Time consistent pricing of options with embedded decisions

Review of Derivatives Research - Many financial contracts are equipped with exercise rights or other features enabling the parties to actively shape the contract’s payoff. These decisions...     

Identifying,valuing and hedging of embedded options in non-maturity deposits

Non-maturity deposits like savings accounts or demand deposits contain significant option risks caused by the bank’s discretionary pricing and the customers’ withdrawal right. Option risks follow from inherent non-linear factor exposures. I propose an ordinal response model for deposit rate jumps to identify non-linear factor exposures and a discrete-time term structure model to value the resulting option risks and to derive hedge measures “outside the model”. My delta profile resembles a constant maturity swap, but vega and gamma are more pronounced, which demonstrates that the widespread practice of static hedging with zero bonds is inadequate.     

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 generalized approach to optimal hedging with option contracts

In this paper, we develop a theoretical model in which a firm hedges a spot position using options in the presence of both quantity (production) and basis risks. Our optimal hedge ratio is fairly general, in that the dependence structure is modeled through a copula function representing the quantiles of the hedged position, and hence any quantile risk measure can be employed. We study the sensitivity of the exercise price which minimizes the risk of the hedged portfolio to the relevant parameters, and we find that the subjective risk aversion of the firm does not play any role. The only trade-off is between the effectiveness and cost of the hedging strategy.     

Optimal exercise of American put options near maturity: A new economic perspective

Review of Derivatives Research - The critical price $$S^{*}\left( t\right) $$ of an American put option is the underlying stock price level that triggers its immediate optimal exercise. We provide...     

Pricing and static hedging of American-style options under the jump to default extended CEV model

This paper prices (and hedges) American-style options through the static hedge approach (SHP) proposed by Chung and Shih (2009) and extends the literature in two directions. First, the SHP approach is generalized to the jump to default extended CEV (JDCEV) model of Carr and Linetsky (2006), and plain-vanilla American-style options on defaultable equity are priced. The robustness and efficiency of the proposed pricing solutions are compared with the optimal stopping approach offered by Nunes (2009), under both the JDCEV framework and the nested constant elasticity of variance (CEV) model of Cox (1975), using different elasticity parameter values. Second, the early exercise boundary near expiration is derived under the JDCEV model.     

Using Richardson extrapolation techniques to price American options with alternative stochastic processes

In this paper the authors investigate the performance of the original and repeated Richardson extrapolation methods for American option pricing by implementing both the original and modified Geske?CJohnson approximation formulae. A comprehensive numerical comparison includes alternative stochastic processes of the underlying asset price. The numerical results show that whether the original or modified formula is implemented, the Richardson extrapolation techniques work very well. The repeated Richardson extrapolation strongly outperforms the original, especially when the underlying asset price follows a stochastic volatility process. Moreover, this study verifies the feasibility of the estimated error bounds of the American option prices under alternative stochastic processes by applying the repeated Richardson extrapolation method and estimating the interval of true American option values, as well as determining the number of options needed for an approximation to achieve a desired accuracy level.     

Real options at the interface of finance and operations: exploiting embedded supply-chain real options to gain competitiveness

Exploiting embedded supply-chain real options creates powerful opportunities for competitive manufacturing in high-cost environments. Rather than seeking competitiveness through standardization as is common to lean production, real-options reasoning explores opportunities to use supply-chain variability as a strategic weapon. We present an illustrative case study of a Swiss manufacturer of cable extrusion equipment supported by a formal real-options model that aids in valuing the embedded options that make up supply-chain flexibility: postponement, contraction, expansion, switching, and abandonment. Real-options reasoning provides a plausible retrospective rationale for the case firm's use of supply-chain flexibility that provided protection against competition from low cost, but less responsive competitors. Their intuitive real-options reasoning facilitated incorporating fuller information concerning volatility, flexibility, and control into choosing what products to make, in what quantity, and with work allocated to which supplier. The case study also highlights how competing through exploiting embedded real options requires a different managerial skill set than does competing through cost reduction. Skills such as customer communication, supplier management, and ability to ensure a smooth flow of production join the ability to reduce and control lead times as key sources of competitive advantage.     

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.      

Accounting information systems and learning theory: an integrated approach to teaching

A background to the adoption of computing in accounting education is discussed. There has been considerable pressure by the accounting profession for information technology to be taught in tertiary accounting courses. While accommodating these expectations, accounting academics have been concerned that such teaching should focus on conceptual understanding, rather than training. Research on effectiveness of computers and the learning of accounting concepts has been considered and found to be inconclusive and conflicting. It has been argued that an understanding of learning theory is necessary to enhance the effectiveness of teaching computerized accounting. An approach to teaching computerized accounting information systems and integrating learning theories is presented via a practical example: the objectives of teaching computerized accounting and reasons for adopting the SYBIZ Rev L software package are presented. The chosen approach in developing the teaching and learning material is outlined and linked to learning theory. It is argued that computers in accounting education should not merely be treated as a fait accompli, but be recognized as a part of a process which we should understand and influence. Research needs to continue on a number of methodological fronts. Suggestions are given for more specific empirical research, as well as suggestions on how to incorporate the findings of other related disciplines.     

Calibration to American options: numerical investigation of the de-Americanization method

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times (compared to a direct calibration to American options). Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors.     

A note on an analytical valuation formula for unprotected American call options on stocks with known dividends

This note provides simple analytic formulas for the value of an American call option on a stock with known dividends.     

A general approach to integrated risk management with skewed,fat-tailed risks

Integrated risk management for financial institutions requires an approach for aggregating risk types (market, credit, and operational) whose distributional shapes vary considerably. We construct the joint risk distribution for a typical large, internationally active bank using the method of copulas. This technique allows us to incorporate realistic marginal distributions that capture essential empirical features of these risks such as skewness and fat-tails while allowing for a rich dependence structure. We explore the impact of business mix and inter-risk correlations on total risk. We then compare the copula-based method with several conventional approaches to computing risk.     

A unified approach for the pricing of options relating to averages

In this paper, we consider generalized Asian options and propose a unified approximation method for the pricing of such options when the underlying process is a diffusion. Through numerical examples, we show that our approximation method is accurate enough to be used in practice for the pricing of any type of Asian options that has been treated separately in the literature. Comparisons are made with the existing methods in the literature to support the usefulness of our method.     

On the valuation of American call options on stocks with known dividends

Both the Roll and the Geske equations for the valuation of the American call option on a stock with known dividends are incorrectly specified. This note presents the corrected valuation formula, explains the misspecifications and provides a numerical example.     

Efficiency tests with overlapping data: an application to the currency options market

This paper presents the results of an empirical study into the efficiency of the currency options market. The methodology derives from a simple model often applied to the spot and forward markets for foreign exchange. It relates the historic volatility of the underlying asset to the implied volatility of an option on the underlying at a specified prior time and then proceeds to test obvious hypotheses about the values of the coefficients. The study uses panel regression to address the problem of overlapping data which leads to dependence between observations. It also uses volatility data directly quoted on the market in order to avoid the biases which may occur when ‘backing out’ volatility from specific option pricing models. In general, the evidence rejects the hypothesis that the currency option market is efficient. This suggests that implied volatility is not the best predictor of future exchange rate volatility and should not be used without modification: the models presented in this paper could be a way of producing revised forecasts.     

Option pricing using a binomial model with random time steps (A formal model of gamma hedging)

This paper provides a new option pricing model which justifies the standard industry implementation of the Black-Scholes model. The standard industry implementation of the Black-Scholes model uses an implicit volatility, and it hedges both delta and gamma risk. This industry implementation is inconsistent with the theory underlying the derivation of the Black-Scholes model. We justify this implementation by showing that these adhoc adjustments to the Black-Scholes model provide a reasonable approximation to valuation and delta hedging in our new option pricing model.