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Abstract:
The valuation and applications of one-touch double barrier binary options that include features of knock-out, knock-in, European and American style are described. Using a conventional Black-Scholes option-pricing environment, analytical solutions of the options are derived. The relationships among different types of one-touch double barrier binary options are discussed. An investor having a particular view on values of foreign exchanges, equities or commodities can use the options as directional trades or structured products in financial market.

barrier options, binary options, double-barrier options

Abstract:
This paper provides a method for pricing options in the constant elasticity of variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for the option values incorporating time-dependent model parameters are obtained in various CEV processes with different elasticity factors. The numerical results indicate that option values are sensitive to volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. Furthermore, the Lie-algebraic approach is very simple and can be easily extended to other option pricing models with well-defined algebraic structures.

Options, constant elasticity of variance, Lie Algebra

Abstract:
Time dependent barrier options have barrier periods covering a portion of option life. This feature makes them hybrids of barrier options and ordinary European options. There are two types of time dependent barrier options: 1. front end barrier options; 2. rear end barrier options. The options are more flexible than regular barrier options for investors who hold particular views on values of foreign exchanges, equities or commodities in certain periods of time. They can be used for hedging and investment in financial market. Analytical solutions of the option values are derived in a conventional Black-Scholes option-pricing environment. Their delta, gamma and vega risks are discussed and compared with the risk factors of the ordinary options.

barrier options, window options, time-dependent parameters

Abstract:
This paper develops a barrier-option pricing model in which the exchange rate follows a mean-reverting lognormal process. The corresponding closed-form solutions for the barrier options with time-dependent barriers are derived. The numerical results show that barrier option values and the corresponding hedge parameters under the proposed model are different from those based on the Black-Scholes model. For an up-and-out call, the mean-reverting process keeps the exchange rate in a small range around the mean level. When the mean level is below the barrier but above the strike price, the risk of the call to be knocked out is reduced and its option value is enhanced compared with the value under the Black-Scholes model. The parameters of the mean-reverting lognormal process therefore have a material impact on the valuation of currency barrier options and their hedge parameters.

barrier options, currency options, mean-reverting process

Abstract:
In this paper we present a simple and easy-to-use method for computing accurate estimates (in closed form) of Black-Scholes barrier option prices with time-dependent parameters. This new approach is also able to provide tight upper and lower bounds (in closed form) for the exact barrier option prices.

barrier options, moving boundary, time-dependent parameters

Abstract:
In this paper we propose a simple and easy-to-use method for computing accurate estimate (in closed form) of the double barrier hitting time distribution of a mean-reverting lognormal process, and discuss its application to pricing exotic options whose payoffs are contingent upon barrier hitting times. This new approach is also able to provide tight upper and lower bounds (in closed form) of the exact result. Within the multi-stage approximation scheme, the estimate and bounds can be easily improved in a systematic manner. Furthermore, this approach can be straight-forwardly extended to those cases with specified moving boundaries as well.

First hitting time, mean-reverting lognormal process, barrier options, method of images

Abstract:
Based upon the Fourier series expansion, we propose a simple and easy-to-use approach for computing accurate estimates of Black-Scholes double barrier option prices with time-dependent parameters. This new approach is also able to provide tight upper and lower bounds of the exact barrier option prices. Furthermore, this approach can be straightforwardly extended to the valuation of standard European options with specified moving boundaries as well.

Double-barrier Options, Fourier Series, Moving Boundaries, Time-dependent Parameters

Abstract:
This study develops a stress-testing framework to assess liquidity risk of banks, where liquidity and default risks can stem from the crystallisation of market risk arising from a prolonged period of negative asset price shocks. In the framework, exogenous asset price shocks increase banks' liquidity risk through three channels. First, severe mark-to-market losses on the banks' assets increase banks' default risk and thus induce significant deposits outflows. Secondly, the ability to generate liquidity from asset sales continues to evaporate due to the shocks. Thirdly, banks are exposed to contingent liquidity risk, as the likelihood of drawdowns on their irrevocable commitments increases in such stressful financial environments. In the framework, the linkage between market and default risks of banks is implemented using a Merton-type model, while the linkage between default risk and deposit outflows is estimated econometrically. Contagion risk is also incorporated through banks' linkage in the interbank and capital markets. Using the Monte Carlo method, the framework quantifies liquidity risk of individual banks by estimating the expected cash-shortage time and the expected default time. Based on publicly available data as at the end of 2007, the framework is applied to a group of banks in Hong Kong. The simulation results suggest that liquidity risk of the banks would be contained in the face of a prolonged period of asset price shocks. However, some banks would be vulnerable when such shocks coincide with interest rate hikes due to monetary tightening. Such tightening is, however, relatively unlikely in a context of such shocks.

Liquidity risk, stress testing, default risk, banks

Abstract:
This paper develops a simple model to study the credit risk premiums of credit-linked notes using the structural model. Closed-form solutions of credit risk premiums of the credit-linked notes derived from the model as functions of firm values and the short-term interest rate, with time-dependent model parameters governing the dynamics of the firm values and interest rate. The numerical results show that the credit spreads of a credit-linked note increase non-linearly with the decrease in the correlation between the asset values of the note issuer and the reference obligor when the final payoff condition depends on the asset values of the note issuer and the reference obligor. When the final payoff condition depends on the recovery rate of the note issuer upon default, the credit spreads could increase with the correlation. In addition, the term structures of model parameters and the correlations involving interest rate are clearly the important factors in determining the credit spreads of the notes.

credit risk, risky bonds, contingent claim analysis

Abstract:
This paper presents a benchmarking model for validation of default probabilities of listed companies for Basel II purposes. The model is based on the recent studies on the predictive capability of structural credit risk models. Benchmark ratings and one-year default probabilities are assigned to companies by mapping the term structures of default probabilities of the companies generated by a structural model based on stochastic leverage ratios to the term structures of default rates reported by rating agencies. The empirical results show that the benchmarking model has adequate discriminatory power of ranking credit risk. The association between the benchmark ratings and external credit ratings is statistically significant. Benchmark default probabilities obtained from the model could thus be used as alternative external and independent estimates for comparisons with banks' internal default probability estimates. Significant deviations from this benchmark provide a reason to review the internal estimates.

Basel II, Default probabilities, Benchmarking models

Abstract:
The theoretical prediction of target exchange rates expects mean reversion of the exchange rates. This paper presents a model for valuing European foreign exchange options, in which the forward foreign exchange rate follows a mean-reverting lognormal process. The mean-reverting process has material impact on the foreign exchange rate option values and their hedge parameters. The numerical results using the forward exchange rates of the Hong Kong dollar and market data of their options show such impact. As the dynamics of target exchange rates may not follow the standard lognormal process as described by the Black-Scholes model, the mean-reverting option-pricing model may be considered for valuation of options and estimation of associated hedge parameters on target exchange rates.

Target foreign exchange rates, currency options, mean-reverting process

Abstract:
The theoretical prediction on targeted exchange rates expects mean reversion of the exchange rates. There is some empirical evidence to support this prediction. This paper presents a model for valuing European foreign exchange options in which the forward foreign exchange rate follows a mean-reverting lognormal process. The corresponding closed-form solutions for the option valuation are derived. The mean-reverting process has material impact on the foreign exchange rate option values and their hedge parameters. This tends to decrease the value of a simple put or call. On the other hand, the process also keeps the exchange rate in a small range around the mean level. As this is the region in which an option's intrinsic value is high because of the level of its strike price, there is also a tendency for option values to be enhanced compared with the values of the Black-Scholes model. The numerical results using the forward exchange rates of the Hong Kong dollar and market data of their options show that both of these effects are important for the realistic choices of parameter values. As the dynamics of targeted exchange rates may not follow the standard lognormal process as described by the Black-Scholes model, the mean-reverting option-pricing model may be considered for the valuation of options and estimation of associated hedge parameters on targeted exchange rates.

Targeted foreign exchange rates, currency options, mean-reverting process

Abstract:
The square root constant elasticity of variance (CEV) process has been paid little attention in previous research on valuation of barrier options. In this paper we derive analytical option pricing formulae of up-and-out options with this process using the eigenfunction expansion technique. We develop an efficient algorithm to compute the eigenvalues where the basis functions in the formulae are the confluent hypergeometric functions. The numerical results obtained from the formulae are compared with the corresponding model prices under the Black-Scholes model. We find that the differences in the model prices between the square root CEV model and the Black-Scholes model can be significant as the time to maturity and volatility increases.

Barrier options, constant elasticity of variance

Abstract:
Based upon the Wei-Norman theorem, this paper presents a Lie-algebraic technique for the pricing of financial derivatives with time-dependent parameters. By exploiting the dynamical symmetry of the pricing partial
differential equations of the financial derivatives, the new method enables us to derive analytical closed-form pricing formulae very straightforwardly. We believe that this new approach will provide an efficient method for the valuation of financial derivatives.

Lie algebra, option pricing, corporate bond pricing

Abstract:
Empirical findings and theoretical studies suggest that firms adjust towards time-varying target leverage ratios. This paper studies the performances of the default probabilities generated from two stationary-leverage models with time-dependent and constant target ratios respectively. The time-dependent model consistently performs better in terms of discriminatory power of differentiating firms' default risk and capability for predicting default rates over the period 1996 to 2006. The model provides appropriate measures of credit risk of firms and evidence to support the existence of a time-varying target leverage ratio.

Leverage, Default probabilities, Credit risk

Abstract:
In this paper we use the method of images to derive the closed-form formula for the first passage time density of a timed-dependent Ornstein-Uhlenbeck process to a parametric class of moving boundaries. The results are then applied to develop a simple, efficient and systematic approximation scheme to compute tight upper and lower bounds of the first passage time density through a fixed boundary.

Ornstein-Uhlenbeck process, Fokker-Planck equation, First passage time density, Method of images, Moving boundary

Abstract:
This paper assesses whether agency ratings and market-based default risk measures are consistent for East Asian banks during the period from 1996 to 2006. While the market-based measures are broadly consistent with the credit rating assessments for the banks in the developed economies, the discrepancy between ratings and the market-based measures for the East Asian banks are significant. The credit ratings had been adjusted slowly for the East Asian banks during the onset of the Asian financial crisis. The relatively higher default risk implied by ratings during the post-crisis period is partly due to the conservatism of rating agencies and the unsolicited ratings. The discrepancy still exists after taking these two factors into account. From a prospective of the banking policies, the use of agency-based or market-based measures for calculating capital requirements of exposures to banks and deposit insurance premiums in the East Asian economies could raise an issue of systematic differences between the two measures.

Asian financial crisis, credit rating agencies, credit risk models

Abstract:
Merton-type models of pricing corporate bonds based on relatively simple default processes cannot generate credit spreads which replicate empirically observed spreads. This paper presents an analytical valuation model of corporate discount bond prices to address this problem. The main feature of the model is a dynamic default barrier. Different default scenarios can be incorporated into the valuation model through adjusting the default barrier's dynamics. We derive a closed-form solution of the corporate bond price based on the model as a function of the firm value and short-term interest rate, with time-dependent model parameters. The numerical results calculated from the solution show that the model is capable of producing term structures of credit spreads that are consistent with some empirical findings. This model could provide new insight for future research on corporate bond analysis and credit risk modelling.

Bond pricing model, Merton model, Default barriers

Abstract:
The "structural approach" to modeling credit risk specifies a stochastic process that the net asset value of the issuing firm is assumed to follow. If firm value falls below a certain "default barrier," bankruptcy is triggered and the firm is assumed to default on its vulnerable obligations. In this article, Hui, Lo, and Lee apply the methodology to price vulnerable options written by a default risky firm. They show how a variety of default scenarios may be accommodated by use of a dynamic default barrier, while maintaining a closed-form valuation equation.

Option pricing, Credit risk, Derivatives

Abstract:
Given the deleveraging process in the banking sector, banks were reluctant to lend funds in the inter-bank market because of uncertainty about their own future need for funds during the financial crisis of 2007-2009. Aggregate liquidity then declined. This paper investigates the impact of the market-wide liquidity risk and carry-trade incentives on exchange rate movements. The results suggest that liquidity risk measured by the spread between Libor and the overnight index swap rate was a significant factor affecting the exchange rate movements of the euro, the British pound and the Swiss franc, while carry trades were important for the yen, the Australia dollar and the New Zealand dollar.

Sub-prime crisis, carry trades, liquidity, leverage

Abstract:
In this paper we have derived the analytical kernels of the pricing formulae of the CEV knockout options with time-dependent parameters for a parametric class of moving barriers. By a series of similarity transformations and changing variables, we are able to reduce the pricing equation to one which is reducible to the Bessel equation with constant parameters. These results enable us to develop a simple and efficient method for computing accurate estimates of the CEV single-barrier option prices as well as their upper and lower bounds when the model parameters are time-dependent. By means of the multi-stage approximation scheme, the upper and lower bounds for the exact barrier option prices can be efficiently improved in a systematic manner. It is also natural that this new approach can be easily applied to capture the valuation of other standard CEV options with specified moving knockout barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, more comparative pricing and precise risk management in equity options can be achieved by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.

CEV option, similarity transformation, Bessel equation, moving barrier

Abstract:
This paper proposes a path-dependent approach for estimating maximum appreciations of the renminbi expected by the market based on first-passage-time distributions. Using market data of the renminbi spot exchange rates, non-deliverable forward rates and currency option prices from 21 July 2005 (the reform of the exchange rate regime) to 28 February 2008 for model parameters, the maximum appreciations of the renminbi estimated under the proposed approach show that the market expected another large movement of the exchange rate during the 14 months after the reform. Subsequently, the few occasions of appreciations beyond the expected maximums coincided with the trade-related issues and speculations of greater momentum of appreciation allowed by the authorities. The PBoC's measures were however largely incorporated into the derivatives' prices. The proposed approach can be used to gauge the range of appreciations of the renminbi anticipated in the market and to identify any exchange rate movements beyond market expectations.

renminbi exchange rate, first-passage-time distributions, currency options

Abstract:
This paper proposes a path-dependent approach for estimating maximum appreciations of the renminbi expected by the market based on first-passage-time distributions. Using market data of the renminbi spot exchange rates, non-deliverable forward rates and currency option prices from 21 July 2005 (the reform of the exchange rate regime) to 28 February 2008 for model parameters, the maximum appreciations of the renminbi estimated under the proposed approach show that the market expected another large movement of the exchange rate during the 14 months after the reform. Subsequently, the few occasions of appreciations beyond the expected maximums coincided with trade-related issues and speculation that greater momentum of appreciation would be allowed by the authorities. The PBoC's measures were however largely incorporated into the derivatives' prices. The proposed approach can be used to gauge the range of appreciations of the renminbi anticipated in the market and to identify any exchange rate movements beyond market expectations.

renminbi exchange rate, first-passage-time distributions, currency options

Abstract:
In this paper we apply the Lie-algebraic technique for the valuation of moving barrier options with time-dependent parameters. The value of the underlying asset is assumed to follow the constant elasticity of variance (CEV) process. By exploiting the dynamical symmetry of the pricing partial differential equations, the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly, and thus provides an efficient way for computing the prices of the moving barrier options. The method is also able to provide tight upper and lower bounds for the exact prices of CEV barrier options with fixed barriers.

In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.

Options, Constant elasticity of variance, Partial differential equation, Lie algebra

Abstract:
This paper develops a model to value defaultable bonds in emerging markets. Default occurs when some signaling process hits a pre-defined default barrier. The signaling variable is considered to be some macro-economic variables such as foreign exchange rates. The dynamics of the default barrier depends on the volatility and the drift of the signaling variable. We derive a closed-form solution of the defaultable bond price from the model as a function of a signaling variable and a short-term interest rate. The numerical results show that the model values generated by using foreign exchange rates as the signaling variables can broadly track the market credit spreads of defaultable bonds in South Korea and Brazil. Given an expected level of the foreign exchange rate, defaultable bond values under stressed market situation can be obtained.

risky bonds, credit risk, emerging markets, stress tests

Abstract:
This paper examines the term structures of default probabilities that are generated by the Collin-Dufresne and Goldstein model and a dynamic-leverage-ratio model. The dynamic-leverage-ratio model is capable of producing term structures of default probabilities which are consistent with some empirical observed default rates. It demonstrates that the leverage ratio is a determinant factor of default risk of firms. The Collin-Dufresne and Goldstein model which considers a leverage ratio mean- reverting towards a constant target leverage ratio however gives default probabilities lower than the empirical observed default rates. The predicted default probabilities of the models are sensitive to the dynamics of the leverage ratio, in particular the mean-reverting property of the leverage ratio towards a constant target leverage ratio.

Credit Risk Models, Credit Ratings, Default Probability

Abstract:
This paper develops a simple model based on an options approach to measure provisions covering expected losses of collateralised retail lending due to default. The measurement of provisions against expected losses of retail lending secured by collateral is important for improving the capital adequacy framework for banks. The numerical results based on the model show that the loan-to-value ratio, correlation between the collateral value and the probability of default of borrowers in the pool, volatility of the collateral value, mean-reverting process of the probability of default and time horizon are the important factors for measuring provisions.

credit risk, retail lending, Basel II

Abstract:
This note analyses the impact of the global credit crisis on the FX swap market and discusses its potential implications. The turbulence in money markets has spilled over to FX swap markets amid a reappraisal of counterparty risks during the recent financial turmoil. We examine the situations of six currencies including the euro, the British pound, the Australian dollar, the Japanese yen, the Hong Kong dollar and the Singapore dollar. We find that (i) the risk premiums have indeed gone in tandem with the spreads of money market rates over their corresponding overnight index swaps across the economies, a popular measure of potential banking insolvency; and (ii) the risk premiums bear a negative relationship with the strength of the spot rates of the respective currencies, which is consistent with the increased pressure in the swap markets.

FX swaps, covered interest parity, counterparty risk

Abstract:
A new Capital Accord (Basel II) proposed by the Basel Committee on Banking Supervision raises the question of how to measure forward credit risk capital charges arising from maturity-mismatched hedges. This article develops a model to measure forward credit risk that is treated as a put option on a firm's asset value with a maturity-mismatched hedge. The hedge is considered a knockout barrier covering part of the put option life. When the firm value breaches the barrier, this triggers the guarantor to provide full protection to the lender. A closed-form formula of this barrier put option is derived and used to calculate forward credit risk premiums. A straight-line method with a premium capital charge and minimum one-year hedge period for treating residual credit risk in maturity mismatches is shown to be conservative and appropriate for the Basel II.

Basel II, Forward Credit Risk, Maturity Mismatches

Abstract:
This paper extends the stationary-leverage-ratio model to incorporate a time-dependent target leverage ratio. The theoretical hypothesis of the existence of a time-dependent target leverage ratio reflects the movement of a firm's initial target ratio toward a long-term target ratio over time. Using some simple scenarios about the time-dependence of the target leverage ratio, the numerical results show that the incorporation of the hypothesis into the stationary-leverage-ratio model is capable of producing term structures of probabilities of default that are consistent with some empirical findings. The results provide some evidences to support the hypothesis.

Credit Risk Models, Credit Ratings, Default Probability

Abstract:
This paper develops a valuation model of European options incorporating a stochastic default barrier, which extends a constant default barrier proposed in the Hull-White model. The default barrier is considered as an option writer's liability. Closed-form solutions of vulnerable European option values based on the model are derived to study the impact of the stochastic default barriers on option values. The numerical results show that negative correlation between the firm values and the stochastic default barriers of option writers gives material reductions in option values where the options are written by firms with leverage ratios corresponding to BBB or BB ratings.

option pricing, credit risk, derivatives

Abstract:
Significant deviations from covered interest parity were observed during the financial crisis of 2007-2009. This paper finds that before the failure of Lehman Brothers the market-wide funding liquidity risk was the main determinant of these deviations in terms of the premiums on swap-implied US dollar interest rates for the euro, British pound, Hong Kong dollar, Japanese yen, Singapore dollar and Swiss Franc. This evidence suggests that the deviations can be explained by the existence and nature of liquidity constraints. After the Lehman default, both counterparty risk and funding liquidity risk in the European economies were the significant determinants of the positive deviations, while the tightened liquidity condition in the US dollar was the main driving factor of the negative deviations in the Hong Kong, Japan and Singapore markets. Federal Reserve Swap lines with other central banks that eased the liquidity pressure reduced the positive deviations in the European economies.

sub-prime crisis, funding liquidity, covered interest parity, FX swaps

Abstract:
In this paper we present a Lie-algebraic technique for the valuation of multi-asset financial derivatives with time-dependent parameters. By exploiting the dynamical symmetry of the pricing partial differential equations of the financial derivatives, the new method enables us to derive analytical closed-form pricing formulae very straightforwardly. We believe that this new approach will provide an efficient and easy-to-use method for the valuation of financial derivatives.

Option pricing, Lie algebraic approach, Time-dependent parameters

Abstract:
This paper proposes a path-dependent approach for estimating realignment probabilities of targeted exchange rates based on the first-passage-time (FPT) density instead of the commonly used path-independent approach. We consider that path dependency is an intrinsic characteristic of realignment risk because a realignment of an exchange rate can occur whenever a committed band by a central bank is breached. A mean-reverting lognormal process is considered in the FPT approach. Based on market data of the British pound and Italian lira during the ERM crisis of 1992, the realignment probabilities of the currencies estimated under the proposed approach show that path dependency is quantitatively significant, compared with the path-independent approach. The first-hitting time and the time of the maximum slope of the FPT density have forward-looking capability of assessing realignment risk of the pound and lira target zones.

realignment risk, ERM crisis, first-passage-time probability

Abstract:
In this paper, we comment on the paper "Pricing Double Barrier Options using Laplace Transforms" by Antoon Pelsser. We illustrate that the same solutions of double barrier option values in terms of Fourier sine series can be obtained by using both Laplace transform and the method of separation of variables. The solutions in terms of the cumulative normal distribution function can be derived by employing the method of reflection. Furthermore, we discuss the numerical characteristics of the pricing solutions.

Barrier options, Black and Scholes model, partial differential equations

Abstract:
In this paper we comment on the paper "Pricing Double Barrier Options using Laplace Transforms" by Antoon Pelsser. We illustrate that the same solutions of double barrier option values in terms of Fourier sine series can be obtained by using both Laplace transform and the method of separation of variables. The solutions in terms of the cumulative normal distribution function can be derived by employing the method of reflection. Furthermore, we discuss the numerical characteristics of the pricing solutions.

Abstract:
This paper investigates the determinants of variations in the yield spreads (swap spreads) between Hong Kong dollar interest rate swaps and Exchange Fund paper for a period from July 2002 to April 2008. A vector error-correction model is used to analyze the impact of various shocks on swap spreads. The issue is whether "liquidity" or "credit" (or both) is the main determinant of swap spread dynamics. The results show that the dynamics are influenced significantly by "credit" between July 2002 and September 2007. However, "liquidity" between the Exchange Fund long-term notes and short-term bills is the major determinant of swap spreads between September 2007 and April 2008. The substantial demand of the Exchange Fund short-term bills, that reflected the strong preference of market participants for holding short-term instruments for liquidity purposes probably due to the sub-prime crisis in the US, is the driving force of the rise in swap spreads in the last quarter of 2007.

Hong Kong dollar interest rates, swap spreads, vector error-correction model, sub-prime crisis

Abstract:
Residential mortgage rates in Hong Kong have fallen to a historic low level since late 2004, largely because of severe competition and the prevailing exceptionally low funding cost of the banks. Because of the abundance of liquidity in the banking system, HIBOR is at an abnormally deep discount to LIBOR of about 200 bps. Under the Currency Board arrangements, HIBOR tracks LIBOR closely in the long run. The average HIBOR-LIBOR differential for the past 16 years is near zero. However, with US interest rates rising, and given the long repayment period of mortgages, there are risks of a reduction on the interest rate margin for mortgage loans made under the prevailing monetary conditions. Such risks could arise from a narrowing of the average spread between Hong Kong's best lending rate and the cost of funds during the tightening phase of US interest rates, and a shift of the risk premium of Hong Kong dollar over the US dollar to a more normal level. For simplicity, loans are classified into three groups for analytical purposes to assess these risks: HIBOR-financed loans, time deposits-financed loans and loans financed by an average mix of time, demand and savings deposits. Currently, banks are generally pricing mortgage loans at BLR -2.75% and providing cash rebates of 1% of loan amounts, with a gross mortgage margin of 130 bps for HIBOR-financed lending and 163 to 167 bps for deposits-financed loans. Simulations derived under different scenarios of interest rate upswings and risk premium reversals indicate that such a margin reduction on loans priced on the currently very low funding cost could be tangible. When HIBOR converges with LIBOR, and assuming US interest rates to increase by 120 bps in the next 12 months as expected by the market, the gross margin of mortgage loans would be reduced because of the lead-lag relationship among the rises in the various interest rates including BLR, and their different responses to the shocks. Taking account of the deposit-acquiring cost (30 bps), operating cost (30 bps) and credit cost (10 bps), the mortgages which are financed by time deposits or with a mix of customers' deposits are expected to maintain a positive, albeit thinner, margin. The expected tightening of the mortgage spread is likely to exert pressures on the earnings of the banking industry. How the margin of mortgage portfolio and earnings of individual banks may be affected depends much on the structure of their own funding sources and actual operating and credit costs. Note that many of the banks involved in the mortgage market have a sizeable retail deposit base.

Interest rate risk, Residential mortgage rate, Banking stability

Abstract:
The empirical results show that after the introduction of the three refinements to the Linked Exchange Rate system in May 2005 the Hong Kong dollar follows a bounded process that is consistent with a fully credible exchange rate band. The bounded process will limit the movements of the exchange rate to between the strong- and weak-side limits because its variance vanishes at the Convertibility Undertakings making it inaccessible to the limits. The Hong Kong dollar does not show any strong tendency to revert towards the centre of the Convertibility Zone. This is perhaps not surprising as there have been no interventions in the foreign exchange market since May 2005. There may be few forces or incentives for market participants to drive the exchange rate towards 7.80.

Linked Exchange Rate system, target zone, mean reversion, bounded process

Abstract:
This paper proposes a path-dependent approach for estimating realignment probabilities of targeted exchange rates based on first-passage-time distributions instead of the commonly used path-independent approach. We consider that path dependency is an intrinsic characteristic of realignment risk because a realignment of an exchange rate can occur whenever a committed band by a central bank is breached. A mean-reverting lognormal process is considered in the first-passage-time approach. Based on market data of the British pound and mark during the ERM crisis of 1992, the realignment probabilities of the pound estimated under the proposed approach show that path dependency is quantitatively significant, compared with the path-independent approach.

realignment risk, mean-reversion, first-passage-time probability

Abstract:
This paper examines pricing anomalies in the interest rate markets during the financial crisis of 2007-2009. Before the failure of Lehman credit and funding constraints weakened the relationship between interest rates of LIBOR and derivatives in the euro, British pound and US dollar, with equivalent discounted cash flows, and hence gave rise to pricing anomalies that would not usually exist. After the Lehman failure, the pricing anomalies in the two European currencies reduced with the relaxation of the funding constraint. The funding and credit constraints however became insignificant for the pricing anomalies in the dollar which persisted during the first half of 2009.

Interest rate markets, sub-prime crisis, funding constraints, pricing anomalies

Abstract:
The Hong Kong Monetary Authority has completed a research study on the setting of mortgage rate by Authorized Institutions (AIs). The purpose of the project is to consider whether in an environment of intensive competition and, until recently, abundant liquidity in the banking system, the AIs have adequately taken into account their long term cost of funds in setting their mortgage rates. The study also compares the Best Lending Rate (BLR) with other alternative mortgage reference rates to consider which one(s) would enable AIs to better track their cost of funds in determining the interest rate for residential mortgage lending. The results are presented in this paper. The use of BLR as the reference rate for setting mortgage rates has been adopted by banks for many years. However, such a practice is not necessarily conducive to banks' management of interest rate risk, as the movement of BLR may deviate significantly from banks' cost of funds. In times when Hong Kong Interbank Offered Rates (HIBORs) and time deposit rates rise faster than BLR (typically during an interest rate hike cycle or when the risk premium of the Hong Kong dollar over the US dollar widens), the interest margin of banks' existing mortgage portfolios would be squeezed. This may lead to a material decline in banks' earnings and may impact on banking and financial stability. The market conditions during late January to April 2005 demonstrate vividly such risk. Drawing on overseas experience, several local interest rates, including the 3-month HIBOR, the effective deposit rate or EDR (a weighted average rate for demand, savings and time deposits), the composite rate (a weighted average rate of 3-month HIBOR and EDR), the Base Rate of the HKMA and the yield of the 3-year Exchange Fund Note (EFN), are examined in order to assess their relevance as alternative reference rates. The assessments are made by evaluating the appropriateness of each rate based on criteria of importance to consumers and factors relevant to banks. Together with other factors, the two key criteria for the assessment are (i) the stability of mortgage rates over time which is regarded as important by both borrowers and AIs, and (ii) conduciveness to interest rate risk management which is important for banking stability. A comparative analysis suggests that the composite rate is probably the best as it reflects closely the cost of funds of most AIs and is more stable than the 3-month HIBOR and the yield of EFN. The use of some "smoothing out" arrangements could further enhance the stability of the rate.

Authorized Institutions, Best Lending Rate, Composite Interest Rate, Banking Stability

Abstract:
In this paper we have formulated a simple model for the dynamics of the target leverage ratio of a firm and performed a theoretical investigation of its time path. In our model the time-dependent target leverage ratio of a firm can be derived from the nonlinear stochastic differential equation governing the firm’s leverage ratio by means of the nonlinear Fokker-Planck equation perspective proposed by Frank [T.D. Frank, “Nonlinear Fokker-Planck Equations: Fundamentals and Applications” (Springer, New York, 2005)]. The gap between a firm’s current target leverage ratio and the long-term target ratio is found to diminish exponentially, and the decay rate is determined by the volatility of the leverage ratio and the long-term target ratio only in the long run. In finite time the pace of the adjustment of the target ratio instead of the long-term target ratio determines the time path of the target ratio. The time-varying target leverage ratios can be readily incorporated into the dynamics of the leverage ratios of individual firms, and the default probabilities of individual firms can be generated to assess the default risks of the firms.

Target leverage ratios, Default risk, Mean-reverting dynamics

Abstract:
Hong Kong's Linked Exchange Rate System (LERS) has been in operation for twenty-five years during which time many other fixed exchange rate systems have succumbed to shocks and/or speculative attacks. This fact alone suggests that the LERS is a robust system which enjoys a large measure of credibility in financial markets. This paper intends to investigate whether this is indeed the case, and whether it has been the case throughout its 25-year history. In particular we will use the tools of modern finance to extract information from financial asset prices about market expectations that are related to the credibility of the LERS. The main focus is on how market participants 'judged' the various changes made to the LERS, such as the 'seven technical measures' introduced in September 1998 and the 'three refinements' made in May 2005. These changes have been characterizes as making the system less discretionary over time, and we hypothesize that they have also made it more credible as revealed in the prices of exchange rate related asset prices. We also investigate the relationship between interest rates and exchange rates in the current system in light of modern models of target-zone exchange rate systems. We will examine whether the intra-marginal intervention in November 2007 changed the dynamic properties of the exchange rate as suggested by such models.

Hong Kong dollar, Linked Exchange Rate system, target zone

Abstract:
This paper studies the discriminatory power and calibration quality of the structural credit risk models under the 'exogenous default boundary' approach including those proposed by Longstaff and Schwartz (1995) and Collin-Dufresne and Goldstein (2001), and 'endogenous default boundary' approach in Leland and Toft (1996) based on 2,050 non-financial companies in 46 economies during the period 1998 to 2005. Their discriminatory power in terms of differentiating defaulting and non-defaulting companies is adequate and the differences among them are not material. In addition, the calibration quality of the three models is similar, although limited evidence is found that the Longstaff and Schwartz model marginally outperforms the others in some subsamples. Overall, no significant difference in the capability of measuring credit risk between the 'exogenous default boundary' and 'endogenous default boundary' approaches is found.

Default probabilities, Credit risk models