Machine Learning Methods
After completing this reading, you should be able to: Discuss the philosophical and... Read More
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Plain vanilla derivatives represent the most basic version of financial derivatives, including futures contracts, forwards, swaps, and over-the-counter (OTC) instruments used in fairly liquid markets. They have a simple expiration date, exercise price and have no additional features. On the other hand, exotic derivatives alter the traditional characteristics to create a complex financial instrument that’s tailored to meet the specifications of a particular counterparty.
In a plain vanilla derivative, most details are precisely outlined and straightforward. Such details include the initial cost, current market value, expiration date, amounts to be paid, and the cost of the existing position. For exotic derivatives, most of these issues are negotiable.
Some of the reasons behind the development of exotic derivatives include the need to:
When two or more derivatives with contrasting features are combined, a package is formed. Common packages include a bull, bear, calendar spread, or even a straddle, as discussed in the previous chapter. Through these packages, a trader can create a zero-cost product.
Take a collar, for example. A trader combines a long position in a put with a lower strike price and a short position in a call with a higher strike price. If the premium received after selling the call offsets the premium paid for the put, the overall cost of the combined position is reduced to zero.
The option premium for a zero-cost product is not paid up-front. Zero cost products have been customized in such a way that the option premium is payable at maturity as x(1+r)^{t} where x is the premium that would have been paid now, t is the time to maturity, and r is the interest rate. In this arrangement, the future value of the option premium, x(1+r)^{t}, is exchanged for the option payoff at option maturity.
One of the most prominent characteristics of standard American options is the possibility to exercise them on or before the expiration date. However, there are certain things that could be done that effectively transform a standard option contract into a non-standard one. These include:
For example, a six-month American call could be exercisable only on the last day of each month. Such a restriction creates what’s called a Bermudan option.
For example, a 3-month lockout period could be imposed on a six-month call. That means the holder is not allowed to exercise the option during the first three months of the contract.
For example, a three-year call could be characterized by strike prices of $30 in the first year, $35 in the second year, and $40 in the final year.
A gap is a European put or call option that has a strike price, \({ K }_{ 1 }\), and a trigger price, \({ K }_{ 2 }\). The trigger price determines whether or not the option will have a nonzero payoff. The strike price determines the actual amount of the payoff. The payoff will always be nonzero (positive or negative) for a gap call option as long as the final stock price exceeds the trigger price. For a gap put option, the payoff will always be nonzero as long as the final stock price is less than the trigger price. If \({ K }_{ 1 }={ K }_{ 2 }\), the gap option payoff will be the same as that of an ordinary option.
When \({ K }_{ 2 }>{ K }_{ 1 }\),
$$ \text{Gap call option payoff}=\begin{cases} { S }_{ T }-{ K }_{ 1 } & if\quad { S }_{ T }>{ K }_{ 2 } \\ 0\quad \quad \quad \quad & if\quad { S }_{ T }\le { K }_{ 2 } \end{cases} $$
Where:
\({ K }_{ 1 }\)=Strike price
\({ K }_{ 2 }\)=Trigger price
Let’s say \({ K }_{ 1 }\) = 100 and \({ K }_{ 2 }\) = 105. This would mean that the trigger price exceeds the strike price.
At expiration, we’ll have the following payoffs:
$$ \begin{array}{lccccc}\text{Stock Price} & 96 & 100 & 104 & 105 & 112 \\ \text{Payoff} & 0 & 0 & 0 & 0 & 12 \end{array} $$
If the trigger price is less than the strike price for a gap call option, negative payoffs are possible.
Let’s say \({ K }_{ 1 }\) = 108 and \({ K }_{ 2 }\) = 100. This would mean the trigger price is less than the strike price.
At expiration, we’ll have the following payoffs:
$$ \begin{array}{lccccc}\text{Stock Price} & 96 & 100 & 106 & 108 & 112 \\ \text{Payoff} & 0 & 0& -2 & 0 & 4 \end{array} $$
We can see that between stock prices of 100 and 108 at expiration, the payoff to the call option holder is negative.
Traders can also buy and sell gap put options:
$$ \text{Gap put option payoff}=\begin{cases} { { K }_{ 1 }-S }_{ T } & if\quad { S }_{ T }<{ K }_{ 2 } \\ 0\quad \quad \quad \quad & if\quad { S }_{ T }\ge { K }_{ 2 } \end{cases} $$
If the trigger price is greater than the strike price for a gap put option, negative payoffs could occur.
A cliquet option, also known as a ratchet option, comprises a series of options with a forward start date and we have some rules for determining the strike price. For example, a two-year put cliquet option consists of two put options – a one-year put option effective now and a one-year put option that will start one year from today.
Now consider a three-year annuity payment arrangement. Payment will occur at year n (one-year option), year n+1 (one-year option starting in one year), and at year n+2 (one-year option starting in two years).
As the words suggest, a forward start option kicks off at some point in the future. For example, today, a trader may purchase a six-month put that will only come into effect three months from today. Forward start in-the-money options are usually used as incentives to boost employee productivity and encourage employee loyalty.It is usually assumed that the option will be at the money at the time the option starts.
A compound option is simply an option on an option,i.e., an option for which the underlying is another option. Thus, a compound option usually has two strike prices and two maturity dates. A compound option can take one of four different forms:
In a chooser option, the holder is allowed to decide whether it is a call or a put prior to the expiration date. The choice between the two depends largely part on the value of each. Chooser options can be viewed as packages of call options and put options with different strike prices and times to maturity.
A barrier option is an option whose existence depends upon the underlying asset’s price reaching a predetermined barrier level. It can be either:
In a binary option, the payoff is either a fixed monetary amount or nothing at all. Binary options are of two types:
Assume that an asset-or-nothing binary option has a payoff of $40,000 for an asset price above $10. The payoff will be $0 if the asset price at maturity is $9.99 and $40,000 if the asset price is $10.01.
A lookback option allows the holder to exercise an option at the most beneficial price of the underlying asset over the life of the option.
Lookback options have two main categories, that is, floating lookback options and fixed lookback options.
In an Asian option, the payoff depends on the average price of the underlying asset over a period of time as opposed to standard options, where the price of the underlying determines the payoff at a specific point in time.
As the name suggests, asset exchange options provide room for investors to be able to exchange their assets for another asset. For example, an investor based in the US may exchange his US dollars for Canadian dollars.
A basket option gives the right but not the obligation to buy or sell a basket of securities. The components of the basket could be bonds, stocks, currencies, e.t.c., and may be specified in advance.
In a volatility swap, volatility is exchanged based on a notional principal. Similarly, a variance swap involves the exchange of variance – the square of volatility – based on a notional principal. Volatility and variance swaps do not bet on the price of the underlying.
Variance swaps can be replicated using a collection of puts and calls. They are easier to price compared to volatility swaps.
Hedging of exotic options can be done by creating a delta-neutral position and rebalancing frequently to maintain delta neutrality. However, some exotic options, such as barrier options, are relatively difficult to hedge. To hedge a barrier option, the portfolio that replicates its boundary conditions must be shorted and unwound when any part of the boundary is reached. The advantage of static options replication is that it does not require frequent rebalancing.
Question
A cash-or-nothing call option has a payout profile equivalent to zero or:
A. The underlying asset price if the value of the asset ends below the strike price.
B. The underlying asset price if the value of the asset ends above the strike price
C. A set amount if the value of the underlying asset ends below the strike price
D. A set amount if the value of the underlying asset ends above the strike price.
The correct answer is D.
A cash-or-nothing call option pays a fixed amount as long as the value of the underlying asset is above the strike price at expiration. It differs from a standard call since the payoff does not increase as the underlying’s market price soars above the strike price.