People’s Republic of China-Hong Kong Special Administrative Region1
Selected Issues and Statistical Appendix

This Selected Issues paper analyzes the long-term fiscal policy in Hong Kong Special Administrative Region (SAR) and the anticipated structural changes in the economy. The paper examines the factors that contributed to the stability of the banking system in Hong Kong SAR by assessing the roles played by banks, equity markets, and debt markets. The study describes a procedure to extract the probability distribution of future exchange rate movements based on currency option data. The paper also provides a statistical appendix report of the country.


This Selected Issues paper analyzes the long-term fiscal policy in Hong Kong Special Administrative Region (SAR) and the anticipated structural changes in the economy. The paper examines the factors that contributed to the stability of the banking system in Hong Kong SAR by assessing the roles played by banks, equity markets, and debt markets. The study describes a procedure to extract the probability distribution of future exchange rate movements based on currency option data. The paper also provides a statistical appendix report of the country.

Extracting Market Beliefs Around the August 1998 Intervention1

A. Introduction

1. Using prices of currency derivatives to extract market beliefs about future exchange rate movements has been a well established practice in economics. The most commonly used variable—the forward exchange rate—while extremely useful and easily obtainable suffers from two drawbacks. First, it reveals only what the market, on average, believes about future exchange movements. On many occasions however, information about the probabilities the market assigns to various possible future exchange rate levels can be useful. For example, it might be useful to know what the market believes is the likelihood of an extreme correction of the exchange rate. The second drawback is that empirical studies often find forward rates to be biased estimators of future exchange rate outcomes.

2. This chapter discusses a procedure to extract the probability distribution of future exchange rate movements based on currency option data. The methodology exploits the fact that an option’s price broadly reflects the probability that it will be profitable (in the money) at maturity. For a given maturity, the difference in option prices at different strike rates reflects differences in the probability of ending in the money. Thus, given a series of option prices at different strike prices (in this case, values of the exchange rate), one can compute the probabilities assigned by the market to different outcomes of the exchange rate. A method due to Malz (1997)2 is used to extract the probability distribution of the Hong Kong dollar around the time of the stock market intervention of August 1998, which reveals the differences in market beliefs before and after the intervention.

3. This procedure and other existing methods do not yield the “true” statistical probability function, but rather the “risk-neutral probability” distribution. The risk neutral probability is a function of (i) the statistical or “true” probability and (ii) the market’s subjective attitude towards risk. For example, if the market is highly risk averse, it will be willing to pay a high price to insure against a crash, which statistically may have a very low probability of occurring. Yet, the probability distribution derived under the risk-neutrality assumption would indicate a high probability of the crash occurring.

4. In this paper, a new procedure that adjusts the risk-neutral probability for the market’s risk aversion is presented. This allows to better gauge how closely shifts in the extracted probability distribution reflect changes in market sentiment.

B. Extracting the Risk-Neutral Exchange Rate Probability Distribution

5. The method used for extracting probability distributions relies on implied volatility data of currency options, available in over-the-counter (OTC) markets. The data consists of five implied volatility3 quotes for each day: two quotes (with deltas 10 percent and 25 percent) represent the prices of out-of-the money options, two quotes (with deltas 75 percent and 90 percent) represent in-the-money options and one quote (50 percent delta) represents the at-the-money forward option. Based on these observations and using the technique described in Box IV.1, probability distributions of expected Hong Kong dollar—U.S. dollar exchange rates are derived for the period around the August 1998 intervention.

6. In the period immediately before the August 1998 intervention, the Hong Kong dollar came under several waves of speculative attacks. At the same time, stock and futures prices plummeted, with the Hang Seng index sinking 25 percent from mid-July, to 40 percent of its pre-crisis level. The authorities, arguing that the markets were being manipulated, and concerned that domestic confidence could be seriously weakened, reacted by intervening in the stock and futures markets between August 14 and 28, acquiring6 percent of market capitalization.

7. While the exchange rate peg remained intact, shifts in the extracted probability distribution reflected market sentiment changing with the intervention. By August 7 there was almost a consensus in the market that the Hong Kong dollar peg would break within 3 months. The mean of the risk-neutral exchange rate probability distribution was HK$8.08=US$1 against the linked rate of HK$7.8=US$1. After the initial round of intervention fears of devaluation calmed temporarily. By August 21 (the first observation after the August 14 intervention), the mean of the risk-neutral exchange rate distribution had moved to HK$7.99=US$1. However by August 28, although widely dispersed, market beliefs again expected a collapse of the peg. The last intervention took place on August 28 and by September 4, market sentiment gravitated almost uniformly back to the linked rate.


Implied Risk-Neutral Probability Distribution

Citation: IMF Staff Country Reports 2001, 146; 10.5089/9781451807790.002.A004

8. How closely do these extracted probability functions reflect market beliefs? The procedure used in this exercise extract the riskneutral probability function and not the true statistical distribution. Riskneutral distributions do not expunge other characteristics of the market, such as the risk aversion of market participants and the liquidity of the market (Box IV.2) from the calculated probabilities. Consequently, it is difficult to unambiguously conclude that a shift in the implied probability distribution reflects a change in beliefs about the future value of the exchange rate or is due to changes in the underlying market structure, such as market liquidity or risk aversion.

Moment, of Risk-Neutral Probability Density Distributions

(Hong Kong dollar)

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Source: Staff estimates.

C. The Volatility Risk Premium

9. Like other derivatives, currency options typically price in premiums for various types of risk. One way of testing whether other types of risks are being priced in, is to estimate how well the implied volatility of currency options predicts realized volatility, since the extracted probability function is derived from quoted implied volatilities. If the market is efficient then implied volatilities should be unbiased predictors of realized volatility, and the risk-neutral distributions should reflect beliefs about future exchange rate changes only.

10. Data for the Hong Kong dollar and the Thai baht around the Asian crisis show that implied volatility is a biased predictor of future realized volatility (Table IV.1). The test was done by estimating:


where σt, T is the realized volatility over the life of the option measured as the annualized standard deviation from day t to T—time of maturity of the option, and σtIV is the implied volatility. If implied volatility are unbiased predictors of realized volatility, the intercept, a, should be close to 0, the slope coefficient b should be close to 1.4 While implied volatility explains a large amount of the variation of realized volatility in both the Hong Kong dollar and Thai baht, it consistently exceeds realized volatility and confirms the bias found elsewhere in the literature. In particular, implied volatility exceeds realized volatility by far more in Hong Kong SAR than in Thailand, reflecting the success of the Hong Kong dollar peg, i.e., while the currency remained stable, the implied volatility varied with market sentiment. In the less rigid exchange rate regime of the Thai baht, implied volatility was a relatively more accurate predictor of future realized volatility.

Table IV.1.

Forecasting Realized Volatility

(Dependent Variable is Realized Volatility)

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Source: Staff estimates.

Implied volatility at ask price.

11. Implied volatility tends to exceed realized volatility, at times by a large margin, as discussed in the previous paragraph. Prices of put and call options are an increasing function of the implied volatility of the asset. Thus, if implied volatility consistently exceeds realized volatility, option buyers are consistently paying more than the ‘fair’ price for options. While option markets on a few underlying securities markets may be sufficiently concentrated for option writers to earn excessive profits, it is unlikely to be the explanation in a market, like that for Hong Kong dollar, where market entry is very open.


Implied Volatility Versus Realized Volatility

(1-Month Hong Kong Dollar Options)

Citation: IMF Staff Country Reports 2001, 146; 10.5089/9781451807790.002.A004


Implied Volatility Versus Realized Volatility

(1-Month Thai baht Option)

Citation: IMF Staff Country Reports 2001, 146; 10.5089/9781451807790.002.A004

12. Asset price volatility is however, not constant over time. Time-varying volatility exposes the option writer—who assumes an unlimited loss potential—to the risk that volatility changes may adversely affect his position, and thus she needs to be compensated for taking on this volatility risk. As a result, there will be a risk premium that is implicit in the observed market price—the implied volatility, very much like the risk premium in the forward market, which drives a wedge between the forward rate and the anticipated rate of domestic currency depreciation. Thus, the volatility risk premium needs to be removed from the implied volatility to arrive at what the market expects to be the future volatility:


where E[σRV] is the anticipated future realized volatility, σIV is the implied volatility, and σVP, is the volatility risk premium the option writer needs to be paid in order to take on volatility risk. Assuming rational expectations, we can extract the volatility risk premium ex post:


Accounting for the volatility risk premium, the equation needs to be reformulated:


where β2 < 0. Substituting for the volatility risk premium and re-arranging the equation the following result obtains:


Thus, there is a downward bias in the coefficients of the predictability equations:

α = α(1 + β2) and β2 = b + (b – 1)β2,

where a and b are the coefficients from the predictability equation in paragraph 10. Since β2 < 0, and b < 1, it follows that the regression coefficients in Table IV.1 are smaller than they would be if the volatility risk premium had been accounted for.

13. Two measures of volatility risk premium were considered: first, the volatility of implied volatility, in market parlance also known as “vol of vol,” and second, the bid-ask spread of implied volatility. Traders pay close attention to the vol of vol as it generates much of the risk in portfolios containing options. For both the Hong Kong dollar and the Thai baht, the bid-ask spread turned out to be a better proxy for volatility premium.5 While the bid-ask spread is a good predictor of the volatility risk premium, it should be noted that it is also affected by the liquidity in the market.

14. Adjusting for volatility premium, however, improved the usefulness of implied volatility in predicting actual volatility only marginally for the Hong Kong dollar. However, it had a sizable impact on the Thai baht (Table IV.3), which operated under more flexible exchange rate arrangement.

D. Adjusting for Risk Aversion

15. The extracted probability distributions, after adjusting for the market’s risk aversion generally reveal a higher implied probability of a devaluation. This can be gleaned from the fact that the adjusted probability distributions are mostly shifted to the right of the unadjusted ones (Charts IV. 1 and IV.2).6 Also the dispersion of the adjusted probability distributions are larger, indicating a higher degree of uncertainty about future outcomes.

Chart IV.1.

Impact of the August 14 Intervention on Market Beliefs

Source: Staff estimates.
Chart IV.2.

Impact of August 28 Intervention on Market Beliefs

Source: Staff estimates.

16. Importantly, the adjusted probability distributions indicate that the impact of August 1998 intervention in calming market sentiment was muted. The changes in the means of the implied distributions after intervention dates were smaller in the risk-adjusted case than in the unadjusted case. At the same time, the standard deviation for risk-adjusted implied distributions did not decline by as much after intervention as it did in the unadjusted case. Thus, the market was not as reassured after the intervention as would be apparent by just considering risk unadjusted probability distribution.

E. Conclusion

17. This chapter showed how using the entire spectrum of market beliefs could be beneficial in analyzing expected exchange rate changes. Given its easy availability, economists generally rely on the average market view—as proxied by the forward exchange rate premium—to study market beliefs about future exchange rate changes. However, as demonstrated in this chapter, extracting the entire probability distribution of expected exchange rate changes is easily implementable and not excessively demanding on data requirements either. The chapter also discussed a methodology that controlled for the risk aversion in the market in extracting exchange rate probabilities from option data, thus generating a probability distribution that was closer to the true function. Using the extracted distributions, it was shown that in the immediate aftermath of the August 1998 intervention by the Hong Kong SAR authorities, market sentiments did calm down, but to smaller extent than revealed by changes in the forward exchange rate premium alone.

Extracting the Risk-Neutral Probability Distribution from Currency Options

The market price of a European call option, c(t, X, T), is the difference between the expected value of the future exchange rate and the exercise price, with the probability weights drawn from the risk-neutral distribution, π(x):


where X is the exercise price, t and T are the current and option maturity dates, τ ≡ Tt, r is the risk-free interest rate, St is the asset price at time t, E* is the expectation operator taken under the risk-neutral probability distribution, and abπ(ST)dSTP*(aSTb), where P* denotes a risk-neutral probability. Notice that all variables in equation (1) are observable, except for the risk neutral distribution, which is to be identified. Akin to the way the risk-neutral probabilities change as market conditions fluctuate (case 2, Box 1), π(X) it is the set of probabilities that changes as other observable variables change, so as to equate both sides of the equation.

In order to uncover the risk-neutral probability distribution, we twice differentiate the price of the option with respect to the exercise price:


where Π(x) ≡ P* (STx) is the risk neutral cumulative distribution function and


Theoretically, one could trace out the entire probability distribution using options with a series of very closely spaced exercise prices. In practice, only a few strike prices are observable, typically at least one for at-the-money, out-of-the money and in-the-money options. Given the scarcity of data, one possible solution is to assume that the risk-neutral probability distribution of the future asset price belongs to a particular parametric family. An alternative involving less restrictive assumptions uses over-the-counter options market data to interpolate between observable strike prices. A detailed procedure which effectively fits a polynomial function through the observed points to extract the probability distribution implied by a set of option prices is described in Malz (1997) and applied in this paper.

Risk Neutrality

To understand the concept of risk neutrality consider the following example. Suppose a non-profit bookmaker accepting bets on both teams in a football game knows that the true probabilities that each team wins are equal, i.e., half. However, among the 10 people placing bets opinions are divided differently. Eight people would like to bet that team A wins and two people are convinced that team B wins. If the bookmaker were to accept bets based on the true probabilities—paying out $2 for every successful and $0 for every unsuccessful $1 bet—he may incur a $6 loss if team A wins: He needs to pay out $16 on the winning bets, but received only $10 for all bets placed (Table 1). If team B wins, the bookmaker would make a profit of $6, as he only needs to pay out $4 for the winning tickets from the $10 collected (Case 1). While on average the bookmaker would break even if the game is repeated several times, he bears the risk for any individual game.

Table 1.

Implied Probabilities in Hypothetical Bet

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In order to break even for each game and thus not bear any risk, the market maker may adjust the payout ratios to reflect aggregate risk preferences in the “market.” In this case, he would pay only $1.25 on the popular bet that team A wins, but would reward the successful bet on team B with $5. Adjusting the payouts such that the bookmaker has a riskless position ensures that he always breaks even: If team A wins, his payout ($1.25 × 8 bets) is exactly covered by his revenue ($10). If team B wins, his payout ($5 × 2 bets) is again covered by the wagers received ($10—Case 2). The relative supplies of bets on the two teams prescribes the “market consensus” and implies the risk-neutral probabilities of victory—80 percent for team A and 20 percent for team B. However, these expectations differ from the true probabilities. Note that the term risk neutrality does not imply that market participants are risk neutral—in general, they are not. Instead, risk neutrality in this context simply means that the calculated probabilities are not adjusted for risk; they are exactly the probabilities that a risk-neutral person would apply.

Suppose the bookmaker cannot know for sure how many people will actually place bets, thus raising the possibility that he may have an unhedged position. In order to prevent losses in the long run, he charges a premium of 25 cents per bet to cover his risk (Case 3). The probabilities implied by this pricing structure sum to more than 100 percent. However, knowing the risk premium charged by the market maker enables us to uncover the true probabilities.

Table IV.2.

Factors Affecting Volatility Risk Premium

(Dependent Variable is Realized Volatility Risk Premium)

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Source: Staff estimates.
Table IV.3.

Effects of Risk Aversion on Realized Volatility

(Dependent Variable is Realized Volatility)

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Source: Staff estimates.

Significantly different from unity at 5 percent level.

Implied volatility at ask price.


This chapter was prepared by Peter Breuer (ext. 36364).


See Allan M. Malz, “Estimating the Probability Distribution of the Future Exchange Rate from Option Prices,” Journal of Derivatives, Winter 1997, pp. 18–36.


Implied volatility is the volatility of the underlying asset returns that is assumed to prevail over the option’s life. Since any option price “implies” only one volatility, quoting prices in the form of absolute prices or implied volatilities is equivalent. The Black-Scholes option pricing formula is used to go back and forth between the two.




where σtHV denotes the historical volatility, it was also tested whether the predictive power of implied volatility was greater than that of historical volatility.


The coefficient of the bid-ask spread, while, different from 1 at the 5 percent significance level, which is a sign of good approximation, was substantially closer to unity than the volatility of implied volatility (Table IV.2).


The exchange rate probability distributions were extracted by adjusting the quoted implied volatility for the market risk aversion using the bid-ask spread as a proxy. However, since only the bid-ask spread around the at-the-money implied volatility was available, it was assumed for the exercise that the spread remained constant over other implied volatilities. In practice, it is likely that the bid-ask spread increases the further away from the money the quote is, which would strengthen the results of this exercise.

Statistical Appendix

Table 1.

Hong Kong SAR—Gross Domestic Product by Expenditure Component at Current Market Prices, 1996–2000 Q3

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Sources: Census and Statistics Department, Annual Report of Gross Domestic Product; Quarterly Report of GDP.
Table 2.

Hong Kong SAR—Gross Domestic Product by Economic Activity at Current Prices, 1995–99

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Sources: Census and Statistics Department, Annual Report of Gross Domestic Product and Quarterly Report of GDP.

An imputed rental charge for owner-occupied premises.

An imputed service charge, equal to net interest receipts for financial intermediaries (e.g., banks).

Difference between production-based GDP and expenditure-based GDP figures reflects statistical discrepancy.

Measured relative to production-based GDP at factor cost.

Table 3.

Hong Kong SAR—Gross Fixed Capital Formation, 1996–2000 Q3

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Sources: Census and Statistics Department, Annual Report of Gross Domestic Product and Quarterly Report of GDP.
Table 4.

Hong Kong SAR—Estimates of External Factor Income Flows by Income Component and by Business Sector, 1995–99

(At current market prices, in millions of Hong Kong dollars)

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Source: Census and Statistics Department, Hong Kong Annual Digest of Statistics and Hong Kong. Monthly Digest of Statistics.
Table 5.

Hong Kong SAR—Selected Price Indicators, 1996–2000 Q3

(Percentage changes)

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Sources: Census and Statistics Department, Monthly Report on the Consumer Price Index, Hong Kong Monthly Digest of Statistics, Quarterly Report of GDP, Rating and Valuation Department.

Data are on a national accounts basis.

Table 6.

Hong Kong SAR—Labor Force, Employment, and Unemployment, 1995–2000 Q3

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Sources: Census and Statistics Department, Hong Kong Monthly Digest of Statistics, Dec. 2000; Quarterly Report on General Household Survey, July to September 2000.

General Household Survey.

Since August 2000, the “resident population” approach has been adopted in place of the “extended de facto” approach for compiling population estimates and revised population figures backdated to 1996 have been compiled. In the above table, statistics which are population-related have been revised accordingly and annotated with *. However, as regards the growth rates marked with **, they are still derived from figures obtained based on the old approach since the figures for 1995 under the “resident population” method are not available. For details of the revision to the method of compiling population estimates of Hong Kong, please see the feature article entitled “Revision to the Method of Compiling Population Estimates of Hong Kong” published in the September 2000 issue of the Hong Kong Monthly Digest of Statistics or visit the website of the Census and Statistics.

The quarterly unemployment rate is seasonally adjusted, while seasonally adjustment is not applicable 10 annual average unemployment rate.

Seasonally adjusted unemployment rates.

Based on data on persons engaged by industry sector. Quarterly Survey of Employment and Vacancies.

Wholesale, retail, import and export trade, restaurants, and hotels.

Refers to manual workers at construction sites only.

Table 7.

Hong Kong SAR—Wages, Labor Productivity, and Unit Labor Costs, 1995–2000 Q3

(Percentage change) 1/

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Sources: Census and Statistics Department, Quarterly Report on Wage and Payroll Statistics, September 2000, Tables 1 and 2; and staff estimates

Data on labor productivity are based on data for the first of September 2000. Percentage changes are calculated over third quarters’ corresponding year-earlier periods.

Based on September data.

Includes wholesale, retail, import and export trades, restaurants, and hotels.

Includes financing, insurance, real estate, and business services.

Based on expenditure based real GDP and GHS annual employment data from the “resident population” approach; backdating to years prior to 1996 not feasible; data on person-hours are unavailable.

Table 8.

Hong Kong SAR—Property Market Developments, 1995–2000 Q3 1/

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Sources: Census and Statistics Department, Hong Kong Monthly Digest of Statistics, Rating and Valuation Department; and CEIC database.

Data are period averages.

Provisional figures.

Table 9.

Hong Kong SAR—Consolidated Government Account, 1995/96–2000/01 1/

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Sources: Data provided by the Government Secretariat, Finance Bureau.

The fiscal year begins April 1.

Consists of the Capital Works Reserve Fund; Capital Investment Fund and Loan Fund beginning 1990/91; Disaster Relief Fund beginning 1993/94; Civil Service Pension Reserve Fund beginning 1994/95 and Innovation and Technology Fund beginning in 1999/2000.

Includes revenue from land sales.

Includes direct financing of airport-related projects as well as government equity injections into the Airport Authority, the Mass Transit railway Corporation and the Kowloon-Canton Railway Corporation.

From July 1, 1997, Land Fund is included.

Balance of fiscal reserves adjusted to take account of outturn in previous year.

The Government Bond Program was launched in November 1991 in an effort to develop a market in fixed-income securities and facilitate the funding of long-term government infrastructural projects. The bonds were issued before the government actually required file funds. The porogram limits the size of gross debt outstanding to HKS5 billion as of June .30. 1997.

Table 10.

Hong Kong SAR-Revenue (General Revenue Account), 1995/96–2000/01 1/

(In millions of Hong Kong dollars)

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Source: Data provided by the Government Secretariat, Finance Bureau.

The fiscal year runs from April 1 to March 31.

Includes only land transactions completed before the coming into force of the Sino-British Joint Declaration (5/27/85), or land transactions conferring a benefit that expired before June 30, 1997. Revenue from other land transactions is credited to the Capital Works Reserve Fund. The only exception is for the period from July 1, 1997 to December 31, 1997, when land revenue was credited to General Revenue Account pending amendment of the Capital Works Reserve Fund resolution.