Discrete hedging of American-type options using local risk minimization

Local risk minimization and total risk minimization discrete hedging have been extensively studied for European options [e.g., Schweizer, M., 1995. Variance-optimal hedging in discrete time. Mathematics of Operation Research 20, 1–32; Schweizer, M., 2001. A guided tour through quadratic hedging approaches. In: Jouini, E., Cvitanic, J., Musiela, M., Option pricing, interest rates and risk management, Cambridge University Press, pp. 538–574]. In practice, hedging of options with American features is more relevant. For example, equity linked variable annuities provide surrender benefits which are essentially embedded American options. In this paper we generalize both quadratic and piecewise linear local risk minimization hedging frameworks to American options. We illustrate that local risk minimization methods outperform delta hedging when the market is highly incomplete. In addition, compared to European options, distributions of the hedging costs are typically more skewed and heavy-tailed. Moreover, in contrast to quadratic local risk minimization, piecewise linear risk minimization hedging strategies can be significantly different, resulting in larger probabilities of small costs but also larger extreme cost.     

A comparative study of the probability of default for global financial firms

This article presents a modification of Merton’s (1976) ruin option pricing model to estimate the implied probability of default from stock and option market prices. To test the model, we analyze all global financial firms with traded options in the US and focus on the subprime mortgage crisis period. We compare the performance of the implied probability of default from our model to the expected default frequencies based on the Moody’s KMV model and agency credit ratings by constructing cumulative accuracy profiles (CAP) and the receiver operating characteristic (ROC). We find that the probability of default estimates from our model are equal or superior to other credit risk measures studied based on CAP and ROC. In particular, during the subprime crisis our model surpassed credit ratings and matched or exceeded KMV in anticipating the magnitude of the crisis. We have also found some initial evidence that adding off-balance-sheet derivatives exposure improves the performance of the KMV model.     

Model risk and capital reserves

We propose a procedure to take model risk into account in the computation of capital reserves. This addresses the need to make the allocation of capital reserves to positions in given markets dependent on the extent to which reliable models are available. The proposed procedure can be used in combination with any of the standard risk measures, such as Value-at-Risk and expected shortfall.     

Modelling the implied volatility surface: Does market efficiency matter?: An application to MIB30 index options

We analyze the volatility surface vs. moneyness and time-to-expiration implied by MIBO options written on the MIB30, the most important Italian stock index. We specify and fit a number of models of the implied volatility surface and find that it has a rich and interesting structure that strongly departs from a constant volatility, Black-Scholes benchmark. This result is robust to alternative econometric approaches, including generalized least squares approaches that take into account both the panel structure of the data and the likely presence of heteroskedasticity and serial correlation in the random disturbances. Finally we show that the degree of pricing efficiency of this options market can strongly condition the results of the econometric analysis and therefore our understanding of the pricing mechanism underlying observed MIBO option prices. Applications to value-at-risk and portfolio choice calculations illustrate the importance of using arbitrage-free data only.     

Unbiased estimation of expected return using CAPM

Estimation of expected return is required for many financial decisions. For example, an estimate for cost of capital is required for capital budgeting and cost of equity estimates are needed for performance evaluation based on measures such as EVA. Estimates for expected return are often based on the Capital Asset Pricing Model (CAPM), which states that expected excess return (expected return minus the risk-free rate) is equal to the asset's sensitivity to the world market portfolio (β) times the risk premium on the “world market portfolio” (the market risk premium). Since the world market portfolio, by definition, contains all assets in the world, it is not observable. As a result, an estimate for expected return is commonly obtained by taking an estimate for β based on some index (as a proxy for the world market portfolio) and an estimate for the market risk premium based on a potentially different index and multiplying them together. In this paper, it is shown that this results in a biased estimate for expected return. This is undesirable since biased estimates lead to misallocation of funds and biased performance measures. It is also shown in this paper that the straightforward procedure suggested by Fama and MacBeth [J. Financ. Econ. 1 (1974) 43] results in an unbiased estimate for expected return. Further from the analysis done, it follows that, for an unbiased estimate, it does not matter what proxy is used, as long as it is used correctly an unbiased estimate for expected return results.     

Do executive stock options induce excessive risk taking?

We examine whether executive stock options can induce excessive risk taking by managers in firms’ security issue decisions. We find that CEOs whose wealth is more sensitive to stock return volatility due to their option holdings are more likely to choose debt over equity as a capital-raising vehicle. More importantly, the pattern holds not only in firms that are underlevered relative to their optimal capital structure but also in overlevered firms. This evidence is inconsistent with executive stock options aligning the interests of managers and shareholders; rather, it supports the hypothesis that stock options sometimes make managers take on too much risk and in the process pursue suboptimal capital structure policies.     

World market risk,country-specific risk and expected returns in international stock markets

This paper determines whether the world market risk, country-specific total risk, and country-specific idiosyncratic risk are priced in an international capital asset pricing model (ICAPM). Portfolio-level analyses, country-level cross-sectional regressions, stacked time-series, and pooled panel regressions indicate that the world market risk is not, but country-specific total and idiosyncratic risks are significantly priced in an ICAPM framework with partial integration. This result is robust to different methods for estimating risk measures, different investment horizons, and after controlling for the countries’ aggregate dividend yield, earnings-to-price ratios, inflation risk, exchange rate uncertainties, aggregate volatility risk, and past return characteristics. The main findings turn out to be insensitive to the choice of one-factor vs. multifactor models used to estimate systematic and idiosyncratic risk measures.     

EXPONENTIAL DURATION: A MORE ACCURATE ESTIMATION OF INTEREST RATE RISK

We develop a new method to estimate the interest rate risk of an asset. This method is based on modified duration and is always more accurate than traditional estimation with modified duration. The estimates by this method are close to estimates using traditional duration plus convexity when interest rates decrease. If interest rates rise, investors will suffer larger value declines than predicted by traditional duration plus convexity estimate. The new method avoids this undesirable value overestimation and provides an estimate slightly below the true value. For risk‐averse investors, overestimation of value declines is more desirable and conservative.     

On the equivalence of the static and dynamic asset allocation problems

A classic dynamic asset allocation problem optimizes the expected final-time utility of wealth, for an individual who can invest in a risky stock and a risk-free bond, trading continuously in time. Recently, several authors considered the corresponding static asset allocation problem in which the individual cannot trade but can invest in options as well as the underlying. The optimal static strategy can never do better than the optimal dynamic one. Surprisingly, however, for some market models the two approaches are equivalent. When this happens the static strategy is clearly preferable, since it avoids any impact of market frictions. This paper examines the question: when, exactly, are the static and dynamic approaches equivalent? We give an easily tested necessary and sufficient condition, and many non-trivial examples. Our analysis assumes that the stock follows a scalar diffusion process, and uses the completeness of the resulting market model. A simple special case is when the drift and volatility depend only on time; then the two approaches are equivalent precisely if (μ (t)? r)/σ²(t) is constant. This is not the Sharpe ratio or the market price of risk, but rather a nondimensional ratio of excess return to squared volatility that arises naturally in portfolio optimization problems.     

Hedging volatility risk

Volatility risk plays an important role in the management of portfolios of derivative assets as well as portfolios of basic assets. This risk is currently managed by volatility “swaps” or futures. However, this risk could be managed more efficiently using options on volatility that were proposed in the past but were never introduced mainly due to the lack of a cost efficient tradable underlying asset.The objective of this paper is to introduce a new volatility instrument, an option on a straddle, which can be used to hedge volatility risk. The design and valuation of such an instrument are the basic ingredients of a successful financial product. In order to value these options, we combine the approaches of compound options and stochastic volatility. Our numerical results show that the straddle option is a powerful instrument to hedge volatility risk. An additional benefit of such an innovation is that it will provide a direct estimate of the market price for volatility risk.     

Are interest rate options important for the assessment of interest rate risk?

Fixed income options contain substantial information on the price of interest rate volatility risk. In this paper, we ask if those options will also provide information related to other moments of the objective distribution of interest rates. Based on dynamic term structure models within the class of affine models, we find that interest rate options are useful for the identification of interest rate quantiles. Two three-factor models are adopted and their adequacy to estimate Value at Risk of zero-coupon bonds is tested. We find significant difference on the quantitative assessment of risk when options are (or not) included in the estimation process of each of these dynamic models. Statistical backtests indicate that bond estimated risk is clearly more adequate when options are adopted, although not yet completely satisfactory.     

Quantitative measures of operational risk: an application to funds management

Basel II defines operational risk as the risk of direct or indirect loss resulting from inadequate or failed internal processes, people or systems or from external events. In the past decade, there have appeared a number of quantitative approaches to measuring this risk, approaches that abstract from market risk and reputational risk. The challenge is to develop operational risk measures in an asset management context where there is only limited information available about the incidence and severity of operational loss events. We survey different approaches to this problem and argue that managing this risk through operational due diligence is a source of alpha in this funds management context.     

Lévy jump risk: Evidence from options and returns

Using index options and returns from 1996 to 2009, I estimate discrete-time models where asset returns follow a Brownian increment and a Lévy jump. Time variations in these models are generated with an affine GARCH, which facilitates the empirical implementation. I find that the risk premium implied by infinite-activity jumps contributes to more than half of the total equity premium and dominates that of the Brownian increments suggesting that it is more representative of the risks present in the economy. Overall, my findings suggest that infinite-activity jumps, instead of the Brownian increments, should be the default modeling choice in asset pricing models.     

Performance and Merton-type default risk of listed banks in the EU: A panel VAR approach

This paper provides empirical evidence that sheds new light into the dynamic interactions between risk and efficiency, a highly debated issue. First, we estimate three alternative measures of bank performance, by employing a directional distance function framework, along with a cost frontier and a profit function. As a second step, we calculate a Merton-type bank default risk. Then, we employ a panel VAR analysis, which allows the examination of the underlying relationships between efficiency and risk without applying any a priori restrictions. Most evidence shows that the effect of a one standard deviation shock of the distance to default on inefficiency is negative and substantial. There is some evidence of a reverse causation. As part of a sensitivity analysis, we extent our study to investigate the relationship between efficiency and default risk for banks with different types of ownership structures and across financial systems with different levels of development.     

Restricting CEO pay

We analyze several proposals to restrict CEO compensation and calibrate two models of executive compensation that describe how firms would react to different types of restrictions. We find that many restrictions would have unintended consequences. Restrictions on total realized (ex-post) payouts lead to higher average compensation, higher rewards for mediocre performance, lower risk-taking incentives, and the fact that some CEOs would be better off with a restriction than without it. Restrictions on total ex-ante pay lead to a reduction in the firm's demand for CEO talent and effort. Restrictions on particular pay components, and especially on cash payouts, can be easily circumvented. While restrictions on option pay lead to lower risk-taking incentives, restrictions on incentive pay (stock and options) result in higher risk-taking incentives.     

Public private partnerships: Incentives, risk transfer and real options

Private financing of large-scale infrastructure projects through public private partnerships (PPPs) has grown in recent decades. Together with changes in conventional construction procedures, there have been changes in the project financing model. The use of PPPs raises questions as to the role of the private sector in infrastructure provision and the conditions governing the long-term contractual relationships between the private and public sectors. In some early examples of PPPs, the government guaranteed a minimum profitability over the cash flows using a set of contractual terms which transferred some of the risk of the project from the private provider back to the government. Using a large toll road project, the Melbourne CityLink Project, as a case study we show how the imposed conditions can be treated as real options, how these options affect the incentive to invest and how the public sector may be transferring considerable value to the private sector through government guarantees.     

Impact of macro-economic surprises on carry trade activity

Can official news and policy announcements affect foreign exchange speculation? A widespread speculative strategy in foreign exchange markets is carry trade. This paper explores the links between macro-economic news and foreign exchange options to identify macro-economic fundamentals most relevant to the pricing of downside risk – measured by risk reversals options contracts – to carry trade activity. Focusing primarily on the Japanese yen carry trade, we identify a significant impact of macro-economic surprises on dollar/yen risk reversals. The effect is sizeable, with news related to bilateral trade balance of particular concern. Moreover, there is a close link between risk reversals and speculative futures positions in Japanese yen. This allows us to quantify a substantial effect of macro-economic news on carry trade activity, with the cost of hedging as the transmission mechanism.     

Stochastic risk premiums,stochastic skewness in currency options,and stochastic discount factors in international economies

We develop models of stochastic discount factors in international economies that produce stochastic risk premiums and stochastic skewness in currency options. We estimate the models using time-series returns and option prices on three currency pairs that form a triangular relation. Estimation shows that the average risk premium in Japan is larger than that in the US or the UK, the global risk premium is more persistent and volatile than the country-specific risk premiums, and investors respond differently to different shocks. We also identify high-frequency jumps in each economy but find that only downside jumps are priced. Finally, our analysis shows that the risk premiums are economically compatible with movements in stock and bond market fundamentals.     

Option-implied correlation between iTraxx Europe Financials and Non-Financials Indexes: A measure of spillover effect in European debt crisis

This paper proposes an analytic method to estimate the option-implied correlation embedded in options on the iTraxx Europe CDS indexes. The option-implied correlation is suggested as a measure of the spillover effect of default risk between the financial and corporate sectors in Europe. In particular, the correlation between the iTraxx Financials and Non-Financials sub-indexes is estimated from options on the iTraxx Main Index, which is considered as a basket option with the two sub-indexes being its underlyings. The abrupt changes of the realized correlation anticipated information of the corresponding option prices. The sovereign default risk, funding liquidity risk, level of risk aversion, and equity market performance are identified to be significant determinants of the option-implied correlation, implying inter-dependence amongst various markets during the European debt crisis.