Szu-Lang Liao

Pricing Black-Scholes Options with Correlated Interest Rate Risk and Credit Risk: An Extension

This article provides a closed-form valuation formula for the Black–Scholes options subject to interest rate risk and credit risk. Not only does our model allow for the possible default of the option issuer prior to the options maturity, but also considers the correlations among the option issuers total assets, the underlying stock, and the default-free zero coupon bond. We further tailor-make a specific credit-linked option for hedging the default risk of the option issuer. The numerical results show that the default risk of the option issuer significantly reduces the option values, and the vulnerable option values may be remarkably overestimated in the case where the default can occur only at the maturity of the option.

Closed-Form Mortgage Valuation Using Reduced-Form Model

Valuing mortgage-related securities is more complicated than valuing regular defaultable claims due to the borrowers prepayment behavior as well as the possibility of default. Some researchers use a structural-form model to obtain the closed-form formulas for the mortgage value. With this method, however, it is difficult to identify the critical region of early exercise. As an alternative, the reduced-form model developed in this article is able to value the mortgage without setting boundary conditions, and it can thereby accurately handle the multidimensional space of correlated state variables. The purpose of this article is to derive a closed-form solution of the mortgage valuation equation under a general reduced-form model that embeds relevant economic variables. This new approach enables portfolio managers to undertake sophisticated portfolio optimization and hedging analyses. An implementation procedure for the model is also provided to demonstrate how the valuation framework can be utilized in practical applications.

Warrant introduction effects on stock return processes

As the underpricing of warrants remains unsolved after many adjustments presented by previous researchers, we further investigate the impact of the warrant introduction on the underlying stock return processes. This research attempts to determine whether the introduction of warrants influences the return processes of underlying stocks. If the introduction creates a potential dilution effect on stock return process, full dilution adjustment pricing models would lead to underpricing. To examine whether full dilution adjustment is required for warrant pricing, the Generalized Autoregressive Conditional Heteroscedasticity in Mean (GARCH-M) model has been extended to derive four models for testing the dilution effect on stock return processes. Empirical results show that the volatilities of underlying stock return processes are significantly reduced following warrant introduction even after distinguishing dilution from asymmetric effect.

An Analysis of Strategic Equity Stakes Acquisition of Chinese Banks by Foreign Financial Institutions

This paper applies a contingent claim model to examine the risk of and returns to foreign financial institutions after they acquire equity stakes in a Chinese bank. The model considers dynamic factors such as individual asset value and exchange rates in maximizing shareholder value. In addition to analyzing the asset value and factors associated with risk after participation, this paper evaluates the optimal acquisition equity stake ratio using numerical analyses under regulatory capital control. For the Chinese banking sector, we discover that the portfolio risk of foreign financial institution will decrease after acquiring equity stakes when its asset increases, the debt ratio decreases, and the required risk-weighted asset increases. Overall, these foreign financial institutions have well-diversified currency portfolios and enjoy better asset quality and surplus earnings; therefore, they will likely increase their optimal acquisition equity stake ratio if the Chinese banks in which they invest have with good quality assets and are focused on local business.

Pricing gold options under Markov-modulated jump-diffusion processes

In this study, we empirically investigate the properties of gold returns, and the European gold options are priced when the underlying gold price dynamics are driven by Markov-modulated jump-diffusion processes. Specifically, the jump events are captured by a compound Poisson process with a log-normal jump size, and the regime-switching intensity rate is governed by a continuous-time finite-state Markov chain. Under an incomplete market setting, we study the valuation of European gold options using the method of Esscher transform. The estimated results and numerical examples are provided.

The valuation of special purpose vehicles by issuing structured credit-linked notes

With the intersection of market and credit risk, the first contribution is to derive the analytic formulas of the Credit Linked Notes (CLNs) and the leveraged total return CLNs issued by an Special Purpose Vehicle (SPV) or the protection buyer. The second contribution is to prove that the values of structured CLNs issued by an SPV are higher than the ones issued by the protection buyer. When the credit quality of the reference obligation and protection buyer becomes worse or the leverage effect is higher, it is a superior solution for the structured CLNs issued through an SPV. Third, the empirical results of credit spreads do not incorporate the correlation coefficient of spot rate and market index into their regression models and show that they are positively correlated with the volatilities of spot rate and return on market index; however, we find that the relationship among them depends on the sign of correlation coefficient of spot rate and equity index market. Finally, using the differences in the maturities of the note and the reference obligation as the proxy for basis risk measure, we demonstrate that the purpose of the SPV is not used to eliminate the basis risk but the credit risk of protection buyer.

The Information Transmission Effect and Asset Prices: Evidence from the China B-Share Discount

ABSTRACT We construct a model based on market microstructure and examine the information transmission effect of equity prices in A-share and B-share markets in China. The data on foreign share discounts raise a question: How are asset prices determined if uninformed foreign traders obtain signals by observing public information? Our investigation on the measure of the information transmission effect presents a substantial segment of the cross-sectional variation in B-share discounts and finds that the information transmission effect plays a critical role in explaining how foreign share discounts become more contractive.

Valuation of Convertible Bond Under Levy Process with Default Risk

Due to the reason that the default events occurred constantly and still continue taking place, empirical log returns exhibit fat tail and excess kurtosis, this paper evaluates convertible bonds under Levy process with default risk using the reduced-form approach. Under the Levy process, the underlying stock prices are set to be normal inverse Gaussian (NIG) and variance Gamma (VG) model to capture the jump components. In the empirical analysis, we use the maximum likelihood method to estimate the parameters of Levy distributions, and apply the least squares Monte Carlo Simulation to price convertible bonds. Five examples are shown in pricing convertible bonds using the traditional model and Levy model. The empirical results show that the performance of Levy model is better than the traditional one.

Dynamic Conditional Correlation Analysis in International Real Estate Security Markets

In this paper, we examine international correlation and volatility of publicly traded real estate investment trusts (REITs) using daily returns from 2005/12/1 to 2010/5/31. We also study, in comparison, the correlations among equivalent stock markets. Based on a multivariate dynamic conditional correlation (DCC) model which captures the time-varying correlations within the full period, this paper empirically shows that there are lower correlations among the real estate security markets returns than among the stock markets returns. We forecast that variations and structural changes in the correlation structure happened within the sample period of subprime mortgage crises. Applying DCC methodology, our results have motivations concerning the potential integration of international real estate security markets and the possibility of including information on changing correlations and volatilities to set up more optimal portfolios of international real estate securities.

An Efficient Valuation and Hedging of Constant Maturity Swap Products under BGM Model

The derivatives of the constant maturity swap (CMS) are evaluated by the LIBOR market model (LMM) implemented by Monte Carlo methods in the previous researches. 1n this paper, we derive an approximated dynamic process of the forward-swap rate (FSR) under LMM. Based on the approximated dynamics for the FSR under one factor model, CMS spread options and CMS ratchet options are valued by the no-arbitrage method in approximated analytic formulas. In the numerical analysis, the relative errors between the Monte Carlo simulations and the approximated closed form formulas are very small for CMS spread options and CMS ratchet options and we also provide an efficient hedging method for these products under one factor LMM.