What determines early exercise of employee stock options in Australia?

Employee stock options (ESOs) are a popular way of remunerating employees. We analyse factors at the firm and option level affecting the employee's decision to exercise ESOs before they mature. Exercises over the period 1998–2004 are analysed and the key factor influencing early exercise is found to be dividends. Exercises frequently occur well before maturity, but in most cases little time value is sacrificed. Our findings have implications for the ‘fair’ valuation of ESOs in companies’ financial statements, as required by the relevant Australian accounting standard, AASB 2.     

On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives

This paper analyses the robustness of Least-Squares Monte Carlo, a technique proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least-squares regressions in which the explanatory variables are certain polynomial functions. We analyze the impact of different basis functions on option prices. Numerical results for American put options show that this approach is quite robust to the choice of basis functions. For more complex derivatives, this choice can slightly affect option prices. This revised version was published online in June 2006 with corrections to the Cover Date.     

Truncation and acceleration of the Tian tree for the pricing of American put options

We present a new method for truncating binomial trees based on using a tolerance to control truncation errors and apply it to the Tian tree together with acceleration techniques of smoothing and Richardson extrapolation. For both the current (based on standard deviations) and the new (based on tolerance) truncation methods, we test different truncation criteria, levels and replacement values to obtain the best combination for each required level of accuracy. We also provide numerical results demonstrating that the new method can be 50% faster than previously presented methods when pricing American put options in the Black–Scholes model.     

Some calculations for Israeli options

Recently Kifer (2000) introduced the concept of an Israeli (or Game) option. That is a general American-type option with the added possibility that the writer may terminate the contract early inducing a payment exceeding the holders claim had they exercised at that moment. Kifer shows that pricing and hedging of these options reduces to evaluating a saddle point problem associated with Dynkin games. In this short text we give two examples of perpetual Israeli options where the solutions are explicit.Received: December 2002, Mathematics Subject Classification: 90A09, 60J40, 90D15JEL Classification: G13, C73I would like to express thanks to Chris Rogers for a valuable conversation.     

An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates

This paper proposes an asymptotic expansion scheme of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density functions of the underlying assets and for pricing currency options based on a third order asymptotic expansion scheme; we do not model a foreign exchange rate’s variance such as in Heston [(1993) The Review of Financial studies, 6, 327–343], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. Finally, numerical examples are provided and the pricing formula are applied to the calibration of volatility surfaces in the JPY/USD option market.     

Reading the smile: the message conveyed by methods which infer risk neutral densities

In this study we compare the quality and information content of risk neutral densities obtained by various methods. We consider a non-parametric method based on a mixture of log–normal densities, the semi-parametric ones based on an Hermite approximation or based on an Edgeworth expansion, the parametric approach of Malz which assumes a jump-diffusion for the underlying process, and Heston's approach assuming a stochastic volatility model. We apply those models on FF/DM exchange rate options for two dates. Models differ when important news hits the market (here anticipated elections). The non-parametric model provides a good fit to options prices but is unable to provide as much information about market participants expectations than the jump-diffusion model.     

Long term spread option valuation and hedging

This paper investigates the valuation and hedging of spread options on two commodity prices which in the long run are in dynamic equilibrium (i.e., cointegrated). The spread exhibits properties different from its two underlying commodity prices and should therefore be modelled directly. This approach offers significant advantages relative to the traditional two price methods since the correlation between two asset returns is notoriously hard to model. In this paper, we propose a two factor model for the spot spread and develop pricing and hedging formulae for options on spot and futures spreads. Two examples of spreads in energy markets – the crack spread between heating oil and WTI crude oil and the location spread between Brent blend and WTI crude oil – are analyzed to illustrate the results.     

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.     

Generalised Geske--Johnson Interpolation of Option Prices

Abstract:  This paper describes four separate option types as special cases of Bermudans with general inter–exercise and time to final maturity. This produces a surface with European, finite American, infinite Bermudan and infinite American options as special cases. This allows Geske–Johnson (1984) two–point pricing to be extended to consider time–to–maturity as well as time–between–exercise opportunities. Due to their position on this 'map', infinite Bermudans are christened Arctic options and their pricing solution is presented. Numerical comparisons to benchmark methods are made for call prices under GBM although the results here hold for other processes and for both puts and calls when symmetry arguments are invoked.