Bank portfolio exposure to emerging markets and its effects on bank market value

This study estimates a model of banking company equity returns taking into consideration book value and market value measures of their exposure to emerging markets debt. In this estimation, general systematic market factors, such as the rate of return on the S&P500 stock index and yields on a constant maturity 5-year Treasury note, are held constant such that the exposure variables are accounting for effects due to banks’ exposure to emerging market debt. The results, although not uniform among banking companies, support the hypothesis that the extent of exposure to emerging market debt are factored into the valuation of banking company equity contemporaneously. The inclusion of a market value indicator adds to the explanation of equity returns of some banks. It is also clear that knowing the extent of the exposure on a book value basis is important information alone that may allow investors to take account of or evaluate the effects of changes in banking company equity valuation from LDC debt exposures. We also perform an event study for three major debt crises to determine whether the market recognizes the effects of these events on bank valuation. The event study results show that there is little information from identifying the time period of the crises on banking company equity returns. Explanations for this are that the information of these possible crises has been embedded in bank changes in exposure and that the market valuation of the emerging market debt is already accounted for by our model.     

Generic pricing of FX,inflation and stock options under stochastic interest rates and stochastic volatility

We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal) and the foreign (real) rates. Having the flexibility to correlate the underlying FX/inflation/stock index with both stochastic volatility and stochastic interest rates yields a realistic model that is of practical importance for the pricing and hedging of options with a long-term exposure. We derive explicit valuation formulas for various securities, such as vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. These vanilla derivatives can be valued in closed form under Schöbel and Zhu [Eur. Finance Rev., 1999, 4, 23–46] stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston [Rev. Financial Stud., 1993, 6, 327–343] model. Finally, we investigate the quality of this approximation numerically and consider a calibration example to FX and inflation market data.     

Market timing and the debt–equity choice

We test the market timing theory of capital structure using an earnings-based valuation model that allows us to separate equity mispricing from growth options and time-varying adverse selection; thus avoiding the multiple interpretations of book-to-market ratio. We find that equity market mispricing plays a significant, if not dominant, role in the security choice decision. Our results are robust to the inclusion of proxies for time-varying growth options and alternate methods of measuring misvaluation.     

Which approach to accounting for employee stock options best reflects market pricing?

We use a residual income valuation framework to compare equity valuation implications of four approaches to employee stock options (ESOs) accounting: APB 25 “recognize nothing”, SFAS 123 (revised) “recognize ESO expense”, FASB Exposure Draft “recognize and expense ESO asset” and “recognize ESO asset and liability”. Theoretical analysis shows only grant date recognition of an asset and liability, and subsequent marking-to-market of the liability, results in accounting numbers that capture the dilution effects of ESOs on current shareholder value. Out-of-sample equity market value prediction tests and in-sample comparisons of model explanatory power also support the “recognize ESO asset and liability” method.     

Valuation of quanto options in a Markovian regime-switching market: A Markov-modulated Gaussian HJM model

We consider the valuation of European quanto call options in an incomplete market where the domestic and foreign forward interest rates are allowed to exhibit regime shifts under the Heath–Jarrow–Morton (HJM) framework, and the foreign price dynamics is exogenously driven by a regime switching jump-diffusion model with Markov-modulated Poisson processes. We derive closed-form solutions for four different types of quanto call options, which include: options struck in a foreign currency, a foreign equity call struck in domestic currency, a foreign equity call option with a guaranteed exchange rate, and an equity-linked foreign exchange-rate call.     

Market impact: a systematic study of the high frequency options market

This paper deals with a fundamental subject that has seldom been addressed in recent years, that of market impact in the options market. Our analysis is based on a proprietary database of metaorders—large orders that are split into smaller pieces before being sent to the market—on one of the main Asian markets. In line with our previous work on the equity market [Said, E., Bel Hadj Ayed, A., Husson, A. and Abergel, F., Market impact: A systematic study of limit orders. Mark. Microstruct. Liq., 2018, 3(3&4), 1850008.], we propose an algorithmic approach to identify metaorders, based on some implied volatility parameters, the at the money forward volatility and at the money forward skew. In both cases, we obtain results similar to the now well-understood equity market: Square-Root Law, Fair Pricing Condition and Market Impact Dynamics.     

Convertible Debt Issuance and Market Completeness

Recent empirical evidence on option listings supports the notion that equity options help to span the market. This paper investigates the role of convertible debt in market completion. To the extent that the warrant portion of convertible instruments is similar to a call option, the securities can provide payoffs in states of nature that were previously unspanned. Stockholders of firms without listed options or pre-existing warrant-related securities suffer less severe wealth declines around convertible offerings than do owners of firms with contingent claims on their stock. The results suggest that, particularly before the rise of options on index futures, convertible debt played a market-spanning role similar to that of equity options.     

When Uncertainty Blows in the Orchard: Comovement and Equilibrium Volatility Risk Premia

We provide novel evidence for an equilibrium link between investors' disagreement, the market price of volatility and correlation, and the differential pricing of index and individual equity options. We show that belief disagreement is positively related to (i) the wedge between index and individual volatility risk premia, (ii) the different slope of the smile of index and individual options, and (iii) the correlation risk premium. Priced disagreement risk also explains returns of option volatility and correlation trading strategies in a way that is robust to the inclusion of other risk factors and different market conditions.     

Fair Terms and Fair Pricing for Multiple Warrant Issues

Abstract

Some firms utilize one or more tranches of warrant issues to supplement their capital base. Unlike exchange-traded options, the exercise of warrants requires the issuance of stock by the company, resulting in a form of dilution. Some previous studies of warrant valuation relied on “the value of the firm,” which is nonobservable, making it difficult to apply the corresponding valuation formula. This paper derives closed-form formulas to value single and multiple tranches of warrants based on the underlying stock price, its volatility, and other known parameter values. The paper first establishes the equivalence of the Black-Scholes formula for both call options and warrants in the case of a single tranche. Thereafter, it considers the impact on the value of previously issued warrants that results when a new tranche of warrants is subsequently issued, showing in each case that fair treatment of the first-issued warrant holders requires an adjustment (due to dilution) in the terms of those warrants and a corresponding modification in the warrants’ value once a second tranche of warrants is issued. To promote such fair treatment, terms of a warrant indenture would specify the nature of the adjustment required when future warrants are issued or exercised, analogous to the antidilution terms related, for example, to stock dividends. Unlike multiple issues of traded options, which are valued independently of one another, multiple warrant issues will be shown to have prices dependent on other warrants outstanding. Also examined is the sensitivity of the fair-value adjustment to changes in the underlying variables, and the theoretical fair-value prices are compared with Black-Scholes prices and with market prices of warrants in the case of two publicly traded companies, each with two warrant issues outstanding. As warrant issues modify the equity structure of a firm, the methodology of valuing warrants presented here will be useful to investment actuaries in situations in which a comprehensive market value for all of a firm’s securities is called for. In addition, risk management practices may sometimes include the use of warrant transactions to hedge stock positions similar to the way that call options are used for that purpose. This may include hedging the risk in equity-linked insurance contracts when the equity position includes stock in companies that have one or more warrant issues that are traded. The methods developed here are also applicable to multiple issues of executive stock options (ESOs) or to combinations of warrant issues and ESOs.     

Option Valuation with Information Costs: Theory and Tests

In this paper, the valuation of stock and index options is analyzed in the context of Merton's model of capital market equilibrium with incomplete information. It is possible to derive a partial differential equation for options in such a context. The derivation gives more understanding of the way an option's future payoff is discounted to the present. In order to estimate some of its parameters, the model is calibrated to market prices. It is tested using market prices and the authors' valuation formula. It is found that model prices are not significantly different from market prices, especially when out-of-the-money and deep-in-the-money options are considered. The model gives an explanation to the “strike bias” and the “smile effect.” Simulations of models based respectively on stochastic volatilities and gamma processes, are in accordance with the findings in this paper concerning biases in the Black and Scholes model, especially for pricing deep-in-the-money and out-of-the-money options. Even if the estimation method has its drawbacks, the costs of gathering and processing information regarding the option and its underlying asset play a central role in explaining the biases observed in the Black and Scholes model and help also the understanding of the U-shaped curve known as the smile of volatilities.     

MARGIN TRADING: A RISK-RETURN ANALYSIS

This paper attempts to present an integrated valuation analysis of investment options involving margin trading. The analysis is based on valuation theories such as Modigliani and Miller's capital structure model, the capital asset pricing model and the option pricing model. It is shown (i) that in margin trading, the return on equity is given by the return on investment plus a risk premium which increases proportionally with the margin-trading rate; (ii) that both the total risk (variance) and systematic risk (beta) of the return on equity increases proportionally with those associated with the return on investment; and (iii) that, when the option pricing model is applied to the case of margin trading, a more precise valuation formula can be employed.     

Equity Risk Premium

Abstract

The equity risk premium (ERP) is an essential building block of the market value of risk. In theory, the collective action of all investors results in an equilibrium expectation for the return on the market portfolio excess of the risk-free return, the ERP. The ability of the valuation actuary to choose a sensible value for the ERP, whether as a required input to capital asset pricing model valuation, or any of its descendants, is as important as choosing risk-free rates and risk relatives (betas) to the ERP for the asset at hand.

The historical realized ERP for the stock market appears to be at odds with pricing theory parameters for risk aversion. Since 1985, there has been a constant stream of research, each of which reviews theories of estimating market returns, examines historical data periods, or both. Those ERP value estimates vary widely from about ?1% to about 9%, based on a geometric or arithmetic averaging, short or long horizons, short- or long-run expectations, unconditional or conditional distributions, domestic or international data, data periods, and real or nominal returns.

This paper examines the principal strains of the recent research on the ERP and catalogues the empirical values of the ERP implied by that research. In addition, the paper supplies several time series analyses of the standard Ibbotson Associates 1926–2002 ERP data using short Treasuries for the risk-free rate. Recommendations for ERP values to use in common actuarial valuation problems also are offered.     

Author’s Reply: Principal Applications of Bayesian Methods in Actuarial Science: A Perspective - Discussion by Marjorie A. Rosenberg; M. Mendoza; Francisco José VáZquez-Polo; James C. Hickman; Donald A. Jones; Enrique de Alba; David P. M. Scollnik

Abstract

This paper considers the pricing of equity-indexed annuities (EIAs). Traditionally, the values of the guarantees embedded in these contracts are priced by modeling the underlying index fund while keeping the interest rates constant. The assumption of constant interest rates becomes unrealistic in pricing and hedging the EIAs since the embedded guarantees are often of much longer maturity. To solve this problem, the authors propose an economic model that has the flexibility of modeling the underlying index fund as well as the interest rates. Some popular EIAs are illustrated to assess the implication of the proposed model.     

Short‐Term Market Risks Implied by Weekly Options

We study short‐maturity (“weekly”) S&P 500 index options, which provide a direct way to analyze volatility and jump risks. Unlike longer‐dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment. Adopting a novel seminonparametric approach, we uncover variation in the negative jump tail risk, which is not spanned by market volatility and helps predict future equity returns. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events that are not always “signaled” by the level of market volatility and elude standard asset pricing models.     

Identifying volatility risk premia from fixed income Asian options

Fixed income options are frequently adopted by companies to hedge interest rate risk. Their payoff dependence on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the interrelations between bond and volatility risk premia in a major emerging fixed income market. We propose a dynamic term structure model that generates an incomplete market compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates a bond risk premium strongly correlated with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market.     

The volatility target effect in structured investment products with capital protection

Designing a structured investment product with capital protection which would be characterized by high capital protection level as well as high equity participation rate is a challenging task in the current market environment. Low interest rates and high volatility levels negatively affect the above key parameters of such investment products. One way to increase the participation rate of a structured investment product with a fixed capital protection level is to use a volatility target (VolTarget) strategy as an underlying asset for a financial option embedded in such a product. We introduce an extended VolTarget mechanism with interest rate dependent volatility target levels and provide a detailed comparative numerical study of European options linked to VolTarget strategies within a hybrid Heston–Vasi?ec model with stochastic volatility and stochastic interest rate.     

Asymptotics of bond yields and volatilities for extended CIR models under the real-world measure

ABSTRACT

The Cox–Ingersoll–Ross CIR short rate model is a mean-reverting model of the short rate which, for suitably chosen parameters, permits closed-form valuation formulae of zero-coupon bonds and options on zero-coupon bonds. This article supplies proofs of the formulae for the expected present value of payoffs under the real-world probability measure, known as actuarial valuation. Importantly, we give formulae for asymptotic levels of bond yields and volatilities for extended CIR models when suitable conditions are imposed on the model parameters.     

Valuación de opciones de tipo de cambio asumiendo distribuciones α-estables

This paper aims to present the valuation of options using the Black-Scholes method assuming α-stable distributions as an alternative option valuation in the Mexican market. The use of α-stable distributions for modelling financial series allows to overcome the classical valuation main weakness which assumes normality, by capturing the presence of heavy tails and asymmetry in financial time series. One of the main results is the price differential between the two models and the effect of alpha and beta parameters on prices; to show the difference valuation is made of a call option and a put option for the peso-dollar exchange rate. Likewise, basic sensitivity measurements of options (delta, gamma, and rho) were made and the effect of the stability parameter (α) was made on the implied volatility of options assuming the α-stable price as the market price.     

A New Premium Principle for Equity‐Indexed Annuities

In this article, we introduce a premium principle for equity‐indexed annuities (EIAs). Traditional actuarial loadings that protect insurance companies against risks cannot be extended to the valuation of EIAs since these products are embedded with various financial guarantees. We proposed a loaded premium that protects the issuers against the financial and mortality risks. We first obtain the fair premium based on a fair value of the equity‐linked contract using arbitrage‐free theory. Assuming a specific risk level for hedging errors, we obtain a new participation rate based on a security loading. A detailed numerical analysis is performed for a point‐to‐point EIA.     

The valuation of multivariate contingent claims under transformed trinomial approaches

This study develops a transformed-trinomial approach for the valuation of contingent claims written on multiple underlying assets. Our model is characterized by an extension of the Camara and Chung (J Futur Mark 26: 759–787, 2006) transformed-binomial model for pricing options with one underlying asset, and a discrete-time version of the Schroder (J Finance 59(5): 2375–2401, 2004) model. However, unlike the Schroder model, our model can facilitate straightforward valuation of American-style multivariate contingent claims. The major advantage of our transformed-trinomial approach is that it can easily tackle the volatility skew observed within the markets. We go on to use numerical examples to demonstrate the way in which our transformed-trinomial approach can be utilized for the valuation of multivariate contingent claims, such as binary options.