministic function both the current asset level S t “Showstyle” S_ and the time display style t ” and the time t display style” Therefore, a local volatility model is a generalization of the Black-Scholes model, where volatility is constant. The concept was developed when Bruno Dupire  and Emanuel Derman and Iraj Kani found that there was a single diffusion process, compatible with the dense risk neutrals arising from European options market prices. See #Development for discussion. Another very common strategy is the protective put, in which a trader buys a stock (or holds a previously purchased long share position) and buys a put. This strategy acts as insurance when it invests in the underlying stock, covers the investor`s potential losses, but also reduces an otherwise larger profit if you only buy the stock without the put. The maximum gain of a protective put is theoretically unlimited, as the strategy involves being on the underlying action for a long time. The maximum loss is limited to the purchase price of the underlying stock minus the exercise price of the put option and the premium paid.
A protective put is also known as a married put. While the ideas behind the black-scholes model were revolutionary and eventually allowed Scholes and Merton to receive the associated award from the Central Bank of Sweden for economic performance (also known as the Nobel Prize in Economics) , the application of the model in trade with real options is clumsy due to assumptions of continuous trade, constant volatility and a constant interest rate. Nevertheless, the Black Scholes model remains one of the main methods and bases of the existing financial market, where the result is within the reasonable range.  An option is a derivative, a contract that gives the buyer the right, but not the obligation, to purchase or sell the base asset at a specified price until a given date (expiry date) (strike priceThe strike price is the price at which the option holder may exercise the option to purchase or sell an underlying guarantee, as the case may be). There are two types of options: calls and puts. U.S. options can be exercised at any time before expiry. European options can only be exercised on the expiry date.
According to the same logic, volatility also increases the value of options. This is because the underlying security market is more volatile and the probability of a profitable outcome of an option contract is even higher. More volatility will mean that the price of the underlying security is more likely to go up and down, thereby increasing volatility, which will increase the price of an option. When a developer wishes to acquire land next to its existing development site in the future to expand its project. If the land to be developed is divided between the owners, a buyer can buy back the entire land piece by piece by obtaining option contracts from each owner. A trader who expects the price of a stock to rise may purchase a call option to purchase the stock at a fixed price (“strike price”) at a later date, instead of buying the stock directly. The cash cost of the option is the premium. The trader would not be obliged to buy the stock, but only has the right to do so on the expiry date or the expiry date.