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I C R A B U L L E T I N Money & Finance J U L Y – S E P T. . 1 9 9 8 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. 50 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. I C R A B U L L E T I N Money & Finance J U L Y – S E P T. . 1 9 9 8 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.” 51 I C R A B U L L E T I N • Money & Finance J U L Y – S E P T. . 1 9 9 8 • • • • 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 52 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 I C R A B U L L E T I N Money & Finance J U L Y – S E P T. . 1 9 9 8 . . . 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. 53 I C R A B U L L E T I N Money & Finance J U L Y – S E P T. . 1 9 9 8 . . . 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. 54 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 I C R A B U L L E T I N Money & Finance J U L Y – S E P T. . 1 9 9 8 . . . 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. 55 I C R A B U L L E T I N Money & Finance J U L Y – S E P T. . 1 9 9 8 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, . . . 56 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. I C R A B U L L E T I N Money & Finance J U L Y – S E P T. . 1 9 9 8 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. 57 I C R A B U L L E T I N Money & Finance J U L Y – S E P T. . 1 9 9 8 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. 58 I C R A B U L L E T I N 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 = Money & Finance J U L Y – S E P T. . 1 9 9 8 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. 59 I C R A B U L L E T I N Money & Finance J U L Y – S E P T. . 1 9 9 8 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. 60