An exploratory study of a risk neutral pricing model of accumulators
| Pages | 93-113 |
| DOI | https://doi.org/10.1108/15587891211191407 |
| Published date | 13 January 2012 |
| Date | 13 January 2012 |
| Author | Thomas Kwong,Daisy Fok,Kern Kwong,Lillian Fok |
| Subject Matter | Strategy |
An exploratory study of a risk neutral
pricing model of accumulators
Thomas Kwong, Daisy Fok, Kern Kwong and Lillian Fok
Abstract
Purpose – Accumulators are cutting-edge stock derivative investments that have been the subject of
much controversy in Hong Kong over the past year.Accumulators are exotic options composed of a full
year of daily long up-and-out call options and short up-and-out put options. Because accumulators are
so new, the understanding of accumulatorsis currently very limited. This paper attempts to characterize
and understand the properties of this fairly unknown and new stock derivative investment.
Design/methodology/approach – The study analyzed and characterized accumulators based on
observations from past history of 11 stocks of the Hang Seng Index. Using historical stock data covering
from January 3, 2006, and onward, the profit and loss for each accumulator contract was calculated.
Findings – Through the research it is understood that the profit and loss of accumulator contracts
depends primarily on the following factors: knockout percentage, discount percentage, variability of the
underlying stock, and the overall market trends, among other factors.
Originality/value – This pioneer simulation is an empirical exploratory post factum study that gives
researchers and practitioners further insight how to formulate a risk neutral pricing model for
accumulators in the future.
Keywords Accumulator, Simulation, Pricing model, Risk management, Stock prices, Hong Kong
Paper type Research paper
Introduction
Financial investment has long been a fast track means of getting wealthy in Asia, especially
in Hong Kong, Japan, and Taiwan. Many individual investors are very knowledgeable about
investing in the stock market, and financial institutions offer many convenient ways to invest.
As the financial market has expanded, the appetite of individual investors has outgrown
traditional instruments such as stocks and bonds and new investment instruments have
been developed. This phenomenon has become more apparent in recent years in Asia,
which has experienced rapid economic growth. When the investin g middle class
accumulates new wealth, it causes investors to eagerly seek cutting-edge instruments
that theoretically can bring superior returns. They turn to more non-traditional instruments
with the expectation that these new instruments can bring them a higher yield than the
traditional stock markets. Foreign currency trading, options, discount accumulators, credit
swap, and others have become quite popular in the Asian markets. As a result of this
development, research has become available on these topics (Chan et al., 2009; Fung et al.,
2009; Hseih and Shyu, 2009). Still, many of these financial instruments are so innovative that
individual investors have difficulty understanding the mechanics behind them. The
investors, in turn, rely on the financial institutions to provide information on these new
instruments. In most cases, the financial institutions that provide information to investors are
the same ones that supply the instruments, creating a conflict of interest. Therefore, it is a
balancing act for the financial institutions to protect the individual investors while keeping the
instrument a profitable one. This paper intends to discuss one such instrument, called the
accumulator, which was most popular in Hong Kong.
DOI 10.1108/15587891211191407 VOL. 6 NO. 1 2012, pp. 93-113, QEmerald Group Publishing Limited, ISSN 1558-7894
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JOURNAL OF ASIA BUSINESS STUDIES
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PAGE 93
Thomas Kwong is a Student
at California Institute of
Technology, Pasadena,
California, USA. Daisy Fok
is a Student at University of
Southern California, Los
Angeles, California, USA.
Kern Kwong is a Professor
at California State
University (LA), Los
Angeles, California, USA.
Lillian Fok is a Professor at
the University of New
Orleans, New Orleans,
Louisiana, USA.
Received: 2 November 2008
Accepted: 2 June 2010
Description of options as a financial instrument
Options and their extensions, such as barrier options, are one of the fastest growing stock
derivative investments in the modern market. Knock out discount accumulator equity linked
investments (KODA ELI), or accumulators for short, are a complex option that recently came
upon the world market. Only having come on to the market in the past few years,
accumulators have shocked investors with enticing but deceptively dangerous deals. Our
research characterizes previously unknown properties of accumulators through the analysis
of historical data and provides methods for evaluating accumulators on the actual market.
History of options, barrier options, and knock out discount accumulator equity linked
investments
Many fields have implemented options over the course of history, dating back as far as the
seventeenth century in England. People have used options to gain the right to purchase
land, use intellectual property, or borrow money. This is only a small part of the list of actions
taken using options. Options have been prevalent in America since the nineteenth century,
but modern options were first popularized and standardized by the founding of the Chicago
Board Options Exchange in 1973. Since then, the popularity of options has expanded
rapidly, as has the researchin their pricing (Merton, 1973). The Black-Scholes model (Black
and Scholes, 1973), for which Fischer Black and Myron Scholes received the Nobel Prize for
Economics in 1997, is a classic and well-used method for evaluating options. Despite the
volatile nature of stock pricing, these models provide frameworks for analyzing option
values.
Barrier options were developed in the wake of the growth of standard options, and provide
exotic alternatives to regular calls and puts. Barrier options add certain barriers to the option
contract, at which the option can be either activated or negated (Cheng, 2003). For instance,
a barrier option could be very similar to a call option but instead implements a barrier at a
certain price above the strike price, and if the stock’s price were to reach the barrier, the
option would become void. There are a wide variety of barrier options implementing one or
more barriers that can add complexity to a standard option. Common barriers are ‘‘knock
out’’, negating the option upon reaching the barrier, and ‘‘knock in’’, activating the option
upon reaching the barrier. In fact, some options have two barriers, and these are called
double barrier options. Many of these barrier options are so new that most people know very
little about their functionality and appropriate pricing.
Accumulators are one of the new barrier options about which very little modeling and pricing
data is known. Accumulators are options that commit the holder to purchase a set amount of
stock, such as 200 shares, every business day for an entire year at a designated strike price.
This strike price generally offers between a three and 15 percent discount from the stock
price at the start of the contract. Accumulators are double barrier options with a ‘‘knock out’’
barrier that often ranges from two to seven percent (South China Morning Post, 2008a)
above the stock’s current value anda strike barrier at the strike price below which the holder
is obligated to purchase twice as many shares, in this case 400, per business day. It is
difficult to give actual percentages for the knockout and strike barriers because accumulator
contracts are not public, and those percentages vary depending on the individual contract
and the reporting media source. Typically, the daily stock price used for the accumulator is
the closing price for the day. Some accumulators may lack the doubling at the strike barrier,
or have a different type of barrier at that location, such as a tripling strike barrier. ‘‘Vanilla’’
accumulators do not have this type of doubling or tripling barrier, whereas ‘‘geared’’
accumulators have a doubling barrier. In this study, all accumulators we studied were
geared. We graph an example accumulator contract showing profit per share of stock
(Figure 1). The slope of the geared accumulator payoff graph doubles when the stock price
drops below the strike price, because the investor is obligated to purchase twice as many
shares as normal. In exchange, the geared accumulator has a lower strike barrier than the
vanilla accumulator. When the underlying stock pricereaches the knockout barrier, the profit
line drops off entirely. A sample accumulator contract for Hong Kong and Shanghai Bank
Corporation (HSBC) is included (Appendix 1, Figures A1 and A2).
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