Discrete-time option pricing with stochastic liquidity

Classical option pricing theories are usually built on the law of one price, neglecting the impact of market liquidity that may contribute to significant bid-ask spreads. Within the framework of conic finance, we develop a stochastic liquidity model, extending the discrete-time constant liquidity model of Madan (2010). With this extension, we can replicate the term and skew structures of bid-ask spreads typically observed in option markets. We show how to implement such a stochastic liquidity model within our framework using multidimensional binomial trees and we calibrate it to call and put options on the S&P 500.     

Stock Liquidity Risk and the Cross‐sectional Earnings‐Returns Relationship

We argue that a higher sensitivity to aggregate market‐wide liquidity shocks (i.e., a higher liquidity risk) implies a tendency for a stock's price to converge to fundamentals. We test this intuition within the framework of the earnings‐returns relationship. We find a positive liquidity risk effect on the relationship between return and expected change in earnings. This effect on the earnings‐returns relationship is distinct from the negative effect observed for stock illiquidity level. Notably, the liquidity risk effect is evident (absent) during periods of neutral/low (high) aggregate market liquidity. We also show that the liquidity risk effect is dominant in firms that: (a) are of intermediate size; (b) are of intermediate book‐to‐market; and (c) are profit making.     

Implied liquidity: Model sensitivity

The concept of implied liquidity originates from the conic finance theory and more precisely from the law of two prices where market participants buy from the market at the ask price and sell to the market at the lower bid price. The implied liquidity λ of any financial instrument is determined such that both model prices fit as well as possible the bid and ask market quotes. It reflects the liquidity of the financial instrument: the lower the λ, the higher the liquidity. The aim of this paper is to study the evolution of the implied liquidity pre- and post-crisis under a wide range of models and to study implied liquidity time series which could give an insight for future stochastic liquidity modeling. In particular, we perform a maximum likelihood estimation of the CIR, Vasicek and CEV mean-reverting processes applied to liquidity and volatility time series. The results show that implied liquidity is far less persistent than implied volatility as the liquidity process reverts much faster to its long-run mean. Moreover, a comparison of the parameter estimates between the pre- and post-credit crisis periods indicates that liquidity tends to decrease and increase for long and short term options, respectively, during troubled periods.     

融资流动性与债券资产流动性的互动特征——基于MS-VAR模型的时变分析

依据2015-2021年货币市场和债券市场的时间序列数据,运用MS-VAR探究了不同违约风险环境下融资流动性与债券资产流动性间的互动关系。研究发现：无论是利率债还是信用债,其资产流动性与货币市场的融资流动性存在互为正反馈的流动性螺旋。此外,两类流动性间的互动特征存在非对称性和异质性,在风险时期,融资流动性与利率债资产流动性互动特征比较明显,而在平稳时期,融资流动性与信用债资产流动性互动特征比较明显。     

Trading and liquidity in the catastrophe bond market

We provide first insights into secondary market trading, liquidity determinants, and the liquidity premium of catastrophe bonds. Based on transaction data from TRACE (Trade Reporting and Compliance Engine), we find that cat bonds are traded less frequently during the hurricane season and more often close to maturity. Trading activity indicates that the market is dominated by brokers without a proprietary inventory. Liquidity is high in periods of high trading activity in the overall market and for bonds with low default risk or close to maturity, which results from lower order processing costs. Finally, using realized bid–ask spreads as a liquidity measure, we find that on average, 21% of the observable yield spread on the cat bond market is attributable to the liquidity premium, with a magnitude of up to 141 bps for high-risk bonds.     

Reprint of: Market liquidity in the financial crisis: The role of liquidity commonality and flight-to-quality

We examine the dynamics and the drivers of market liquidity during the financial crisis, using a unique volume-weighted spread measure. According to the literature we find that market liquidity is impaired when stock markets decline, implying a positive relation between market and liquidity risk. Moreover, this relationship is the stronger the deeper one digs into the order book. Even more interestingly, this paper sheds further light on so far puzzling features of market liquidity: liquidity commonality and flight-to-quality. We show that liquidity commonality varies over time, increases during market downturns, peaks at major crisis events and becomes weaker the deeper we look into the limit order book. Consistent with recent theoretical models that argue for a spiral effect between the financial sector’s funding liquidity and an asset’s market liquidity, we find that funding liquidity tightness induces an increase in liquidity commonality which then leads to market-wide liquidity dry-ups. Therefore our findings corroborate the view that market liquidity can be a driving force for financial contagion. Finally, we show that there is a positive relationship between credit risk and liquidity risk, i.e., there is a spread between liquidity costs of high and low credit quality stocks, and that in times of increased market uncertainty the impact of credit risk on liquidity risk intensifies. This corroborates the existence of a flight-to-quality or flight-to-liquidity phenomenon also on the stock markets.     

Is Volatility the Best Predictor of Market Crashes?

The objective of this paper is to determine the best predictor of equity market crashes by focusing particularly on volatility and market liquidity. In finance, volatility has traditionally been regarded as the best measure of market risk. However, this paper shows that the forecast value of market liquidity, in particular our modified calculated market depth, predicts equity market crashes much more accurately than does the forecast values of EGARCH or Implied Volatility.     

Coming of age – a comparative study of emerging foreign exchange markets

We developed a market maturity index as a composite of the relative liquidity index (which was used historically to measure market maturity) and a market sophistication index, constructed by analyzing market volume and transaction data. We also constructed a risk management index using volatility and V2 (volatility of the volatility) to measure ease of risk management. Five (out of 14) emerging markets we studied – India, Brazil, Malaysia, Turkey and Poland – improved their risk management index scores from 2007 to 2009, suggesting increasing maturity. On the other hand, South Africa, Taiwan and South Korea, all markets that had seemed reasonably mature in 2007, performed extremely poorly from a risk management perspective in 2009, suggesting that their original high market maturity index scores were probably not very stable.     

货币政策冲击对股票市场流动性的影响——基于Markov区制转换VAR模型的实证研究

本文首先对货币政策影响股市流动性的机理进行分析,在此基础上,尝试构建了一个新的股票市场流动性指标,通过引入MS-VAR模型,考察了货币政策在不同区制下对股市流动性的动态影响。基于MSIH(3)-VAR(4)模型和累积脉冲响应的结果表明,货币政策扩张有助于提高市场流动性,货币政策收紧,会导致市场流动性降低。但在不同区制下,影响程度存在显著差异,当股市处于膨胀期时,货币政策冲击对市场流动性的影响比股市处于低迷期时表现得更加明显。同时,股市收益率和股市波动率对股市流动性也存在显著影响。     

Investigating risk contagion initiated by endogenous liquidity shocks: evidence from the US and eurozone interbank markets

This paper investigates liquidity spillovers between the US and European interbank markets during turbulent and tranquil periods. We show that an endogenous model with time-varying transition probabilities is effective in describing the propagation of liquidity shocks within the interbank market, while predicting liquidity crashes characterised by changed dynamics. We show that liquidity shocks, originating from movements of the spread between the Asset Backed Commercial Paper and T-bill, drive regime changes in the euro fixed-float OIS swap rate. Our results support the idea of endogenous contagion from the US money market to the eurozone money market during the global financial crisis.     

The impact of aggressive orders in an order-driven market: a simulation approach

This article investigates resiliency in an order-driven market. On basis of a vector autoregressive model capturing various dimensions of liquidity and their interactions, I simulate the effect of a large liquidity shock, measured by a very aggressive market order. I show that, despite the absence of market makers, the market is resilient. All dimensions of liquidity (spread, depth at the best prices and order book imbalances) revert to their steady-state values within 15 orders after the shock. For prices, a long run effect is found. Furthermore, different dimensions of liquidity interact. Immediately after a liquidity shock, the spread becomes wider than in the steady state, implying that one dimension of liquidity deteriorates, while at the same time, depth at the best prices increases, meaning an improvement of another liquidity dimension. In subsequent periods, the spread reverts back to the steady-state level but also depth decreases. Also, I find evidence for asymmetries in the impact of shocks on the ask and bid side. Shocks on the ask side have a stronger impact than shocks on the bid side. Finally, resiliency is higher for less-frequently traded stocks and stocks with a larger relative tick size.     

沪深300股指期货与现货市场间风险传染效应及影响因素

本文选取2005—2019年我国沪深300股指期货和沪深300股票指数日收盘价数据,结合股票推出时间、股价波动性,设置样本组、对照组,运用GARCH模型、DCC-GARCH模型、Granger因果关系检验及多元线性回归模型分析了沪深300股指期货与现货间的风险传染效应及影响因素,并结合研究结论提出对策,以期促进资本市场健康发展。结果表明:沪深300股指期货市场与现货市场间存在双向的风险传染效应,且经DCC-GARCH模型分析表明风险传染效应在动荡期尤为明显;影响这种风险传染效应的因素有很多,主要表现为微观因素中的股票市场流动性和股票市场不确定性与极端事件两个方面。     

Implied liquidity risk premium in the term structure of sovereign credit default swap and bond spreads

In this study, we focus on the dynamic properties of the risk-neutral liquidity risk premium specific to the sovereign credit default swap (CDS) and bond markets. We show that liquidity risk has a non-trivial role and participates directly to the variation over time of the term structure of sovereign CDS and bond spreads for both the pre- and crisis periods. Secondly, our results indicate that the time-varying bond and CDS liquidity risk premium move in opposite directions which imply that when bond liquidity risk is high, CDS liquidity risk is low (and vice versa), which may in turn be consistent with the substitution effect between CDS and bond markets. Finally, our Granger causality analysis reveals that, although the magnitude of bond and CDS liquidity risk is substantially different, there is a strong liquidity flow between the CDS and the bond markets, however, no market seems to consistently lead the other.     

Performance of Thinly Traded Assets: A Case in Real Estate

Thinly traded private assets do not fit into the traditional finance paradigm of a liquid and well‐functioning market where trading is continuous and instantaneous. Since private assets cannot be bought and sold easily, they bear liquidity risk. Classical finance theories cannot properly gauge the performance of illiquid private assets because they implicitly assume such illiquidity is trivial. This paper proposes an alternative performance metric for the illiquid private asset, which explicitly captures liquidity risk in a formal analysis. Applying the new performance metric, we are able to explain the decades‐old “real estate risk premium puzzle.”     

Internalisation by electronic FX spot dealers

Dealers in over-the-counter financial markets provide liquidity to customers on a principal basis and manage the risk position that arises out of this activity in one of two ways. They may internalise a customer's trade by warehousing the risk in anticipation of future offsetting flow, or they can externalise the trade by hedging it out in the open market. It is often argued that internalisation underlies much of the liquidity provision in the currency markets, particularly in the electronic spot segment, and that it can deliver significant benefits in terms of depth and consistency of liquidity, reduced spreads, and a diminished market footprint. However, for many market participants, the internalisation process can be somewhat opaque, data on it are scarcely available, and even the largest and most sophisticated customers in the market often do not appreciate or measure the impact that internalisation has on their execution costs and liquidity access. This paper formulates a simple model of internalisation and uses queuing theory to provide important insights into its mechanics and properties. We derive closed form expressions for the internalisation horizon and demonstrate—using data from the Bank of International Settlement's triennial FX survey—that a representative tier 1 dealer takes on average several minutes to complete the internalisation of a customer's trade in the most liquid currencies, increasing to tens of minutes for emerging markets. Next, we analyse the costs of internalisation and show that they are lower for dealers that are willing to hold more risk and for those that face more price-sensitive traders. The key message of the paper is that a customer's transaction costs and liquidity access are determined both by their own trading decisions as well as the dealer's risk management approach. A customer should not only identify the externalisers but also distinguish between passive and aggressive internalisers, and select those that provide liquidity compatible with their execution objectives.     

Commonality in equity options liquidity: evidence from European Markets

This paper examines commonality in liquidity for individual equity options trading in European markets. We use high-frequency data to construct a novel index of liquidity commonality. The approach is able to explain a substantial proportion of the liquidity variation across individual options. The explanatory power of the common liquidity factor is more pronounced during periods of higher market-wide implied volatility. The common factor's impact on individual options' liquidity depends on options' idiosyncratic characteristics. There is some evidence of systematic liquidity spillover effects across these European exchanges.     

Firm size,ownership structure,and systematic liquidity risk: The case of an emerging market

Previous studies support the hypothesis that institutional ownership leads to an enhanced systematic liquidity risk by increasing the commonality in liquidity. By using a proprietary database of all incoming orders and ownership structure in an emerging stock market, we show that institutional ownership leads to an increase in commonality in liquidity for mid- to-large cap firms; however, only individual ownership can lead to such an increase for small cap firms, revealing a new source of systematic liquidity risk for a specific group of firms. We also reveal that commonality decreases with the increasing number of investors (for both individual and institutional) at any firm size level; suggesting that as the investor base gets larger, views of market participants become more heterogeneous, which provides an alternative way to decrease the systematic liquidity risk.     

巴塞尔协议Ⅲ下我国商业银行流动性风险监管研究

近年来,遵照巴塞尔协议Ⅲ,我国的流动性风险监管新规促使我国商业银行优化了优质流动性资产的配置,提高了商业银行抵御金融风险的能力。但是目前我国商业银行的流动性风险监管仍然存在着流动性监管指标因存款增长不足而导致的优化困难、中小型银行流动性风险监管压力持续增加、监管难度因商业银行同方向调整资产负债结构而增加、金融市场存在一定程度的扭曲、流动性监管指标监管效果尚需评估等诸多问题。为进一步完善商业银行流动性风险的监管体系,我国亟需有效引导商业银行完善资产负债配置、引导中小型商业银行实施差异化发展策略、建立差异化的流动性监管指标、建立业务数据动态报备制度、及时更新与修正流动性风险的监管政策等。     

宏观流动性过剩与商业银行流动性风险管理

流动性过剩是近年来全球宏观经济领域的一个显著特征。在此背景下,商业银行流动性管理遇到了新的挑战。商业银行资金来源更加依赖金融市场,市场上的任何风吹草动都会影响到商业银行的流动性,甚至出现从流动性过剩到流动性不足的突然转化。有效管理商业银行流动性需要各国中央银行、金融监管者以及商业银行经营者的共同努力。     

The intraday determination of liquidity in the NYSE LIFFE equity option markets

We exploit an extensive high-frequency data set of all individual equity options trading at New York Stock Exchange London International Financial Futures and Options Exchange (Amsterdam, London and Paris) in order to study the determination of liquidity during the trading day. In particular, we focus on two main aspects of option liquidity: (i) the intraday behaviour of equity option liquidity and its determinants and (ii) the influence of macroeconomic events and commonality on intraday equity option liquidity. Inventory management models cannot explain the intraday variation in option spreads and depths. Instead, we show that the option liquidity measures are strongly correlated with option volatility. Increases in volatility are associated with decreases in liquidity, a finding that is in line with information asymmetry models and the derivatives hedging theory. However, the relationship between spreads and volume varies across the three markets. Option liquidity reacts strongly to macroeconomic news announcements, especially US events. The average systematic liquidity component is 12% for Amsterdam, 14% for London and 16% for Paris.