PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCY

We solve in closed form a parsimonious extension of the Black–Scholes–Merton model with bankruptcy where the hazard rate of bankruptcy is a negative power of the stock price. Combining a scale change and a measure change, the model dynamics is reduced to a linear stochastic differential equation whose solution is a diffusion process that plays a central role in the pricing of Asian options. The solution is in the form of a spectral expansion associated with the diffusion infinitesimal generator. The latter is closely related to the Schrödinger operator with Morse potential. Pricing formulas for both corporate bonds and stock options are obtained in closed form. Term credit spreads on corporate bonds and implied volatility skews of stock options are closely linked in this model, with parameters of the hazard rate specification controlling both the shape of the term structure of credit spreads and the slope of the implied volatility skew. Our analytical formulas are easy to implement and should prove useful to researchers and practitioners in corporate debt and equity derivatives markets.     

卖空交易与市场波动性、流动性研究——基于中国香港证券市场的实证分析

本文利用中国香港证券市场数据实证研究了卖空交易机制与市场流动性和波动性的关系。研究结果表明:卖空交易额变动与市场流动性变动之间并没有长期协整关系,但在短期内卖空交易机制会在一定程度上为市场提供流动性;从长期来看市场流动性变化是卖空交易额变化的原因。卖空交易额变化可以解释市场波动性的变化,卖空交易额增加,则市场波动性也将放大,即在一定程度上卖空交易机制会增加市场的波动性。秩和检验显示:推出卖空机制后会显著提升市场流动性和波动性;启用Up-Tick会显著降低市场流动性和波动性,反之反是;暂停"卖空价规则"对卖空交易额没有显著影响,但可显著提升市场波动性和流动性。     

Do Inflation‐Linked Bonds Still Diversify?

The diversifying power of inflation-linked (IL) bonds relative to traditional asset classes has changed significantly. In this paper, we study the dynamics of conditional volatilities and correlations for three asset classes, IL bonds, nominal bonds and equities, in the USA and Europe. Using a DCC-MVGARCH for the period 1997–2007, we highlight the change that took place in 2003. Although IL bonds once had definite diversification power, they are now highly correlated with nominal bonds and have reached similar volatility levels. As a result, the two asset classes are practically substitutable. This seems to be due to more stable inflation expectations and to a more liquid IL bond market. Although diversification was a valuable reason for introducing IL bonds in a global portfolio before 2003, this is no longer the case. Dynamic portfolio optimisation using our estimates of conditional correlations and volatilities clearly demonstrates that the optimal weight of IL bonds in a portfolio decreased sharply in 2003 in favour of nominal bonds and equities.     

Globalization, Financial Volatility and Monetary Policy

Recently it has often been claimed that globalization eases the job of central banks as it helps to tame inflation. This is used to argue that central banks (particularly the ECB, referring to the objectives as laid down in the EU Treaty) could or should reduce their efforts in the fight against inflation in favor of supporting the general economic policies of the governments. This paper takes a critical look at this argument, pointing to the structural changes associated with globalization and to the corresponding increase in uncertainty by which the central banks are affected. As an example of this, the increase in financial volatility is analyzed and explained as the result of optimal portfolio allocation, and its implications for monetary policy are discussed.     

Calibration of implied volatility for the exchange rate for the Chinese Yuan from its derivatives

Revised implied volatility curves and surfaces for the Chinese Yuan (CNY) exchange rate are obtained from market quotations for CNY non-deliverable options by solving an inverse problem of foreign exchange option pricing, which is calculated using a regularization approach in an optimal control framework. To take account of the market expectation for the CNY exchange rate, a stochastic adjusted factor is applied that follows a Vasicek model with parameters fitted from market quotations for CNY non-deliverable forwards. A well-posed numerical scheme is implemented.