Optimal design of derivatives in illiquid markets*

Abstract

The aim of this paper is to determine the optimal structure of derivatives written on an illiquid asset, such as a catastrophic or a weather event. This transaction involves two agents: a bank which wants to hedge its initial exposure towards this illiquid asset and an investor which may buy the contract. Both agents also have the opportunity to invest their residual wealth on a financial market.

Based on a utility maximization point of view, we determine an optimal profile (and its value) such that it maximizes the bank's utility given that the investor decides to make the deal only if it increases its utility. In the case of exponential utility, we show that the pricing rule is a non-linear function of the structure and that the bank always transfers the same proportion of its initial exposure. In the general case, an additional term appears, depending only on the relative log-likelihood of the two agents' views of the distribution of the illiquid asset.     

Optimal Refunding Strategies, Transaction Costs, and the Market Value of Corporate Debt

The primary purpose of this paper is to consider both qualitatively and quantitatively the effects of refunding transaction costs and interest rate uncertainty on optimal refunding strategies and the market value of corporate debt. A dynamic model of corporate bond refunding with transaction costs is developed that simultaneously solves for the optimal refunding strategy, the value of the refunding call option, the value of the bond liability to the firm, and the market (investor) value of the fixed-rate contract. We provide examples in which the price of the callable bond does exceed the call price, and we examine whether or not typical levels of refunding costs are sufficient to explain the magnitude and duration of frequently observed premiums on callable corporate bonds.     

Transaction costs and asset prices: a dynamic equilibrium model

In this article we study the effects of transaction costs onasset prices. We assume an overlapping generations economy witha riskless, liquid bond, and many risky stocks carrying proportionaltransaction costs. We obtain stock prices and turnover in closedform. Surprisingly, a stock's price may increase in transactioncosts, and a more frequently traded stock may be less adverselyaffected by an increase in transaction costs. Calculations basedon the 'marginal' investor overestimate the effects of transactioncosts. For realistic parameter values, transaction costs havevery small effects on stock prices but large effects on turnover.     

Do Convertible Bond Issuers Cater to Investor Demand?

We examine the impact of fluctuations in investor demand for convertible securities on convertible bond issue volumes, pricing, and design. We find evidence of a positive impact of investor demand proxies on convertible bond issue volumes. We also document significantly lower convertible bond underpricing in periods with higher investor demand. The results hold in a variety of specifications, and are robust to controlling for firm‐specific and macroeconomic financing cost proxies. However, we obtain only limited evidence that issuers adjust the design of their convertible bond offerings in response to investor demand.     

Optimal Portfolios with Credit Default Swaps

Using a continuous-time, stochastic, and dynamic framework, this study derives a closed-form solution for the optimal investment problem for an agent with hyperbolic absolute risk aversion preferences for maximising the expected utility of his or her final wealth. The agent invests in a frictionless, complete market in which a riskless asset, a (defaultable) bond, and a credit default swap written on the bond are listed. The model is calibrated to market data of six European countries and assesses the behaviour of an investor exposed to different levels of sovereign risk. A numerical analysis shows that it is optimal to issue credit default swaps in a larger quantity than that of bonds, which are optimally purchased. This speculative strategy is more aggressive in countries characterised by higher sovereign risk. This result is confirmed when the investor is endowed with a different level of risk aversion. Finally, we solve a static version of the optimisation problem and show that the speculative/hedging strategy is definitely different with respect to the dynamic one.     

Optimal Bond Portfolio for Investors with Long Time Horizons

We study the optimal bond portfolio for an investor with long time horizonusing Japanese interest rate data. A simple one-factor term structure modelis used for our numerical example. The optimal portfolio is computed using thetechnique of stochastic flows and Monte Carlo simulation. The hedgingportfolio is not negligible and the mean variance portfolio is very sensitiveto parameter values. The optimal portfolio is highly leveraged for a typicalparameter value. The investor holds a zero-coupon bond because of the lowerbound restriction on investor's wealth. The lower bound constraint may makethe optimal portfolio more realistic.     

Portfolio optimisation with strictly positive transaction costs and impulse control

One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a nontrivial asymptotically optimal solution for the problem of exponential utility maximisation.     

Optimal hedging in an extended binomial market under transaction costs

We develop an approach to optimal hedging of a contingent claim under proportional transaction costs in a discrete time financial market model which extends the binomial market model with transaction costs. Our model relaxes the binomial assumption on the stock price ratios to the case where the stock price ratio distribution has bounded support. Non-self-financing hedging strategies are studied to construct an optimal hedge for an investor who takes a short position in a European contingent claim settled by delivery. We develop the theoretical basis for our optimal hedging approach, extending results obtained in our previous work. Specifically, we derive a no-arbitrage option price interval and establish properties of the non-self-financing strategies and their residuals. Based on the theoretical foundation, we develop a computational algorithm for optimizing an investor relevant criterion over the set of admissible non-self-financing hedging strategies. We demonstrate the applicability of our approach using both simulated data and real market data.     

Decomposing the Bid-Ask Spread in a Segmented Equity Market: Analyzing Chinese A Shares Versus B Shares

Because of a regulatory policy change in February 2001, the segmentation of the Chinese stock market significantly decreased. Using this event, we show that the Chinese A-share market is more informationally efficient than the B-share market, both before and after the opening of the B-share market. Furthermore, after the event, both the adverse selection and the order-processing component of B shares decreased, as a result of a larger investor base and possibly a lower proportion of informed investors. This study thus sheds new light on the market segmentation and its effect on transaction costs.     

Optimal mean-reversion strategy in the presence of bid-ask spread and delays in capital allocations

A portfolio optimization problem for an investor who trades T-bills and a mean-reverting stock in the presence of proportional and convex transaction costs is considered. The proportional transaction cost represents a bid-ask spread, while the convex transaction cost is used to model delays in capital allocations. I utilize the historical bid-ask spread in US stock market and assume that the stock reverts on yearly basis, while an investor follows monthly changes in the stock price. It is found that proportional transaction cost has a relatively weak effect on the expected return and the Sharpe ratio of the investor's portfolio. Meantime, the presence of delays in capital allocations has a dramatic impact on the expected return and the Sharpe ratio of the investor's portfolio. I also find the robust optimal strategy in the presence of model uncertainty and show that the latter increases the effective risk aversion of the investor and makes her view the stock as more risky.     

Speculative Futures Trading under Mean Reversion

This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein–Uhlenbeck, Cox–Ingersoll–Ross, or exponential Ornstein–Uhlenbeck model. The futures term structure is derived and its connection to futures price dynamics is examined. For each futures contract, we describe the evolution of the roll yield, and compute explicitly the expected roll yield. For the futures trading problem, we incorporate the investor’s timing option to enter or exit the market, as well as a chooser option to long or short a futures upon entry. This leads us to formulate and solve the corresponding optimal double stopping problems to determine the optimal trading strategies. Numerical results are presented to illustrate the optimal entry and exit boundaries under different models. We find that the option to choose between a long or short position induces the investor to delay market entry, as compared to the case where the investor pre-commits to go either long or short.     

Robust portfolio choice with stochastic interest rates

We determine the optimal investment strategy for an ambiguity-averse investor in a setting with stochastic interest rates. The investor has access to stocks, bonds, and a bank account and he is ambiguous about the expected rate of return of both bonds and stocks. The investor can have different levels of ambiguity aversion about the two types of risky assets. We find that it is more important to take model uncertainty about the stock dynamics than model uncertainty about the bond dynamics into account. Furthermore, the investor’s ambiguity increases his hedging demand. Consequently, the bond/stock ratio increases with his ambiguity and implies less extreme positions in the bank account. Altogether, our model yields portfolio allocations which are more in line with what is implementable in practice. Finally, we demonstrate that neglecting model uncertainty implies significant losses for the investor.     

Earning the right premium on the right factor in portfolio planning

The optimal portfolio as well as the utility from trading stocks and derivatives depends on the risk factors and on their market prices of risk. We analyze this dependence for a CRRA investor in models with stochastic volatility, jumps in the stock price, and jumps in volatility. We find that the compartment of the total variance into diffusion risk and jump risk has a small impact on the utility in an incomplete market only. In contrast, the decomposition of the equity risk premium into a diffusion component and a jump risk component and the compartment of the latter into its various elements has a huge impact on the utility in a complete market. The more extreme the market prices of risk, i.e. the more they deviate from their equilibrium values, the larger the utility of the investor. Additionally, we show that the structure of the optimal exposures to jump risk crucially depends on which elements of jump risk are priced.     

Creditor rights and the corporate bond market

This study examines whether investor protection affects capital markets, specifically the development of corporate bond markets versus equity markets. Using a dataset of 42 countries, we show that countries with strong creditor rights have more developed corporate bond markets than equity markets. However, we find only weak evidence that countries with stronger shareholder protection have more developed equity markets than corporate bond markets. Additionally, we find that the effect of financial reforms on capital markets is strongly dependent on the strength of investor protection and on the associated information disclosure in a given country.     

Is the disposition effect in bonds as strong as in stocks? Evidence from an emerging market

Does the disposition effect appear in bond trades as in stocks? We apply Odean's measurement (1998) to a proprietary transaction database with unique investor IDs from an emerging market exchange that holds both stock and bond trading. We find some disposition effect in treasury bonds, but much lower than in stocks, and a positive relation between the two measures by investor. In addition, we find a significant disposition effect for local individuals and family offices, in both markets. In contrast, long-term institutions, brokerage firms, and foreign investors do not exhibit this bias. This is the first study to report evidence of the disposition effect in a fixed-income market.     

Bond market event study methods

The procedures used in corporate bond event studies to date fail to control for heteroskedasticity due to differences in return volatility by term-to-maturity, rating, and other factors resulting in low test power. Bond return standardization yields considerably more powerful tests. Also, due to infrequent trading, use of bond transaction price observations over several days before and after an event, while giving more weight to returns calculated from transactions closer to the event, yields considerably more powerful tests than returns based solely on transactions the day before and the day after the event. Exploring the test bias caused by overlapping event dates, we find that, adjusted for rating and maturity, the correlation among standardized abnormal bond returns is small but that even fairly small correlations can result in biased test statistics. A bond market modification of the Kolari and Pynnönen (2010) procedure corrects this bias.     

In search of a theory of debt management

The complete market approach to government debt management argues that a portfolio of non-contingent bonds at different maturities should be chosen so that fluctuations in market value offset changes in expected future deficits. However, this approach recommends huge fluctuations in positions, enormous changes in portfolios for minor changes in maturities and no presumption it is always optimal to issue long and invest short term in a wide array of model specifications. These extreme, volatile and unstable features are undesirable for two reasons. Firstly fragility of portfolios to small changes in assumptions means that it is often better to follow a balanced budget rather than issue the optimal debt portfolio under some possibly misspecified model. Secondly for even miniscule transaction costs, governments prefer a balanced budget rather than the large positions complete markets recommends. The complete market recommendations conflict with a number of features we believe are integral to bond market incompleteness, e.g. transaction costs, liquidity effects, robustness, etc. and which need to be explicitly incorporated into the portfolio problem.     

An economic evaluation of stock–bond return comovements with copula-based GARCH models

Owing to their importance in asset allocation strategies, the comovements between the stock and bond markets have become an increasingly popular issue in financial economics. Moreover, the copula theory can be utilized to construct a flexible joint distribution that allows for skewness in the distribution of asset returns as well as asymmetry in the dependence structure between asset returns. Therefore, this paper proposes three classes of copula-based GARCH models to describe the time-varying dependence structure of stock–bond returns, and then examines the economic value of copula-based GARCH models in the asset allocation strategy. We compare their out-of-sample performance with other models, including the passive, the constant conditional correlation (CCC) GARCH and the dynamic conditional correlation (DCC) GARCH models. From the empirical results, we find that a dynamic strategy based on the GJR-GARCH model with Student-t copula yields larger economic gains than passive and other dynamic strategies. Moreover, a less risk-averse investor will pay higher performance fees to switch from a passive strategy to a dynamic strategy based on copula-based GARCH models.     

The Impact of Information Diffusion on Comparisons among Various Trading Mechanisms

The information environment and investor order strategy are both important determinants when comparing the market performance of trading mechanisms. However, less is known about what happens when trading mechanisms are compared. In this paper, we link the information environment, trading mechanisms, investor order strategy and market performance to form a model of the securities market. The primary goal of this study is to examine the impact of various call markets in an agency market on liquidity, price volatility and market efficiency under various information regimes. The results indicate that an optimal transaction frequency appears at the trade-off of liquidity, volatility and market efficiency.     

Investor behaviour and reaching for yield: Evidence from the sterling corporate bond market

We provide evidence on how corporate bond investors react to a change in yields, and how this behaviour differs in times of market‐wide stress. We also investigate ‘reaching for yield’ across investor types, as well as providing insights into the structure of the corporate bond market. Using proprietary sterling corporate bond transaction data, we show that insurance companies, hedge funds and asset managers are typically net buyers when corporate bond yields rise. Dealer banks clear the market by being net sellers. However, we find evidence for this behaviour reversing in times of stress for some investors. During the 2013 ‘taper tantrum’, asset managers were net sellers of corporate bonds in response to a sharp rise in yields, potentially amplifying price changes. At the same time, dealer banks were net buyers. Finally, we provide evidence that insurers, hedge funds and asset managers tilt their portfolios towards higher risk bonds, consistent with ‘reaching for yield’ behaviour.