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 Speculative Trading with Options: Volatility Plays
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 Volatility smiles and Black swans

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OPTIONS TRADING
Exotic Options
In all our articles until now we have focused on the simple put and call options also known as vanilla options and related strategies. In this last article we will focus on exotic options.
Exotic options are characterized by a greater complexity than that of the commonly traded vanilla options. Vanilla options are considered simple since the payoff profile is continuous and is only dependent on the value of the underlying at expiry. Exotic options are everything else  which is a very large definition.
Therefore, in this article we will only focus on the vanilla option with in and out features known as knockin, knockout, reverseknockin, and reverseknockout. Furthermore, we will look at the American digital option onetouch, notouch, and doublenotouch.
The knockout option functions by being an ordinary vanilla option, put or call, unless a prespecified barrier level is reached, or touched, before expiry. The option is termed reverse if the barrier is placed where the option is inthemoney. That is, if the barrier is above the strike for a call option or the barrier is below the strike for a put option (see Figure 1 and 2 for illustrations of the knockout feature). The knockin option functions by being worthless unless the barrier is touched, in which case it converts into a normal vanilla option. Again the reverse termed is used if the barrier is placed where the option is inthemoney (see Figure 3 and 4 for illustrations). Notice that holding a knockin and knockout based on the same barrier and vanilla option strike is the same as holding the vanilla option itself. Therefore, the price of holding a knockin and a knockout with the same barrier and strike should be equal to the price of the vanilla option with the same strike. It should now be obvious that the prices of the knockin and knockout options are expected to be lower than the vanilla option with the same strike. In this way, a purchaser of an exotic option may strive essentially to gain the same exposure to a vanilla option but at a lower price  on the condition that his prediction about whether the underlying will reach the barrier level holds true.
While the purchaser of the exotic option does gain an exposure similar to the vanilla option, the pricing dynamics do change dramatically. With vanilla options, the price is always increasing with respect to the volatility parameter. However, barrier options can behave quite differently. For example, a reverseknockout call option with the underlying trading close to the barrier will decrease in value from an increase in volatility as the chance of hitting the barrier increases. On the other hand, the value of the same option will increase in value from an increase in the volatility, if the underlying is far from the barrier, as the increased likelihood of hitting the barrier is compensated by the increased value of the option with respect to its strike. This implies that simple gamma scalping strategies as explain in previous articles, for example, become very difficult to manage, due to the complex influence of both the strike and the barrier on the delta of the option. Therefore, knockin, knockout, reverseknockin, and reverseknockout’s are often best suited as directional option trades, as described in the article about speculative trading.
Another class of exotics options are the American digitals also known as touch options. They function like bets by paying a predetermined amount if a certain condition is met. The payoff is thus the full amount or nothing, which gives rise to the term digital. The onetouch option pays out if the price of the underlying touches the barrier before expiry (see Figure 5). The notouch option works the other way around and pays out if the price of the underlying does not touch the barrier before expiry (see Figure 6). The doublenotouch option pays out if the price of the underlying stays within a range not touching either the lower or the upper barrier of this range before expiry (see Figure 7).
Quotation of touch options is done as a percentage of the possible payout amount, which can be seen as the (discounted) probability of the payout happening. Looking at the quotation as the probability of hitting the barrier, we will see for the onetouch option the effect of the varying volatility and black swans, explained in the previous article. Since we have many small moves compared to a normal distribution, options close to the barrier will be more expensive than if the moves where normally distributed. Likewise if there are more extreme moves, onetouch options with more extreme touch levels will be more expensive due to the increased likelihood of touching. Finally, onetouch options inbetween the two extremes will actually trade at a lower price than if the price moves of the underlying were normally distributed.
In this article we have touched upon the subject of exotic options, there exist many other forms of exotic options such as chooser options, basket options, lookback options, to mention a few of their colorful names. These will be left alone for now. The options explained in this article cover the most heavily traded exotic options which we consider an interesting starting point for most traders.
Steffen Gregersen