Market Risk and Model Risk of Financial Institutions Writing Derivative Warrants: Evidence from Taiwan and Hong Kong

Transcription

1 Market Risk and Model Risk of Financial Institutions Writing Derivative Warrants: Evidence from Taiwan and Hong Kong Huimin Chung Department of Finance and Applications Tamkang University, Taipei 106, Taiwan Chin-Shen Lee Department of Finance and Financial Research Center Ming-Chuan University, Taipei, Taiwan Soushan Wu Institute of Business and Management National Chiao-Tung University, Taipei 100, Taiwan. Address correspondence to Huimin Chung, Department of Finance and Applications, Tamkang University, Taipei 106, Taiwan. tel.: , fax:

2 Market Risk and Model Risk of Financial Institutions Writing Derivative Warrants: Evidence from Taiwan and Hong Kong Abstract This paper investigates market risk and model risk for financial institutions writing derivative warrants in Hong Kong and Taiwan markets. Important market imperfections such as transaction costs and primary market effects are considered in the simulation design. Understanding model risk in the valuation and trading of derivative securities is particularly important for emerging markets, because asset returns are too fat-tailed to be normal, and volatility is hard to forecast accurately by any method and forecast errors remain very large. The empirical simulation results show that model risk is remarkable for derivative warrant issuers in emerging markets such as Taiwan and Hong Kong. We also discuss some strategies to remedy market imperfections and to reduce model risk, including shortening the issuing period, marking up for volatility, and timing of issuance. Keywords: Model risk, Derivative warrants, Volatility forecast, Up-and-out call 2

3 1. Introduction While derivative risks can be classified in terms of market risk, credit risk, operational risk, and legal risk, the heavy use of theoretical models in the derivative industry inevitably involves an important new type of risk, model risk. Model risk relates to the risks involved in using models to price and hedge securities. As derivative activities of financial institutions expand with more outstanding contracts and more complex derivative instruments, model risk can be substantial in many circumstances. In particular, the percentages of derivative losses attributed to models in recent years have been increasing. 1 Recently, derivative warrants have been very successfully traded in Hong Kong and Taiwan stock markets. Hong Kong and Taiwan derivative warrants are issued by independent financial institutions and are listed on the major stock exchanges. Derivative warrants are more popular than standard option contracts in these markets, partly because most of the investors in these markets are individual investors, and derivative warrants provide the convenience that no margin account is required. As Crouhy, Gailai, and Mark (1998) and Figlewski (1998) note, important sources of model risk for financial institution writing options include model misspecification, unobservable input parameters, and hedging risk. Model misspecification occurs if the underlying model for derivative trading is incorrectly applied. Model risk may be considerable if there are large forecast errors in volatility. While the risk of using an incorrect model can be enormous, a frequent error in model building is misspecification of the underlying stochastic process. We focus on measuring the model risk and market risk of a financial institution that issues derivative warrants in Pacific Basin financial markets. Despite tits unsatisfactory empirical performance in emerging derivative market, the Black-Scholes model is widely applied in the derivative industry 2. Understanding model risk in the valuation and trading of derivative securities is particularly important in emerging markets, because volatility is hard to forecast accurately and the sizes of the forecast errors tend to be 1 See Falloon (1998) and Paul-Choudhury (1997) for details and the challenges to market regulators. 2 See, for example, Chang, Chang, and Lim (1998). 3

4 considerable. Empirical evidence usually indicates that actual returns in emerging markets are too fat-tailed to be lognormal. Local economic and political events are more important in causing major shifts in emerging markets' volatility and forecast error in volatility is large. Model risk is substantial as a result of large forecast errors in volatility. This article extends previous study of Green and Figlewski (1999) by providing a more extensive and systematic study of model risk and market risk of derivative warrants issuers in several respects. First, international evidence on the return and risk for financial institutions writing derivative warrant are explored. This task is particularly important for the Asian Pacific financial markets, because of the growing popularity of the derivative warrant market. Second, emerging markets are characterized by frequent, sudden changes in variance. Because of large forecasting errors attributable to the volatility of emerging markets, our results have important implications for risk management in emerging derivative markets. Third, our historical simulation setup covers many important aspects of the derivative warrant market. We include, for example, the effects of transaction costs and primary market effects such as issue costs and the issuing process in local markets. We also discuss possible methods for reducing the model risks, namely shortening the issuing period, marking up the volatility, and timing of issuance. Based on the simulation results, strategic implications of issuing derivative warrant in emerging markets are provided. The plan for the rest of the paper is as follows. Section 2 introduces the simulation methodology in this study. Section 3 provides the simulation results. Section 4 concludes this paper. 2. Derivative warrant markets and the simulation design The simulation in this study uses the Hang Seng Index (Hong Kong), the Morgan Stanley Capital International (MSCI) Taiwan Stock Index and four industrial indexes in Taiwan as the underlying assets. The use of market indexes as the underlying asset allows us to investigate the average risk and return structure of the overall derivative issuing industry, although most of the underlying assets in these markets might be individual stocks. Daily data from January 5, 4

5 1989 through June 30, 1999 are used in the empirical simulation. The total number of observations for the Hong Kong market is 2570, for the Taiwan stock market The underlying assets also include value-weighted industry indexes of electronics, banking and insurance, plastic, and construction on the Taiwan Stock Exchange (TAIEX). Among the emerging stock markets, the Taiwan and Hong Kong stock markets are known for both their liquidity and volatility; their volatility constantly breaks historic records amidst political uncertainty. In terms of annual turnover velocity, the Taiwan stock market is second only to the NASDAQ. While the first Hong Kong derivative warrant was issued in 1989, derivative warrants have been traded in the Taiwan Stock Exchange only since The Hong Kong and Taiwan derivative warrants are issued by an independent party, a financial institution, and give the holder the right to buy or sell a specified number of shares in an unrelated company. 3 Issuers are required to conduct dynamic hedging to protect their obligations during the life of the warrant. While derivative warrants are the most successful product of all the option related derivatives traded on Hong Kong and Taiwan exchanges, they have some distinct features that make them different from exchange-traded options. First, warrants have much longer expiration dates than options. Their prices are more sensitive to price jumps and shifts in volatility. Hedging becomes a more difficult task in the presence of more significant gamma and vega risks. Warrants cannot be sold short, so arbitrage trading from selling overvalued warrants is limited. Second, no margin account is required to trade derivative warrants. Buyers of derivative warrants are, however, exposed to credit risk, while options are settled through a clearing house instead of individual issuers. In these markets, individual investors, rather than institutional investors, account for a large percentage of transactions. Derivative warrants have been accepted more rapidly than standard options, because of the convenience of no margin 3 Before Jan. 2000, only call warrants are allowed to be issued in Taiwan. Financial institutions writing put warrants were prohibited, because they are not allowed to sell short. 5

6 account. One important feature of the derivative warrant market is that, unlike writers of standard option contracts, financial institutions writing warrants are exposed to significant issuing risk. There are five to ten trading days of processing time for warrants to be listed on an exchange. Issuing failure for call warrants occurs when a huge drop in the underlying asset price makes the shares not marketable. Consequently, the issuer suffers from a loss due to the sharp decrease in market value of the initial hedge position of underlying assets. We investiagte this primary market effects on the return and risk of issuers. 2.1 Volatility Forecast While most of the parameters of the Black-Scholes model can be directly observed, the variance of the underlying asset must be estimated. Hence, before we introduce the simulation design, it is important to discuss suitable methods of forecasting volatility. The simplest way to forecast the volatility of a series is to take its historical volatility over some prior window. The historical volatility is then estimated from the standard deviation of past returns: HV 1 N 2 1/ 2 σ ˆ t = [( N 1) = ( r ) ] 1 j t j r, where rt is the rate of return of a particular stock or portfolio from time t-1 to t, and r is the average return. The major drawback of the historical volatility method is that it doesn't exploit the volatility clustering property optimally. Alternatively, implied volatility (IV), the market's assessment of the underlying asset's volatility as reflected in the option price, can be used to provide a forecast of future volatility. To use IV as a viable forecasting tool, we must have a broad range of prices for traded options with different strike prices and maturities. Because there are no such data in the market, we do 6

7 not examined IV here. 4 Besides, another method for forecasting volatility is the GARCH model, first introduced by Engle (1982) and later extended by Bollerslev (1986). Application of GARCH processes and their extensions to represent the time-dependent heteroskedasticity present in many economic and financial economics series is now a widespread econometric procedure. Let rt be the rate of return of a particular stock or portfolio from time t - 1 to t and F t 1 be the information available at time t-1. We denote the expected return and volatility conditional on F t 1 as µ t and σ 2 t, respectively. The unexpected return at time t is εt = r t µ t. The most successful model in the ARCH literature in empirical modeling of conditional variance is the GARCH(1, 1) process of Bollerslev (1986), ε = σ u t t t, where u t is NID(0, 1), and is a positive, time varying and measurable function with respect to the information set that is available at time t-1, and α + β t = ω + α ε t 1 + β σ t 1 2 σ t σ, where ω 0, α, β > 0, and <1. If the GARCH models characterize the dynamics of underlying asset better than other models, standard option pricing models under GARCH processes, e.g., Duan (1995) or Duan (1999), can be applied. The GARCH model has been criticized as providing poor forecasting performance for long-horizon forecasts. It is well known that emerging markets are characterized by high sample average returns, low correlations with developed market returns, more predictable returns and high volatility. Aggarwal, Inclan, and Leal (1999) use the ICSS algorithm of Inclan and Tiao (1994) to detect discrete changes in variance and provide evidence showing that local events are more important in causing major shifts in emerging markets' volatility. Local political and economic events rather than global information variables more likely influence emerging market returns. They also demonstrate that the values of GARCH coefficients are reduced when sudden variance changes are accounted for, and most of them are no longer significant. 4 The poor forecasting performance of implied volatility is usually observed in emerging derivative markets, see for example Lee and Chung (1999). 7

8 Lee and Chung (1999) examine the forecasting performance of various volatility models, i.e., historical volatility, implied volatility, and GARCH models, for Hong Kong and Taiwan stock markets. They conclude that out-of-sample volatility forecast errors of even the best method tend to be quite large, a result similar to that of Figlewski (1997). Of the three models the historical volatility model outperform the rest. Our simulation process is first to conduct performance evaluations over different sample lengths of the historical volatility model for various forecasting horizons. The sample length that produces the least mean squared error is selected to calculate historical volatility estimates. 2.2 Simulation Design of Derivative Warrant Markets We assume a financial institution writes European calls every day for contracts with maturity equal to 3 months, 6 months, and 1 year and two degrees of moneyness (at-themoney and out-of-money with the strike set to 0.4 daily standard deviation away from the asset price). The options are priced at model values using the standard formula of Black and Scholes, and volatility input is calculated using historical return data. 5 We provide simulation results only for call warrants, because a large portion of warrants issued in Hong Kong are call warrants, and put warrants have no issue history in Taiwan. To gurantee that the results of the analysis can be interpreted as percentage returns per dollar of option premium, the simulation design assumes that at each day financial institutions write enough contracts so that a premium inflow of 100 is received. We consider two separate cases: that financial institutions do not hedge at all, and that they delta hedge using the valuation model on a daily basis. If a financial institution delta hedges, each day the hedge ratio is recalculated and the hedged portfolio is rebalanced. Pricing options based on models requires an input of estimated volatility. Volatility estimation error will 5 While most of the derivative warrants traded in Hong Kong and Taiwan are American options, they are dividend protected. The exercise price is adjusted at the ex-dividend date. Hence, using a argument similar to Geske, Roll, and Shastri (1983), the Black-Scholes and Binomial models are suitable for pricing and hedging the warrants. 8

9 produce model risk, which will cause mispricing of options and inaccurate hedging calculations. To examine how much of the observed model risk is due to incorrect volatility estimates, we also compare pricing and hedging error under both estimated volatility and actual volatility. Actual volatility is represented as the standard deviation calculated using the actual daily returns observed in the life of a warrant. We also consider important market imperfections such as transaction costs and issuing costs in the simulation design. We discuss possible strategies to remedy market imperfections and reduce model risk, namely, shortened issuing periods, volatility markup, and issue timing. (1) Transaction costs The simulation design is extended to compare cases considering transaction costs and no transaction costs. The Black-Scholes model assumes the continuous rebalancing of a hedged portfolio, and no transaction costs. In practice, this assumption is incorrect, and a discrete hedge is inevitable because of transaction costs. Our empirical simulation setup thus provides a discussion of the effect of transaction costs. Leland (1985) and Whalley and Wilmott (1993) discuss option pricing and hedging with transaction costs. However, as explained below, their methods are not suitable to the Taiwan stock market. The Taiwan stock exchange levies a 0.3% security transaction tax for each sale of securities and % of the amount for brokerage fees. In the Hong Kong stock market there is a 0.13% charge of the transaction value for security transaction tax and brokerage fees. 6 Because transaction costs tend to be higher in the Taiwan stock market, the effect of transaction costs would be greater in the case of deltahedging. Thus, model risk due to the miscalculation in delta hedge is also expected to increase. 6 Transaction costs for securities traded on the Taiwan Stock Exchange are asymmetric; i.e., the transaction costs is % of the amount of each sale of securities and a % of each purchase. On the Hong Kong stock market stockbrokers charge a fee of not less than 0.25% of the value of transaction to either a buyer or a seller, so that on average the brokerage fee is 0.125%. The Hong Kong Stock Exchange charges a transaction levy of % of the amount of each purchase or sale of securities. Hence, a total 0.138% of the value of trade is charged for each transaction. 9

10 (2) Primary market effects: issuing failure Issuers of derivative warrants face the risk of issue failure. Usually, there are nearly 5 to 10 trading days of processing time for warrants to be listed on an exchange. If a large issuing amount is required, financial institutions are exposed to significant issuing risks. Issuing failure of derivative call warrants occurs when a huge drop in the underlying asset price makes the required shares not being sold out. Consequently, the issuer suffers a loss due to a sharp decrease in the market value of the initial hedge position of underlying assets. In the simulation setup, we assume that issuing failure of derivative call warrants occurs if the underlying price drop enough during the issuing period so that the probability that the derivative call warrant will expire at the money falls to only half of the original probability. The simulation also examines that the effect of reducing the issuing period on the return and risk of issuers. (3) Volatility markup If a financial institution writes and delta hedge the warrants based on Black-Scholes model, the expected profit is equal only to the risk free rate. In practice, no warrant issuer would simply do so. The return of delta hedged portfolio worsens if important market imperfections such as transaction costs and issuing costs are considered. A practical procedure for writing a derivative warrant is to obtain the best available volatility forecast and increase it by a suitable amount to price the option. An appropriate volatility boosting strategy clearly enhances the mean return of writing call options, but the probability of issuing failure and variation of returns on writing calls might increase as the volatility markup increases. Simulations assume issuers markup the estimated volatility 5%, 10% and 15%. Such simulation results might be useful for the design of markup strategies. (4) Timing of issuance 10

11 In order to capture the average risk and return characteristics of the issuers in derivative warrant markets, previous simulation designs assume financial institutions issue derivative warrants daily. Clearly, no financial institution does this. In particular, derivative warrant issuers in Taiwan tend to apply a relative price issuing strategy to enhance the probability of successful issuance, so that if current asset price is lower than a certain historical average level, a new call warrant will be initiated. Besides, investors would prefer to buy derivative call warrants if the underlying asset price is relatively low, so that the probability of a successful issuance tends to be higher. Hence, the simulation design is further conducted to investigate such scenarios. Let P denote the average return on the underlying asset for the past week, and σ be the daily standard deviation of return. The issuing strategy is designed such that when the current asset price is lower than P(1 θ σ ), a new call warrant will be initiated. To investigate the effects of such a relative price issuing strategy on the risk and return of writing warrants, we simulate the cases of θ between 0.2 and 1.2 by steps of Simulation Results 3.1 Basic Simulation Results Table 1 provides the forecast accuracy of volatilities estimated from historical data. For the MSCI Taiwan Stock Index, the results seem to favor the short number of days in samples for calculating historical volatility. The lowest root mean squared error (RMSE) forecast method for each horizon is then used to forecast volatility in the simulation. Table 2A presents the simulation result for two strategies of writing calls (unhedged and delta hedged) on the Hong Kong Heng Seng Index and the MSCI Taiwan Stock Index. The unhedged strategy is simply to sell the option at its model values, invest the proceeds at the risk-free interest rate, and hold the short position until maturity without hedging. Delta-hedging 11

12 is performed on a daily basis using the Black-Scholes model delta over the lifetime of the option. The results therefore reflect model error due both to inaccurate volatility inputs and to errors in the models. The last four columns in Table 2A show the results if the same options are priced using the realized volatility over the remaining life of the option; this can be interpreted as the payoff if issuers have perfect foresight of volatility. Volatility estimation error no longer exists in this case. What is left then is the effect of inaccuracy in the valuation model itself. The column labeled worst case gives those figures of extremely serious losses. If without hedging, the worst loss of writing 3-month MSCI Taiwan stock index is 26 times the initial premium received. Delta-hedging limits the largest loss to a 371% of the initial premium. Simulation results for the realized volatility cases clearly indicate the market risks. Table 2A also presents the results for written options positions delta-hedged over their lifetime on a daily base. The hedge ratio adopted is the model delta. Clearly, delta-hedging greatly reduces risk exposure. The standard deviation of the return on the 1-year at-the-money Heng Seng index drops from % to 40.35%. Hedging reduces risk, the size of the mean return and the extent of the worst-case results. The worst cases still produce losses that are 2 to 4 times the initial premium received. Table 2B gives the simulation results for return and risk of writing options with estimated volatility when the underlying assets are value-weighted indexes (VWI) of electronics, banking and insurance, plastic, and construction on the Taiwan Stock Exchange. Without hedging, on average issuing call options on VWI of electronics produces serious losses with standard deviations equal to 2 to 4 times those of other underlying assets. The losses in issuing call options on VWI of electronics are exacerbated with the high-tech boom in recent years. An interesting result is that the delta hedged standard deviations of the four different indexes are very close. The test results of the Kruskal-Wallis test show that the null hypothesis of equal 12

13 variance for each case cannot be rejected In general, the simulation results in Table 2 illustrate that writing options and deltahedging positions using the most common valuation models involves exposure to considerable model risk. Hedging is much better than not hedging, although a great deal of risk remains. Even with delta hedges, the maximum loss is 220% of the initial premium received for the oneyear ATM call options of the MSCI Taiwan Index and 108% for the Heng Seng Index. For the out-of-the money call, the situation is worse. A common feature for every underlying asset is that as the maturity of call warrant increases from six month to one year, the mean return increases, and standard deviation decreases. 3.2 Market Imperfections and Issuing Strategies (1) Primary market effects and transaction costs Derivative warrant issuers face the risk of issue failure. If a large issue amount of warrants is required, the issuing financial institutions are exposed to significant issuing costs. Usually, there are nearly 10 trading days of processing time for warrants to be listed on an exchange. Issuers who cannot sell the required number of shares on the primary market have to withdraw the registration. Facing the problem of distributing more shares of warrants than the market can absorb, issuers are forced to collaborate with other large shareholders or fund holders in order to reduce the probability of failure in primary market sales. The issuing costs of financial institution are thus related to the loss resulting from the failure of issuing. Obviously, there should be higher issuing failure for the out-of-the-money call than for the at-the-money call. The simulation results show that the probability of issuing failure decreases as the maturity of the contract lengthens. A comparison of the results in Table 3 with those in Table 2 demonstrates that, as issuing costs are considered, the mean returns decrease for all cases and the standard deviations increase. In general, at least 2% of the expected return 13

14 of writing derivative call warrants is due to issuing costs. In practice, continuous rebalancing of a hedged portfolio is impossible because of transaction costs. On the Taiwan Stock Exchange a 0.3% securities transaction tax is levied on the sell side of each transaction. The impact of transaction costs on the issuing might be more severe when the underlying asset becomes bearish. The simulation results in Tables 3A and 3B show the effect of transaction costs on these markets. Commission fees are also considered in the empirical simulation. When transaction costs are taken into account, there are significant decreases in the risk and return of writing derivative warrants in the Taiwan market. The reduction in mean return is close to 20% for the daily delta-hedge method. The impact of transaction costs is smaller for the derivative warrant issuers in Hong Kong. If important market imperfections such as transaction costs and issuing costs are considered, for the delta-hedge cases, the maximum loss is 290% of the initial premium received for the one-year ATM call options on the MSCI Taiwan Index and 139% of that on the Heng Seng Index. The results are worse for shorter-maturity contracts. The recent Value at Risk (VaR) risk management concept emphasizes the value of providing a single number summarizing the total risk in a portfolio of financial asset. Hence, to limit the maximum loss, an up-and-out call that provides a stop-loss mechanism might be issued instead of the plain vanilla call. Table 4 presents the results of the effects of reducing the issuing period on the risk and return of writing warrants. The simulation results show that shortening the issuing period indeed reduces the risk exposure of financial institutions. The effect is most significant for short term call options on the Heng Seng Index and MSCI Taiwan Stock Index. If the issuing period is shortened, a 10% to 20% improvement in worst-case loss is observed. Hence, controlling the length of issuing period is an acceptable strategy to monitor the exposure of 14

15 issuing risk. In general, reducing the issuing period produces all kinds of positive effects: higher mean return, lower risk, and a reduced maximum loss. (2) Volatility markup In practice, the normal procedure for writing a derivative warrant is to obtain the best available volatility forecast and increase it by a suitable amount to price the option. An appropriate volatility boosting strategy clearly enhances the mean return of writing call options. At the same time, an increase in the markup of volatility induces a higher probability of issuing failure and an increase in the standard deviation of return of the issuer. Tables 5A and 5B present the return and risk of writing call options for different markup strategies as to the input volatility. The effect of transaction costs is considered in each market. We consider the cases that historical volatilities are markup by 5%, 10%, and 15%. Marking up the volatility clearly helps to increase the mean returns to option writing. Standard deviations are affected only slightly, but the fraction of trades that lose money is decreased, and the probability of issuing failure increases. Simulation results in Table 5A show that a 15% markup in the input volatility produces an average return of 38.69% for the one-year ATM Heng Seng index. For the one-year at the money call warrant on the MSCI Taiwan Index, the worst case loss amounts to 290% of initial premium (Table 3B), while for a 10% markup in volatility it is 258%. (3) Timing of issuance Derivative warrant issuers in Taiwan tend to apply a relative price issuing strategy to enhance the probability of successful issuance. To examine whether such issuing strategy can help to reduce model risk and the possibility of issuing failure, the following simulation design is conducted. We assume financial institution use a relative price issuing strategy to enhance the probability of successful issuance, so that if the current asset price is lower than a certain 15

16 historical level, a new call warrant will be initiated. Let P denote the average return on the underlying asset for the past week, and σ be the daily standard deviation of return. The issuing strategy is designed such that if the current asset price is lower than P ( 1 θ σ ), a new call warrant will be initiated. We simulate the cases of θ between 0.2 and 1.2 in steps of 0.2. This represents six strategies of issue timing. Obviously, the number of issuance times decreases as θ increases. The simulation results provided in Tables 6A and 6B show that selecting a good issuing time does reduce model risk and the possibility of issuing failure, although the possibility that the call warrants will expire in the money increases. It is important to note that the optimal choice of θ varies with the maturity of contracts. For a one-year call on the MSCI Taiwan Stock Index, a stringent issue timing strategy indeed provides the highest return and lowest risk. 4. Concluding Remarks Despite its unsatisfactory empirical performance in emerging derivative market, the Black- Scholes model is widely applied in the derivative industry. Understanding model risk in the valuation and trading of derivative securities is particularly important in the emerging markets, because the extent of the forecast errors tends to be greater. Volatility is hard to forecast accurately by any method, and model risk is considerable. Empirical simulation evidence drawn from several important asset markets shows that model error can be quite high and can be expected to lead to significant risk in derivatives pricing and risk management. The simulation results in this study illustrate that writing options and delta-hedging the positions using the most common valuation models involves exposure to considerable model risk. Hedging is much better than not hedging. Even so, considerable degree of risk remains. The maximum loss still accounts for two to five times the initial premiums received. One way to limit the loss is to issue an up-and-out call that embeds a stop loss mechanism. Simulation 16

17 results also show that writing derivative warrants in emerging markets involves greater risk than those in developed market, because volatility input error tends to be high in emerging markets. A key feature in Taiwanese stock market is that annual volatility of high-tech stocks average to 50-70%, a 20% higher than that of other stocks. Although different industrial groups in Taiwan have different risk, with delta hedge, standard deviations of the returns of writing options for electronics, banking and insurance, plastic, and construction indexes are very close. Strategies to remedy market imperfections and to reduce model risk include reducing the issuing period, applying higher volatility markup, and good timing of issuance. Issue strategies based on the relative current and historical moving average spot prices do reduce model risk and the possibility of issue failure, although there is a higher possibility that the call warrants will expire in the money. Marking up in volatility clearly helps to increase the mean returns to option writing; standard deviations are affected only slightly and the fraction of trades that lose money is decreased, but the probability of issue failure is heightened. Jacquier and Jarrow (2000) propose a Bayesian method to remedy model errors usually observed in pricing options. Further studies can be extended using their approach. 17

18 References 1. Aggarwal, R., C. Inclan and R. Leal, "Volatility in Emerging Markets", Journal of Financial and Quantitative Analysis, 1999, Bekaert, G. and C. R. Harvey (1997), "Emerging Equity Market Volatility," Journal of Financial Economics 43, Black, F., and M. Scholes, ''The Pricing of Options and Corporate Liabilities," Journal of Political Economy, 1973, 81, pp Bollerslev, T., ''Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, 1986, 31, pp Chang C., J. S.K. Chang, and K.G. Lim, "Pricing and Hedging Hong Kong Derivative Warrants in Information Time", Paper presented at Chinese Finance Association Annual Conference, Crouhy M., D. Galai, and R. Mark, "Model Risk", The Journal of Financial Engineering, 1998, Duan J.C., "The GARCH Option Pricing Model," Mathematical Finance 5, 1995, pp Duan J.C., "Condition Fat-tailed Distribution and the Volatility Smile in Options", Working paper, Department of Finance, Hong Kong University of Science and Technology, Falloon W. Rogue Models and Model Cops, Risk, 1998, September Figlewski, S., "Forecasting Volatility," Financial Markets, Institutions, and Instruments, 1997, 6, pp Figlewski, S., "Derivative Risks, Old and New, Brookings-Wharton Papers on Financial Services, Geske, R., R. Roll, and K. Shastri, Over-the-Counter Option Market Dividend Protection and biases in the Black-Scholes Model: A Note, Journal of Finance, 1983, Green T. C. and S. Figlewski, Market Risk and Model Risk for a Financial Institution Writing Options, Journal of Finance, 1999, forthcoming. 14. Jacquier E. and R. Jarrow, "Bayesian Analysis of Contingent Claim Model Error", Journal of Econometrics, 94, 2000, Lee C.-S. and H.-M. Chung, Alternative Conditional Volatility Models for Taiwan Stock Market, Forthcoming in Advances in Pacific Basin Business, Economics and Finance, Vol. 4, Leland,H.E., 1985, Option pricing and replication with transaction costs, Journal of Finance 40, Paul-Choudhury, S. 1997, This Year s Model, Risk, 10, no. 5, May, 1997, Simons K., Model Error, New England Economic Review, Nov./Dec. 1997, Whalley, R. E and P. Wilmott, Counting the Costs, Risk, Octorber 1993,

19 Figure 1. Typical issuing process of derivative call warrants in Taiwan Stock Exchange. Application day Issuance day End of primary market sales List day Expiration day t=0 t=1 t=10 t=13 t=t Risk In the Issuing Process Risk In the Listing Process Issuing Risk: a sudden decline in underlying asset price causes losses in the initial hedge position Market Risk; Model Risk: volatility input error, miscalculation of delta hedging, underlying asset price not log-normal.

20 Table 1 Root Mean Squared Errors of Volatility Estimation Using Historical Data The table shows the root mean squared of forecast error for volatility calculated from daily data. Forecast horizon is expressed in terms of days. Forecast Heng Seng Index (Hong Kong) Days in Sample Forecast MSCI Taiwan Stock Index Days in Sample Horizon Horizon % 0.693% 0.697% 0.699% % 0.718% 0.721% 0.724% % 0.761% 0.764% 0.769% % 0.766% 0.764% 0.765% % 0.811% 0.807% 0.805% % 0.809% 0.812% 0.811% % 0.835% 0.829% 0.820% % 0.865% 0.869% 0.870% Heng Seng Index MSCI Taiwan Stock Index

21 At the Money Calls Table 2A. Return and risk in writing options with estimated volatilities 1. Underlying asset Heng Seng Index Mean Standard Worst Case % In- Mean Standard Worst Case without hedge Return Deviation Date Return the-money Return Deviation Date Return 3 months months months months year year Delta Hedge 3 months months months months year year Underlying asset MSCI Taiwan Stock Index without hedge 3 months months months months year year Delta Hedge 3 months months months months year year Out of Money Calls 1. Underlying asset Heng Seng Index without hedge 3 months months months months year year Delta Hedge 3 months months months months year year Underlying asset MSCI Taiwan Stock Index without hedge 3 months months months months year year Delta Hedge 3 months months months months year year

22 Table 2B. Return and risk in writing options with estimated volatilities for different industrial indexes in Taiwan as underlying asset Without Hedge In-the-Money Call Out-of-the-Money Call Volatility forecast using historical data Volatility forecast using historical data Underlying Mean Standard Worst Case Mean Standard Worst Case % In- Mean Standard Worst Case Mean Standard Worst Case % In- Asset Maturity Return Deviation Date Return Return Deviation Date Return the-money Return Deviation Date Return Return Deviation Date Return the-money 3 months % % Electronics 6 months % % 1 year % % 3 months % % Banking and 6 months % % Insurance 1 year % % 3 months % % Plastics 6 months % % 1 year % % 3 months % % Construction 6 months % % 1 year % % Delta hedge Underlying Asset Electronics Banking and Insurance Plastics Construction In-the-Money Call Out-of-the-Money Call Volatility forecast using historical data Volatility forecast using historical data Mean Standard Worst Case Mean Standard Worst Case % In- Mean Standard Worst Case Mean Standard Worst Case % In- Maturity Return Deviation Date Return Return Deviation Date Return the-money Return Deviation Date Return Return Deviation Date Return the-money 3 months % % 6 months % % 1 year % % 3 months % % 6 months % % 1 year % % 3 months % % 6 months % % 1 year % % 3 months % % 6 months % % 1 year % % 21

23 Table 3A. Return and risk in writing options with estimated volatilities: 10-day issuing period and transaction costs Underlying Asset: Heng Seng Index without hedge At the Money Calls Mean Standard Worst Case % In- Failure Mean Standard Return Deviation Date Return the-money Times Return Deviation 3 months months year Out of the Money Calls 3 months months year Delta Hedge At the Money Calls and Delta Hedge With Transaction Costs Forecasted Volatility Mean Standard Worst Case % In- Failure Mean Standard Mean Standard Worst Case Mean Standard Return Deviation Date Return the-money Times Return Deviation Return Deviation Date Return Return Deviation 3 months months year Out of the Money Calls and Delta Hedge Forecasted Volatility 3 months months year

24 without hedge Table 3B. Return and risk in writing options with estimated volatilities: 10-day issuing period and transaction costs At the Money Calls Mean Standard Worst Case % In- Failure Mean Standard Return Deviation Date Return the-money Times Return Deviation 3 months months year Out of the Money Calls 3 months months year Delta Hedge At the Money Calls and Delta Hedge Underlying Asset: MSCI Taiwan Stock Index With Transaction Costs Forecasted Volatility Mean Standard Worst Case % In- Failure Mean Standard Mean Standard Worst Case Mean Standard Return Deviation Date Return the-money Times Return Deviation Return Deviation Date Return Return Deviation 3 months months year Out of the Money Calls and Delta Hedging Forecasted Volatility 3 months months year

25 Table 5A Return and risk in writing options with different markup strategies (5%, 10%, 15%) in estimated volatilities Underlying asset Heng Seng Index At the Money Calls and Delta Hedge Mean Standard Worst Case % In- Failure Mean Standard Worst Case markup5% Return Deviation Date Return the-money Times markup5% Return Deviation Date Return 3 months months months months year year markup10% markup10% 3 months months months months year year markup15% markup15% 3 months months months months year year Out of the Money Calls and Delta Hedge Mean Standard Worst Case % In- Failure Mean Standard Worst Case markup5% Return Deviation Date Return the-money Times markup5% Return Deviation Date Return 3 months months months months year year markup10% markup10% 3 months months months months year year markup15% markup15% 3 months months months months year year

26 Table 5B Return and risk in writing options with different markup strategies (5%, 10%, 15%) in estimated volatilities Underlying asset MSCI Taiwan Stock Index At the Money Calls and Delta Hedge Mean Standard Worst Case % In- Failure Mean Standard Worst Case markup5% Return Deviation Date Return the-money Times markup5% Return Deviation Date Return 3 months months months months year year markup10% markup10% 3 months months months months year year markup15% markup15% 3 months months months months year year Out of the Money Calls and Delta Hedge Mean Standard Worst Case % In- Failure Mean Standard Worst Case markup5% Return Deviation Date Return the-money Times markup5% Return Deviation Date Return 3 months months months months year year markup10% markup10% 3 months months months months year year markup15% markup15% 3 months months months months year year