Pricing and static hedging of American-style knock-in options on defaultable stocks

This paper applies the static hedge portfolio approach (SHP) of Chung et al. (2013) in two new directions. First, the SHP approach is generalized from the constant elasticity of variance (CEV) model of Cox (1975) to the jump to default extended CEV (JDCEV) framework of Carr and Linetsky (2006). For this purpose, the recovery value of the American-style down-and-in put is hedged through the one attached to a European-style plain-vanilla contract whereas for an up-and-in put it is necessary to use the recovery component of the corresponding European-style up-and-in option. Second, the SHP methodology is adapted from single to double barrier American-style knock-in options by matching the value of the hedging portfolio along both lower and upper barriers. Finally, and to benchmark the accuracy of the novel SHP pricing solutions, the optimal stopping approach of Nunes (2009) is also extended to price American-style double knock-in options under the JDCEV framework. Such extension highlights the relevant credit derivative component embedded in American-style knock-in equity puts.     

Commodity futures hedging,risk aversion and the hedging horizon

This paper examines the impact of management preferences on optimal futures hedging strategy and associated performance. Applying an expected utility hedging objective, the optimal futures hedge ratio is determined for a range of preferences on risk aversion, hedging horizon and expected returns. Empirical results reveal substantial hedge ratio variation across distinct management preferences and are supportive of the hedging policies of real firms. Hedging performance is further shown to be strongly dependent on underlying preferences. In particular, hedgers with high risk aversion and short horizon reduce hedge portfolio risk but achieve inferior utility in comparison to those with low aversion.     

Evaluating the sovereign and household credit risk in Singapore: A contingent claims approach

This study evaluates the credit risk of the household and government (sovereign) sectors in Singapore using the contingent claims approach (CCA). The CCA model estimates the default probability of both sectors based on the market value of the assets and liabilities of the sectors. Compared to the traditional credit rating system, this model is able to provide numerical estimates of the exposures and default probabilities. We find that from the year 2000 to 2013, variations in the credit risk measures correspond to the economic growth of Singapore. In addition, we suggest that the main factor affecting the credit risks in the government and household sectors in Singapore is the volatility of the assets held by both sectors, given that the asset-to-distress barrier ratios are relatively stable over the past 14 years for both sectors.     

Dynamic, nonparametric hedging of European style contingent claims using canonical valuation

The canonical valuation, proposed by Stutzer [1996. Journal of Finance 51, 1633–1652], is a nonparametric option pricing approach for valuing European-style contingent claims. This paper derives risk-neutral dynamic hedge formulae for European call and put options under canonical valuation that obey put–call parity. Further, the paper documents the error-metrics of the canonical hedge ratio and analyzes the effectiveness of discrete dynamic hedging in a stochastic volatility environment. The results suggest that the nonparametric hedge formula generates hedges that are substantially unbiased and is capable of producing hedging outcomes that are superior to those produced by Black and Scholes [1973. Journal of Political Economy 81, 637–654] delta hedging.     

Model risk of contingent claims

Paralleling regulatory developments, we devise value-at-risk and expected shortfall type risk measures for the potential losses arising from using misspecified models when pricing and hedging contingent claims. Essentially, P&L from model risk corresponds to P&L realized on a perfectly hedged position. Model uncertainty is expressed by a set of pricing models, each of which represents alternative asset price dynamics to the model used for pricing. P&L from model risk is determined relative to each of these models. Using market data, a unified loss distribution is attained by weighing models according to a likelihood criterion involving both calibration quality and model parsimony. Examples demonstrate the magnitude of model risk and corresponding capital buffers necessary to sufficiently protect trading book positions against unexpected losses from model risk. A further application of the model risk framework demonstrates the calculation of gap risk of a barrier option when employing a semi-static hedging strategy.     

Information risk and credit contagion

This paper demonstrates a positive relationship between information risk and the credit contagion effect. We use abnormal changes in the Credit Default Swaps (CDS) spreads to measure the contagion effect, and the dispersion of analyst forecasts as a proxy for information risk. We find that firms with higher information risk suffer a greater contagion effect that occurs in advance to the credit default events. This finding is robust under controls of key firm-specific characteristics and general condition of stock and credit markets.     

两类银行组合型汇率避险产品应引起关注

随着企业对汇率风险关注度的提高,企业对汇率避险产品的需求日趋旺盛。文章以江苏省为例,重点考察了两类组合型汇率避险产品的运作模式及其对外汇管理和跨境资金流动的相关影响,并从加强对外债和银行综合头寸管理、鼓励银行合理创新产品和构建完善的汇率避险产品统计监测体系等方面,就规范汇率避险产品发展提出建议。     

A comprehensive structural model for defaultable fixed-income bonds

An exact valuation formula for defaultable corporate coupon bonds is proved. The model incorporates discrete coupons, bankruptcy costs, taxes and the market risk generated by a stochastic risk-free structure. The aim of this paper is twofold: first, we generalise previous pricing models for corporate bonds; second, we provide a comprehensive formula in order to properly disentangle the contribution of several risk factors to credit spreads.     

Optimal incentives and securitization of defaultable assets

We study optimal securitization in the presence of an initial moral hazard. A financial intermediary creates and then sells to outside investors defaultable assets, whose default risk is determined by the unobservable costly effort exerted by the intermediary. We calculate the optimal contract for any given effort level and show the natural emergence of extreme punishment for defaults, under which investors stop paying the intermediary after the first default. With securitization contracts optimally designed, we find securitization improves the intermediary's screening incentives. Furthermore, the equilibrium effort level and the surplus converge to their first best levels with sufficiently many assets.     

Corporate reputation and hedging activities

This study examines whether corporate reputation affects derivative hedging. We posit that high-reputation firms are more likely to engage in hedging due to greater reputation costs and/or their commitment to lower financial risks. We find that high-reputation firms are more likely to engage in hedging, especially when their hedging efforts or effects are more observable to stakeholders. We also find that high-reputation firms are less likely to disclose the notional values of hedging positions and that interest rate hedging by high-reputation firms is detrimental to firm value. Our results shed light on the impact of reputational concerns on corporate risk management and disclosure policies.     

Pricing and hedging contingent claims using variance and higher order moment swaps

This paper suggests perfect hedging strategies of contingent claims under stochastic volatility and random jumps of the underlying asset price. This is done by enlarging the market with appropriate swaps whose pay-offs depend on higher order sample moments of the asset price process. Using European options and variance swaps, as well as barrier options written on the S&P 500 index, the paper provides clear cut evidence that hedging strategies employing variance and higher order moment swaps considerably improves upon the performance of traditional delta hedging strategies. Inclusion of the third-order moment swap improves upon the performance of variance swap-based strategies to hedge against random jumps. This result is more profound for short-term out-of-the money put options.     

The minimum variance hedge and the bankruptcy risk of the firm

In this paper, we analyze the influence of hedging with forward contracts on the firm's probability of bankruptcy (POB). The minimization of this probability can serve as a substitute for the maximization of shareholders' wealth. It is shown that the popular minimum variance hedge is generally neither necessary nor sufficient for the minimization of the firm's POB. Moreover, our model suggests a correction of the widespread view that a reduction in the variance of the future value of the firm is inevitably accompanied by a reduction in its default risk. We derive an analytical solution for the variance-minimizing hedge ratio of a firm exposed to both input and output price uncertainty that takes into account the issue of correlation. Based on this solution, we provide a graphical analysis to prove our claim that there is a fundamental difference between hedging policies focused on bankruptcy risk and those following conventional wisdom even if positive correlation constitutes a “natural” hedge.     

Conditional extreme risk,black swan hedging,and asset prices

Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.     

Pricing electricity risk by interest rate methods

We address a method for pricing electricity contracts based on the valuation of the ability to produce power, which is considered as the true underlying factor for electricity derivatives. This approach shows that an evaluation of free production capacity provides a framework where a change-of-numeraire transformation converts the electricity forward market into the common settings for money market modelling. Using the toolkit of interest rate theory, we derive explicit option pricing formulas.     

Valuation of vulnerable American options with correlated credit risk

This article evaluates vulnerable American options based on the two-point Geske and Johnson method. In accordance with the Martingale approach, we provide analytical pricing formulas for European and multi-exercisable options under risk-neutral measures. Employing Richardson’s extrapolation gets the values of vulnerable American options. To demonstrate the accuracy of our proposed method, we use numerical examples to compare the values of vulnerable American options from our proposed method with the benchmark values from the least-square Monte Carlo simulation method. We also perform sensitivity analyses for vulnerable American options and show how the prices of vulnerable American options vary with the correlation between the underlying assets and the option writer’s assets.      

Behavioral currency hedging for international portfolios

The purpose of this paper is to incorporate behavioral issues as it relates to the active currency hedging of international portfolios in the context of traditional expected utility maximization approach. The uniqueness of the approach is that separate risk aversion parameters are introduced for asset and currency markets. The paper is similar in spirit to Black (Black, F. 1989, Universal hedging, Financial Analysts Journal (July-August), 16-22.), who argued that a portion of foreign equity investments should be permanently unhedged, which is basically postulating that one should take a buy-and-hold position in currency with a fraction of the capital. The behavioral twist included in the traditional expected utility maximization approach results in lower hedge ratios, ceteris paribus, partly due to the asymmetric nature of the compensation structure of currency managers.Since the asymmetric nature of incentive schemes of asset and currency managers dictates how one optimizes the investment portfolio of a pension or endowment fund, the unusual behavior of a given institutional fund manager should not be called “irrational,” only because the optimal currency hedging level deviates from the one derived under rational expectations. This only justifies the use of different hedging strategies by various institutional investors. We describe in detail how the level of hedging should be revised downwards because of behavioral factors. Conclusions are in the context of what people would predict to see in the market, if certain investors behave in an “irrational” way.     

A contingent claims analysis of the interest rate risk characteristics of corporate liabilities

This paper provides a contingent claims analysis of the interest rate risk characteristics of corporate liabilities by identifying Merton's (1973) option pricing model with Vasicek's (1977) mean reverting term structure model. Only a non-zero positive range of duration values for the firms' assets is shown to be consistent with the previous empirical evidence on the interest rate sensitivity of corporate stocks and bonds. Chance's (1990) duration measure is shown to be biased downward under empirically realistic conditions. Theoretical conditions are derived under which the duration of a default-prone zero coupon bond can be either higher or lower than the duration of the corresponding default-free bond. The duration of the default-prone bond of a firm with high (low) interest rate sensitive assets is shown to be an increasing (decreasing) function of the bond's default-risk.     

Understanding and managing interest rate risk at banks

Banks in many countries hold significant quantity of bonds issued by their sovereign. This nexus of bank balance sheets with the sovereign debt can amplify in a two-way loop the effect of a rise in sovereign debt yields on banks and vice-versa. The rise in sovereign debt yields tends to be episodic, exhibiting conditional volatility, and banks need to manage this risk proactively to dampen the two-way loop. Lessons are drawn from this perspective for understanding and managing of interest rate (or ‘duration’) risk at Indian banks from their holdings of government securities. Moral hazard implications of regulatory forbearance policies when the two-way loop materializes are also discussed.