Download 50 The LC Gupta Committee Report: Some Observations

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The L.C. Gupta Committee
Report: Some Observations
SUMON KUMAR BHAUMIK
Introduction
. . . human and
technological capital
are of paramount
The previous two issues of Money & Finance highlighted the nature
of financial derivatives, the risks associated with derivatives trading, and
some regulatory measures that can alleviate the risk-related problems
(Bhaumik, 1997b, 1998). To recapitulate, the two papers pointed out the
following:
•
importance in the
context of derivatives
•
trading. These are
necessary to avoid
miscalculations and to
•
bring about market
efficiency which forms
•
the basis of pricing of
a number of
derivatives
instruments.
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financial derivatives can be used to effectively hedge against
risks associated with volatility of financial variables, but that
these instruments can also be used for speculative purposes;
speculation is an essential ingredient of a liquid financial
market, and the risk of a financial crisis by way of speculative
activity is perhaps overstated because dealers of over-thecounter (OTC) derivatives are careful about the choice of
counterparties and derivatives exchanges mitigate such risks
through use of regulatory provisions like daily marking
portfolios to the market;
standard trading practices like dynamic hedging of positions in
the cash market using, for example, stock index futures
contracts can lead to greater volatility (and hence risk) during
periods of sharp downturn in market sentiments;1 and
most of the major disasters involving financial derivatives have
been consequences of sustained failures in internal monitoring
mechanisms.2
Further, the papers argued that stylised regulatory measures like
capital adequacy of dealers and exchange members, and ad hoc measures
like trading halts are perhaps the best possible way to avoid sudden crises
that can adversely affect liquidity and solvency of the traders, thereby
precipitating systemic problems. They also brought into focus the fact that
human and technological capital are of paramount importance in the
context of derivatives trading. These are necessary to avoid miscalculations
as in the case of Orange County, and to bring about market efficiency which
forms the basis of pricing of a number of derivatives instruments.3
1
See Bhaumik (1998) for a description of the events during the 1987 collapse at
the New York Stock Exchange.
2
The high-profile insolvency of Barings, and the de facto absence of monitoring
of the its Singapore based trader Nick Leeson is a case in point.
3
If a market is efficient then it offers few (and ideally no) arbitrage
opportunities, and this absence of arbitrage opportunities forms the basis for estimation of
“correct” prices of futures contracts.
Since the publication of these papers, the Securities and Exchange
Board of India (SEBI) has gone a long way towards the introduction of
financial derivatives in India. The apex body has accepted the proposals of
the L. C. Gupta Committee, and has decided to introduce derivatives
trading in the form of stock index futures contracts. This decision has been
welcomed by the central government, and these instruments are expected to
make their appearance at the National Stock Exchange (NSE) by the end of
the year. Hence, time is ripe to take a close look at the Gupta Committee
Report Specifically, it would be of interest to see whether the report
recognises the problems associated with trading of financial derivatives in
India, and how it proposes to address these problems within the regulatory
framework.
L. C. Gupta Committee Report
The Findings and the Proposals
The Committee came out strongly in favour of “introduction of
financial derivatives in order to provide the facility for hedging in the most
cost-efficient way against market risk.” More importantly, it recognised the
fact that “the market should ...... have speculators who are prepared to be
counterparties to hedgers,” and that while a market comprising largely of
speculators is unwarranted, “[a] soundly based derivatives market requires
the presence of both hedgers and speculators.” It should be noted that the
Committee restricted the scope of its report to exchange traded derivatives,
thereby leaving out of its purview structured instruments like swaptions.4
The important findings of the Committee include the following:
•
•
of the 112 respondents to the questionnaire sent to brokers and
financial institutions, about 67 per cent favoured the
introduction of stock index futures as the first step towards
introduction of financial derivatives trading in India,5 and
stock index options came a distant second with 39 per cent
support; and
an overwhelming 70 per cent of the respondents viewed
financial derivatives as hedging instruments, the shares those
expressing interests about participation as dealer/ speculator,
broker and option writer being 39 per cent, 64 per cent and
36 per cent respectively.
After taking into consideration the views expressed by the
respondents, as well as experiences of other developed financial markets like
those in the United States, the Committee floated several proposals
pertaining to the regulatory paradigm. These include:
4
A swaption is a combination of a swap and an option. Indian corporates and
banks are familiar with OTC derivatives in the foreign exchange market, by way of trades
involving forward and swap contracts. More complex OTC products involve combinations
of forward and options contracts, and are often known as structured notes. One such note
precipitated the high profile insolvency of Orange County.
5
This is hardly surprising given that 67 out of the 112 respondents to the
Committee’s questionnaire are members of the broking community.
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The committee
recognised the fact
that “the market
should ...... have
speculators who are
prepared to be
counterparties to
hedgers,” and that
while a market
comprising largely of
speculators is
unwarranted, “[a]
soundly based
derivatives market
requires the presence
of both hedgers and
speculators.”
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•
•
•
•
the development of a two track framework for derivatives
trading comprising of SEBI’s rules and regulations regarding
derivatives exchanges and their members, and the exchanges’
own rules and regulations governing concerning net worth of
members/ traders, amount of security deposits that they would
have to maintain with the exchanges, maintenance of order
books, price bands for each contract, and the maximum
permissible open positions;
use of on-line screen-based systems for all trades in financial
derivatives, and making all rules pertaining to trading,
clearing, settlement, margin maintenance, reporting and
monitoring more stringent than those in the cash market6
[possibly because derivatives trading is more leveraged and
sophisticated and hence inherently more risky];
creation of an independent clearing corporation which will
strictly enforce the rules pertaining to maximum exposure
limit(s), marking of portfolios to the market, and margin
maintenance;
introduction of strict risk disclosure norms governing options
trades between options dealers and their customers, given the
nature of options [which impose contingent liabilities on the
one of the trading parties], and the complexity associated with
the pricing of these products [see Box 1]; and
exposing the traders/brokers to the nature and uses of financial
derivatives through intensive and extensive training
programmes.
The Report at First Glance
It is evident that the Committee has recognised the importance of
technology and prudential norms like capital adequacy and marking to
market in the context of derivatives trading. Further, it has also taken
cognisance of the fact that human capital is a crucial element of this market
and hence the emphases on training programmes for trading participants
and on the gradual phasing in of regulated options trading at a later date.7
Indeed, the Committee has signalled significant conservatism by deciding to
initiate trade in financial derivatives by way of stock index futures which
have several advantages from the regulators’ standpoint:8
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6
For example, the Committee proposed that all members of derivatives
exchanges and clearing houses, not just 10 per cent of them, should be inspected annually
during the initial years, for verification of their compliance with SEBI and exchangespecific rules.
7
There is an informal and, therefore, unregulated market for options in India. In
this market a call option is known as teji and a put option is known as mandi. The two
strategies that are most often used in this market are the straddle (or bhav-bhav) and the
top vertical combination (or fatak). For details see Endo (1998), p. 159-161.
8
Bhaumik (1997a) has shown that the movements of the market indices
approximate a random walk, and that hence a key precondition for the introduction of
stock index futures has been met.
•
•
•
•
•
stock index futures contracts use equities as the underlying
security, and the institution of the secondary equity market in
India has seen significant improvements during the nineties
with the introduction of screen-based trading, creation of
depositories, and dematerialisation of some of the shares;
the participants in equity trading have had long exposures to
this activity and hence have a fairly good understanding of the
market and, given that stock index futures are fairly simple
financial instruments, they are likely to move up the learning
curve rapidly;
trading in stock index futures does not involve actual delivery
of shares, and obligations by way of outstanding positions are
met through cash settlements, thereby enabling traders to avoid
the problems associated with bad deliveries;
the estimation of daily “gains” and “losses” is easy, and hence
it should not be difficult to mark traders’ portfolios to market
on daily basis; and
there is a significantly long time series of stock prices which
can, in principle, be used to estimate the appropriate margin
requirement with a reasonably high degree of confidence.
In other words, prima facie the Committee has set forth a vision of
a deeper financial market which is implementable and yet cautious about
circumventing the possible pitfalls of trading in exotic financial instruments.
But still dissenting voices both within and outside the Committee have
argued that Indian financial markets are unprepared for the derivatives
instruments. Some of these objections involve technical issues like the
possible tax treatment of profits arising out of derivatives activities and
stamp duty for such trades, and hence lie outside the scope of this
discussion. In any event, these are matters that can easily be addressed
within a short period of time. Similarly, while it can be argued, for
example, that short selling can make cash markets more efficient through
increased (inter-temporal) arbitrage opportunities, and that hence it is an
essential precondition of derivatives trading, such issues can, in principle, be
addressed within a relatively short period of time.
Further, while it is difficult to be optimistic about the possibility of
an alleviating impact of stock index futures (and the options products) on
the sentiments prevailing in the secondary equity market, this is hardly a
relevant issue. As correctly mentioned in the Committee’s report, financial
derivatives are instruments which have evolved as a consequence of the
perceived need for hedging exposures in various markets. They provide
depth and liquidity to the markets and hence encourage trading. But they
are not the primary determinants of market sentiments; such sentiments are
determined by economic and political signals. Hence the expected impact of
such instruments on market sentiments cannot be the basis for determining
whether or not they should be introduced in a financial market.
However, there are other issues which require more thought and a
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. . . financial
derivatives are
instruments which
have evolved as a
consequence of the
perceived need for
hedging exposures in
various markets. They
provide depth and
liquidity to the markets
and hence encourage
trading. But they are
not the primary
determinants of market
sentiments; such
sentiments are
determined by
economic and political
signals.
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. . . a country with
volatile inflation rate
and (international)
capital flows is much
more in need of
interest rate derivatives
products than stock
index futures
contracts.10 This
argument can be
closer look. Specifically, there are two questions that beg satisfactory
responses.9 First, given that derivatives exchanges would have to work in
harmony with other institutions in the financial market, will the setting up
of an efficiently functioning derivatives exchange necessarily ensure the
avoidance of major systemic crises? Second, given the reasonable
assumption that other forms of derivatives products will enter the market
once trading in stock index futures becomes established, will the Indian
trading community ready for the more exotic varieties of these products in
the short to medium run?
Although the former question is perhaps more relevant in the short
run, the importance of the latter question is paramount. As argued by
Bhaumik (1998), a country with volatile inflation rate and (international)
capital flows is much more in need of interest rate derivatives products than
stock index futures contracts.10 This argument can be extended to the
currency market where cost-efficient hedging in the face of currency
volatility might require the introduction of products like path-dependent
options [see Box 2].11 However, such products are more complex and
require a higher level of human capital than plain vanilla products like
stock index futures. Indeed, human capital is important not only from the
traders’ perspective but also from the perspective of the regulators who
would have to understand the nature and magnitude of the risks associated
with the products in order to be able to determine prudential norms like
margin and capital requirements (Estrella et al., 1994). It is important to
verify, therefore, whether the Committee, which has acknowledged the
operational complexity of options, has envisaged a way in which the human
capital of those involved with derivatives trading can be improved.
extended to the
currency market . . .
However, such
products are more
complex and require a
higher level of human
capital than plain
vanilla products like
stock index futures.
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9
At this point, it is extremely tempting to get into a discussion about the merits
and demerits of stock index futures vis a vis the badla. However, at the outset one has to
recognise the fact that, by their very nature, the two instruments are very different. The
badla allows an investor to postpone taking delivery of one or more listed scrips, subject to
some margin requirements [for details, see Endo, 1998, p. 107-112]. In other words, badla
trading allows investors to take quasi-forward positions on individual scrips and provides
for flexibility by allowing the investors to postpone settlement up to a maximum of 90
days. On the other hand, stock index futures contracts allow investors to bet on the market
movement and, in the process, helps avoid problems associated with volatility in prices of
individual stocks. More importantly, we should take into cognisance the fact that the
Gupta Committee Report is not about the introduction of stock index futures per se but
addresses the broader issue of introduction of financial futures in India, the scope of such
financial instruments being far wider than that of stock index futures alone.
10
International capital flows affect the liquidity of the banks, and might also
affect the money supply by way of changes in the reserve or high powered money. Both
these, in turn, affect interest rates in an economy where such rates are market determined.
It is hardly surprising that both in the options and futures markets interest rate products
contribute to the lion’s share of outstanding notional capitals.
11
Some of these products like knock out options are such that the options expire
once the exchange rate exceeds or falls below some pre-determined value (Malz, 1993).
Since there is a higher probability, vis a vis standard American and European options, that
these products would expire unused, their prices are lower than those of standard options.
Hence, they are more cost efficient from a hedger’s point of view.
The Report Revisited
At the outset, let us take a look at the institutional requirements that
can be deemed important for smooth functioning of derivatives markets
when the product concerned is stock index futures contracts. As discussed in
Bhaumik (1998), effective enforcement of margin requirements is an
important precondition for avoidance of a derivatives-market-initiated
systemic crisis. This, in turn, requires daily settlement of margin calls by
traders and, by extension, brings into focus the ability of the traders to meet
their obligations on a daily basis.12 The Committee has recognised the
importance of a trader’s ability to pay, and has recommended that each
trader should have some minimum recommended net worth, and should be
subjected to payment of a security deposit. It has also recommended the
establishment of a margin requirement and the marking of portfolios to the
market on a daily basis.13 Finally, it has recommended that each clearing
member be subjected to the dual requirements of net worth of Rs. 300 crore
and a deposit of a minimum of Rs. 50 lakhs with the derivatives exchange
or the clearing corporation.14
However, while appropriate laws facilitate the prevention of
systemic crises arising out of payments related problems, they require the
support of infrastructure related to transfer of funds. Indeed, unless funds can
be transferred from the traders’ and/or the clearing members’ bank accounts
to the accounts of the clearing house every trading day, marking portfolios
to the market and margin calls might not act as effective checks for systemic
problems. Can, therefore, the Indian derivatives market(s) depend on sameday funds transfer facilities? The National Stock Exchange (NSE), which is
likely to play a pioneering role in the introduction of stock index futures
(and possibly other derivatives products) in India, is indeed in a position to
enforce same day settlement of margin requirements. The exchange has
operational relationships with three banks—Canara Bank, HDFC Bank, and
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. . . unless funds can
be transferred from the
traders’ and/or the
clearing members’
bank accounts to the
accounts of the
clearing house every
trading day, marking
portfolios to the
market and margin
calls might not act as
effective checks for
12
Note that if a trader loses money on a sustained basis, and hence faces margin
calls every day, then it should act as a signal that (s)he has taken positions in the
derivatives market that are inimical to the financial health of the firms/funds/individuals
on whose behalf (s)he has taken such positions. Thereafter, it is the responsibility of these
firms/funds/individuals to force the trader to reverse or liquidate his/her positions. In the
absence of such market discipline, a trader might continue to maintain a loss-making
position over a long period and thereby precipitate a systemic problem of significant
dimensions. A case in point, once again, is the insolvency of Barings by the hands of Nick
Leeson.
13
Note that the margin requirement implicitly establishes an upper limit for the
exposure of each trader in the derivatives market. The Committee took cognisance of the
inadequacy of a minimum net worth based criterion in the Indian context, and hence felt
that it was necessary to juxtapose the net worth based criterion with the margin
requirement for an effective prevention of systemic crises.
14
In the words of the Committee, a clearing member is one “who is admitted by
the Clearing Corporation and who may clear and settle transactions either on their own
account or on account of their client [or on account of other trading members] in the
manner prescribed in [the] bye-laws.” Given that the clearing corporation will be a
counterparty to all traders in the derivatives market, it is evident that in the event of a
default by a trading member of the derivatives exchange, the financial burden associated
with the defaulting member’s position(s) has to be borne by the clearing members. Hence,
their solvency is a matter of extreme importance.
systemic problems.
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While prices of
standard derivatives
products are stylised
and can hence be
obtained off-theshelves, the use of the
products for both
hedging and
speculation require an
understanding of both
sophisticated
mathematics and
strategies, . . .
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Global Trust Bank—which help the exchange to settle trades in the cash
market that are routed through the National Securities Clearing Corporation
Limited (NSCCL).15 In other words, the existing institutional set up allows
effective use of the practice of marking portfolios to market, and margin
requirements, to mitigate potential systemic problems arising out of
positions taken by traders in the derivatives market.
The ability of human capital to rapidly adapt to the financial
innovation that is implicit in derivatives trading is less apparent, and is
more likely to pose a problem in the medium to long run if more
sophisticated derivatives products are introduced. While prices of standard
derivatives products are stylised and can hence be obtained off-the-shelves,
the use of the products for both hedging and speculation require an
understanding of both sophisticated mathematics and strategies, 16 and
anecdotal evidence suggests that such understanding is not wide-spread
among Indian financial professionals.17
Taking a step in the right direction, therefore, the Committee has
recognised this lacuna in the Indian trading community and the end-users of
derivatives products, and has suggested that (i) all approved users of
derivatives terminals should compulsorily undergo training prior to the
initiation of trading in such instruments, and should pass a SEBI-approved
certification program; and (ii) all brokers-dealers of relatively complex
instruments should compulsorily obtain and verify information about the net
worth of their customers, as well as their investment related experience, and
should offer investors an explanation about the nature of the products and
the risks associated with them. It has further suggested that investors should
not be allowed to open, for example, options positions if it is felt that (s)he
would subsequently not be able to evaluate the related risks and bear the
financial consequences of the market movements. It can be argued that it is
15
As highlighted in the NSE’s information brochures, “[t]he clearing members
may maintain accounts with any one of the clearing banks at their designated branches
through which settlement transactions are processed. The banks are electronically
connected to the NSCCL and electronic funds transfer is effected for pay-in and pay-out
on the instruction of the NSCCL.”
16
For example, a simple strategy might involve the use of options and holding
cash (or cash equivalents like T-bills) to meet obligations if the options are exercised. How
can the extent of cash requirement be determined? The simplest rule involving the
determination of such capital requirement involve the use of the delta equivalent rule.
“[C]onsider a portfolio consisting of a $100 long position in the underlying asset, and a
written call option on $100 of the asset. If the delta of the option were to equal 0.25, then
the delta of the portfolio is 0.75 (the written call has a negative delta of 0.25 and the
underlying has a delta of 1, where both are weighted equally since the underlying amount
is the same for each position). Assuming [that] a three standard deviation confidence
interval for the capital rule represents a $20 change in the price of the underlying asset, the
capital charge is $15, ($15 = 0.75 x $20) (Estrella et al., 1994, p. 9).” While the estimation
of delta itself is a non-trivial process, the mathematics gets more complicated if one takes
into consideration the need for additional capital to hedge against volatility risk.
17
It has, for example, been pointed out that Indian traders/investors routinely
misprice warrants in the secondary market, warrants essentially being American call
options written (and often bundled with other securities) by companies listed in various
stock exchanges. {See Are we ready for derivatives? by Samir Barua, Business Standard,
May 25, 1998.)
difficult, and perhaps impossible, to ascertain whether the dealers-brokers
would honestly implement these norms, even if they are enshrined in the
bye-laws of the derivatives exchange. However, the risk of dishonesty
among one or more brokers-dealers is a possibility in all markets, and the
best an exchange and a supervisory body like the SEBI can do is to ensure
that such an act does not go unpunished, and that the traders, investors and
clearing members are financially capable of absorbing the loss(es) arising
out of such indiscretion. The onus of understanding the nature of the
instruments and their appropriate uses, as well as the monitoring of the
activities of in-house traders, lies with the individual and institutional
investors, and rightly so.
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Concluding Remarks
There has been a sustained debate (reportedly) both within and
outside the Committee about the efficacy of the use of derivatives in India.
The nature of the debate has ranged from the ludicrous—suggestions that
financial derivatives are superfluous because of the existence of the badla—
to the more credible stance that the Indian institutional set up might not be
adequate for sophisticated instruments like derivatives. As discussed in the
previous sections, neither the institutional framework nor the degree of
sophistication of human capital is likely to be the limiting factor in so far as
trade in plain vanilla derivatives products is concerned, especially if
standardised and exchange traded and products are used during the initial
years of such trade in India.
Indeed, an important aspect of the Committee’s report, one that is
surprisingly not highlighted, is that it restricts the discussion of financial
derivatives to those that are standardised and exchange traded. This is
extremely important in so far as human capital development and systemic
risk management is concerned. It is obvious that it would be easier for
traders, investors and brokers to move up the learning curve is standardised
products are traded in the derivatives market, thereby enabling them to
learn from market trends as well as experiences of their own and those of
others.18 Further, the existence of an exchange and a clearing corporation,
along with prudential norms like marking portfolios to market, margin
requirements, maximum exposure, security deposits, and minimum net
worth of trading and clearing members, render it easier to mitigate systemic
problems by way of early detection. Indeed, with the notable exception of
the Barings fiasco, high profile derivatives related crises like those related to
Procter and Gamble, and Orange County have typically been associated
with OTC derivatives, primarily because OTC products typically combine
attributes of several derivatives instruments and are, therefore, more
complex than their exchange traded counterparts.19
. . . an important
aspect of the
Committee’s report,
one is that it restricts
the discussion of
financial derivatives to
those that are
standardised and
exchange traded.
18
This idea, formalised by Adam Smith, is as old as human civilisation, and
merely suggests that an individual can be made to enhance his/her productivity and
efficiency by making him/her use an instrument repeatedly.
19
Moreover, dealers of OTC products are usually banks and hence defaults and
payments problems related to such products can get transformed into systemic problems
much faster than those related to exchange traded derivatives.
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At the end of the day, one has to take note of the fact that while
these products pose a challenge to the combined ability and the creativity of
both the finance professionals and the regulators, they add depth to the
financial market through their potential for facilitating both hedging and
speculation. Individually, and in some cases together, they would have to
rise to the challenge by way of developing the skills and regulatory
institutions required for efficient functioning of derivatives markets. The
importance of the development of institutions and human capital cannot and
should not be overlooked, but the process of progressive policy making
cannot wait indefinitely for the market players in emerging economies to
catch up with the skills and intuitions of their counterparts in the more
developed financial markets. Liberalisation, after all, is not a process
whereby the powers that be wait for behavioural and institutional changes
before they change the parameters of a system. Rather, it is a process
whereby they change the parameters, and create institutions, such that the
resultant change in the behaviour of the economic agents paves the way for
a better future.
References
Bhaumik, S. K., “Stock Index Futures in India: Does the Market Justify its Use?”
Economic and Political Weekly, XXXII(41): 2608-2611, 1997a.
______, “Financial Derivatives I: A Bird’s Eye View of the Products,” Money &
Finance, December, 45-71, 1997b.
______, “Financial Derivatives II: The Risks and Their Regulation,” Money &
Finance, April, 42-62, 1998.
Endo, T., The Indian Securities Market: A Guide for Foreign and Domestic
Investors, Vision Books, 1998.
Estrella, A. et al., “Options Positions: Risk Management and Capital
Requirements,” Federal Reserve Bank of New York Research Paper, No. 9415, 1994.
Malz, A. M., “New Varieties of Foreign Currency Options,” Federal Reserve
Bank of New York Research Paper, No. 9331, 1993.
Securities and Exchange Board of India, L. C. Gupta Committee Report,
SEBI Web Site (in html format), 1998.
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BOX 1: Options Pricing
The most widely used formula for computation of options prices was developed by
Fischer Black and Myron Scholes in 1973. According to the Black-Scholes formula, the
price of an European call option (C) is given by
C = S 0 N ( d1 ) − Xe − rT N ( d 2 )
when
d1 =
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ln( S 0 / X ) + ( r + σ 2 / 2)T
σ T
and
d 2 = d1 − σ T
The interpretation of the symbols are as follows:
S0
=
current price of the security
N(d) =
the probability that a number drawn randomly from standard normal
distribution will have value less than d
X
=
exercise or strike price of the option
r
=
the annualised continuously compounded rate on a safe asset with the
same maturity as that of the option
T
=
time to maturity of option expressed in years
s
=
standard deviation of the annualised continuously compounded rate of
return of the security
The symbols e and ln have their usual meaning, i.e., e is equal to 2.718, and ln refers to
the natural logarithm of some numerical value.
The price of the corresponding European put option can be estimated using the put-call
parity relationship which argues that in an efficient market the payoff from a strategy
which involves purchasing a security (of value S0) and a put option (priced as P) should
equal the payoff from that which involves purchasing a call option (prices as C) and
holding the required amount of money (ST) in the form of a risk-free and liquid asset
(yielding rf rate of return). Hence, if the time to maturity of the call and the put options is
T then the put-call parity relationship is given by
C+
ST
= S0 + P
(1+ rf ) T
Apart from the advantages usually associated with a closed-form solution, the above
formula/ algorithm has another major advantage. The hedge ratio or delta, the use of
which was explained in some detail in Bhaumik (1997b), can easily be obtained from the
Black-Scholes formulation. The delta for a call option is given by N(d1) and that for a put
option is given by [N(d1) - 1]. Since hedging using options requires extensive and
continual use of the delta, the Black-Scholes model can be of substantial advantage to
options traders and fund managers.
Source: Z. Bodie, A. Kane and A. Marcus, Investments, Irwin, 1993.
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Box 2: Path Dependent Options
The increased sophistication of the global financial markets has seen yet another
manifestation in the form of the so-called path dependent options. The three most common
varieties of path dependent options are average rate options, barrier options and lookback
options. Unlike standard European options, whose payoffs depend on, among other
things, the strike price and the spot price on the strike date, the payoffs for the path
dependent options depend on the relationship between the strike price and some function
of the current and/or historical spot prices. The computation of their prices/premia,
therefore, involve mathematical formulations that are more complicated than the simple
Black-Scholes variety.
Average rate options, which are strictly European in nature, yield a payoff which is a
function of a pre-determined strike price and some average of the price of the underlying
asset computed during some period that precedes the strike date. In the simplest of
averate rate options, the aforementioned time period could span the entire lifespan of the
option. Alternatively, it could be some pre-determined sub-period with the sampling
frequency varying from daily to monthly. It is easily seen that the volatility of the average
of the spot price of an underlying asset would be much less than the volatility of the spot
price itself. Hence, given the nature of the Black-Scholes formulation, the price/premia for
an average rate option would be lower, and this is an important reason behind the rising
popularity of the option. Part of the popularity can also be explained by the fact that an
average rate option can act as a cubstitute for an European strip for which a liquid market
may be non-existent.
An even more exotic form of path dependent option is the barrier option which is another
low (up front) cost hedging instrument in the foreign exchange market. A barrier option
belongs to two broad categories: it either gets activated or stands canceled if the price of
the underlying asset exceeds or falls below some pre-determined level. These are popularly
known as knock-in and knock-out options respectively. For example, an up-and-out option
is one which stands canceled if the price of the undrelying asset increases beyond some
pre-determined level. As with the average rate options, the sampling frequencies of the
underlying asset price, which determines whether an option is knocked in or knocked out,
are contract specific. Further, given that a barrier option might never be knocked in or
might be knocked out, the price of such an option is lower than the simple European
variety, thereby contributing to its popularity. The problem with barrier options, however,
is that if it is not in force on maturity then a significant proportion of an investor’s portfolio
might remain unhedged.
Finally, lookback options are designed such that the payoff for one such option is a
function of the difference between the price of the underlying asset at expiration and the
lowest price prevailing during some pre-determined period prior to the strike date.
Alternatively, a lookback option can yield a payoff that is a function of some strike price
and the aforementioned lowest price. It is evident that, on the average, a lookback option
yields a higher payoff than a simple European option of otherwise similar specifications,
and hence such options are more expensive than their plain vanilla counterparts.
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