Question

Describe each of the following exotic options, and explain when an investor would use them:

1. A lookback option (specifically discussing the difference between a floating lookback option and a fixed lookback option)   

2. An Asian option (specifically discussing the difference between an average price option and an average strike option)              

Answer 1

LOOKBACK OPTIONS

Options that allow the option holder the right to purchase the underlying asset at the lowest price (call option), or sell the underlying asset at the highest price (put option) over a specified period. At expiration, the investor looks back and chooses the largest in-the-money amount that occurred over the life of the option. Lookback options are never out-of-the-money.
Lookback options are exotic contracts that offer the holder the advantage of being able to exercise at an optimal point. Essentially, at expiration the holder can look back (hence the name) at how the price of the underlying asset has performed and maximize their profits by taking advantage of the biggest price differential between the strike price and the price of the underlying asset.
For options traders this is obviously a major benefit, as lookback options can be used to solve one of the biggest problems they face: market timing. This is basically choosing when to enter a position and when to exit it, with the aim obviously being to time entry and exit to make the largest possible returns.
Because of the way lookback options work, the issue of market timing becomes less important as profits are effectively guaranteed to be maximized. Also, the chances of a contract of this type expiring worthless are much lower than other types of options. For these reasons lookbacks are generally more expensive, so the advantages do come at a cost.
Lookbacks can be either calls or puts, so it's possible to speculate on either the price of the underlying security going up in value or going down. They are also known as hindsight options, as they actually give the holder the benefit of hindsight when determining when to exercise.
To fully understand how they work, you need to be aware of the two different types of lookback options – fixed strike and floating strike. Although the concept of these two types is very similar, and both offer the potential for maximizing returns. There is a fundamental difference between the two and the way they work. On this page we have explained both types in more detail.

Fixed Strike:-

Fixed strike lookback options, as the name suggests, have a fixed strike price like most other options contracts. The advantage is in the fact that, at the time of expiration, the holder of fixed strike contracts can choose to exercise them at the point during the term of the contract where the underlying asset was at the most favorable point.
These are cash settled options, meaning the holder is paid a cash settlement equal to the profits they could have made through exercising and buying or selling the underlying asset.

Floating Strike:-

The floating strike lookback option is different to the fixed strike in the way that the name suggests; the strike price is not fixed at the time that the contract written. Instead, the strike price is automatically set at the lowest price of the underlying security during the life of the contract if the call or at the highest price of the underlying security if a put.

ASIAN OPTIONS

The payoff of an Asian style option (or average price option) depends on the difference between the average price of the underlying asset over a certain time period, and the strike price. Such options allow the investor to buy or sell the underlying asset at the average price instead of at the spot price. They are prevalent in commodity markets where a party may have regular and ongoing transactions in a particular underlying asset and hence a desire to hedge itself against price fluctuations. Asian options are also used in situations where the purchaser wants to cover many spot transactions using only one hedging instrument or in situations where it is prudent to reduce the dependence of an option on the spot price of the underlying on a single date. In general (but not always), Asian options are less expensive than their European counterparts, since the volatility of the average price will be less than the volatility of the spot price.
As an example, consider regular consumers of crude oil whose supply price is not fixed, but is set weekly from a particular benchmark. They are concerned that there may be a spike in oil prices over the next few months and want to hedge themselves using options. They require that the payoff of the hedge reflects the weekly purchases made over a specified time period. An Asian style option can be tailored to meet this requirement through the use of weekly price fixings over the applicable period. The option captures changes in the commodity over the averaging period and is significantly less expensive than the alternative of purchasing a basket of European options each maturing on a given fixing date. Most Asian style options use an arithmetic average and sample at discrete and regular time intervals (daily, weekly or monthly closing prices). In addition, there are options that use a geometric averaging procedure.
FINCAD provides functions for pricing European, Bermudan and American style Asian options in all of these situations. Since it can be important to take into account of the effects of the implied volatility smile when valuing Asian options, FINCAD provides the ability to use local volatility models (normal, shifted lognormal and constant elasticity of variance (CEV) processes) and the Heston model of stochastic volatility to price European Asian options.