High option trading

The Basics. Listed Options. Longs and Shorts. A Bit More Terminology. Offsetting Option Trades. Expiration, Exercise, and Assignment. American versus European. The Special Properties of Options.

Market Overview

How Options Respond to Changing Conditions. The Greeks. The Role of the Market Maker. Volume and Open Interest. Long Call. Short Covered Call. Short Naked Call. Long Call with Short Stock. Long Put. Short Covered Put. Short Naked Put. Long Put with Long Stock. Equivalent Strategies. Combinational Strategies. Volatility Trading—Buying and Selling Volatility.

Tools of the V-Trade. Selling High Volatility.

Buying Low Volatility. Delta-Neutral Trading—In a Nutshell. Seasonal Patterns in the Grains. Other Commodities.

Some Words of Warning about Naked Writing. The Relationship between Volatility and Price. Debit Spreads—The Calm Approach. Strategies for Trending Markets. Condors—Two-Winged Creatures. Covered Writing—Enhancing Your Returns. The Synthetic—Another Alternative to Stock. Similar to the straddle is the strangle which is also constructed by a call and a put, but whose strikes are different, reducing the net debit of the trade, but also reducing the risk of loss in the trade.

One well-known strategy is the covered call , in which a trader buys a stock or holds a previously-purchased long stock position , and sells a call. If the stock price rises above the exercise price, the call will be exercised and the trader will get a fixed profit.

If the stock price falls, the call will not be exercised, and any loss incurred to the trader will be partially offset by the premium received from selling the call. Overall, the payoffs match the payoffs from selling a put. This relationship is known as put—call parity and offers insights for financial theory. Another very common strategy is the protective put , in which a trader buys a stock or holds a previously-purchased long stock position , and buys a put. This strategy acts as an insurance when investing on the underlying stock, hedging the investor's potential losses, but also shrinking an otherwise larger profit, if just purchasing the stock without the put.

The maximum profit of a protective put is theoretically unlimited as the strategy involves being long on the underlying stock. The maximum loss is limited to the purchase price of the underlying stock less the strike price of the put option and the premium paid. A protective put is also known as a married put.

Another important class of options, particularly in the U. Other types of options exist in many financial contracts, for example real estate options are often used to assemble large parcels of land, and prepayment options are usually included in mortgage loans. However, many of the valuation and risk management principles apply across all financial options. There are two more types of options; covered and naked.

Because the values of option contracts depend on a number of different variables in addition to the value of the underlying asset, they are complex to value. There are many pricing models in use, although all essentially incorporate the concepts of rational pricing i. The valuation itself combines a model of the behavior "process" of the underlying price with a mathematical method which returns the premium as a function of the assumed behavior. The models range from the prototypical Black—Scholes model for equities, [17] [18] to the Heath—Jarrow—Morton framework for interest rates, to the Heston model where volatility itself is considered stochastic.

See Asset pricing for a listing of the various models here. As above, the value of the option is estimated using a variety of quantitative techniques, all based on the principle of risk-neutral pricing, and using stochastic calculus in their solution.

The most basic model is the Black—Scholes model. More sophisticated models are used to model the volatility smile.

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These models are implemented using a variety of numerical techniques. More advanced models can require additional factors, such as an estimate of how volatility changes over time and for various underlying price levels, or the dynamics of stochastic interest rates. The following are some of the principal valuation techniques used in practice to evaluate option contracts. Following early work by Louis Bachelier and later work by Robert C. Merton , Fischer Black and Myron Scholes made a major breakthrough by deriving a differential equation that must be satisfied by the price of any derivative dependent on a non-dividend-paying stock.

By employing the technique of constructing a risk neutral portfolio that replicates the returns of holding an option, Black and Scholes produced a closed-form solution for a European option's theoretical price. While the ideas behind the Black—Scholes model were ground-breaking and eventually led to Scholes and Merton receiving the Swedish Central Bank 's associated Prize for Achievement in Economics a. Nevertheless, the Black—Scholes model is still one of the most important methods and foundations for the existing financial market in which the result is within the reasonable range.

Since the market crash of , it has been observed that market implied volatility for options of lower strike prices are typically higher than for higher strike prices, suggesting that volatility varies both for time and for the price level of the underlying security — a so-called volatility smile ; and with a time dimension, a volatility surface. One principal advantage of the Heston model, however, is that it can be solved in closed-form, while other stochastic volatility models require complex numerical methods.

As such, a local volatility model is a generalisation of the Black—Scholes model , where the volatility is a constant. The concept was developed when Bruno Dupire [24] and Emanuel Derman and Iraj Kani [25] noted that there is a unique diffusion process consistent with the risk neutral densities derived from the market prices of European options.

See Development for discussion. For the valuation of bond options , swaptions i. The distinction is that HJM gives an analytical description of the entire yield curve , rather than just the short rate. And some of the short rate models can be straightforwardly expressed in the HJM framework. For some purposes, e. Note that for the simpler options here, i. Once a valuation model has been chosen, there are a number of different techniques used to implement the models. In some cases, one can take the mathematical model and using analytical methods, develop closed form solutions such as the Black—Scholes model and the Black model.

The resulting solutions are readily computable, as are their "Greeks". Although the Roll—Geske—Whaley model applies to an American call with one dividend, for other cases of American options , closed form solutions are not available; approximations here include Barone-Adesi and Whaley , Bjerksund and Stensland and others.