A short introduction into exotic non-vanilla options as well as the weaknesses of Black-Scholes
Besides the plain vanilla options we can trade on E*Trade, there's in fact a whole universe of bespoke and exotic derivatives that are traded Over-The-Counter with sophisticated institutions. Here, we'll go through a few types of exotic options and then speak a little about where Black Scholes is insufficient.
Types of Exotic Options
Weakness of Black Scholes
Black-Scholes option pricing model assumes a few things about financial markets which do not fit reality: no gap risk, deterministic rates, deterministic dividends, deterministic volatility. With respect to gap risk, the model assumes that one can hedge stocks continuously and for any size. In reality, assets can gap or jump instead of trading continuously, thereby preventing a short option holder from effectively hedging with the underlying. Also, the Black-Scholes model assumes that interest rates and dividends are constant over the period of the option, but in reality, these parameters vary over time. The volatility of interest rates and dividends can significantly impact long-term option prices. (For a discussion on tail volatility of long-term interest rates and its impact on equity options: http://relavalue.blogspot.com/2013/12/hyperinflation-other-tail-in-equity.html). Lastly, asset volatility is not constant as assumed by Black-Scholes. When a position will realize volatility impacts the profit and loss from that position since the gamma of an at-the-money option is greatest at maturity; hence, the specification that vanilla options are "path-dependent."
Option Pricing Models
A few models have attempted to resolve these shortcomings of Black-Scholes. Before the crash of 1987, most market participants assumed that the implied volatility was the same for options across different strikes and moneyness. However, repeated catastrophes verify that market crashes happen more frequently than predicted by a normal distribution of returns. This phenomenon is known as volatility skew or volatility smile. In the local volatility model, volatility is a function of terminal spot and time; therefore, this model tries to address the existence of volatility skew. Nonetheless, local volatility has shortcomings in pricing option payouts with multiple observations, such as cliquets. The Heston model is a stochastic volatility model where the volatility of assets are not deterministic, but rather random. After Heston, there are other models which address short-comings of Black-Scholes, to be followed up in future posts...
- Digital Options - Digital options are also known as “cash-or-nothing” options and pay a fixed amount if an option expires in the money or nothing if the option expires out of the money.
- Quanto and Compo options - These reference options whose pay-off can be in a currency which is different from the underlying. A client may want exposure to a foreign underlying, but not want the exposure to the foreign exchange rate. In those scenarios, the client can trade an quanto option or swap, where the pay-off is only dependent on the underlying performance and not on the F/X.
- Auto Callable Note - These structured products are issued to private banking clients and get automatically redeemed (“autocalled”) when the the underlying price crosses a pre-determined barrier. As a result, the maturity of the trade is not known because the product could be canceled at any date up to the maturity of the note.
- Cliquet - Also known as a rachet option, a cliquet is a series of forward-starting at-the-money options where the strike is reset periodically.
- Options on a basket - Instead of having a call on just one underlying, a client may have a view on a sector or group of companies and want to trade an option on a basket of stocks. Examples of these types of options would be a best-of call or worst-of put. The correlation between underlyings would impact the pricing; for example, a client can get cheaper bearish exposure by buying a worst-of put and would be long correlation through that structure.
- Hybrids - These options combine equity and fixed income characteristics. For example, one can trade a hybrid SPX option which knock-outs if oil futures trade below a certain level.
- And the list goes on...
Black-Scholes option pricing model assumes a few things about financial markets which do not fit reality: no gap risk, deterministic rates, deterministic dividends, deterministic volatility. With respect to gap risk, the model assumes that one can hedge stocks continuously and for any size. In reality, assets can gap or jump instead of trading continuously, thereby preventing a short option holder from effectively hedging with the underlying. Also, the Black-Scholes model assumes that interest rates and dividends are constant over the period of the option, but in reality, these parameters vary over time. The volatility of interest rates and dividends can significantly impact long-term option prices. (For a discussion on tail volatility of long-term interest rates and its impact on equity options: http://relavalue.blogspot.com/2013/12/hyperinflation-other-tail-in-equity.html). Lastly, asset volatility is not constant as assumed by Black-Scholes. When a position will realize volatility impacts the profit and loss from that position since the gamma of an at-the-money option is greatest at maturity; hence, the specification that vanilla options are "path-dependent."
Option Pricing Models
A few models have attempted to resolve these shortcomings of Black-Scholes. Before the crash of 1987, most market participants assumed that the implied volatility was the same for options across different strikes and moneyness. However, repeated catastrophes verify that market crashes happen more frequently than predicted by a normal distribution of returns. This phenomenon is known as volatility skew or volatility smile. In the local volatility model, volatility is a function of terminal spot and time; therefore, this model tries to address the existence of volatility skew. Nonetheless, local volatility has shortcomings in pricing option payouts with multiple observations, such as cliquets. The Heston model is a stochastic volatility model where the volatility of assets are not deterministic, but rather random. After Heston, there are other models which address short-comings of Black-Scholes, to be followed up in future posts...
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