Ghulam Sorwar

Spectral Risk Measures: Properties and Limitations

Spectral risk measures (SRMs) are risk measures that take account of user risk-aversion, but to date there has been little guidance on the choice of utility function underlying them. This paper addresses this issue by examining alternative approaches based on exponential and power utility functions. A number of problems are identified with both types of spectral risk measure. The general lesson is that users of spectral risk measures must be careful to select utility functions that fit the features of the particular problems they are dealing with, and should be especially careful when using power SRMs.

Determinants of Takeover Premium in Cash Offers: An Option Pricing Approach

In takeovers bidders offer a premium to target firm shareholders but the determinants of such premium are not clearly identified. Among the factors previously examined in the literature are prior target undervaluation, expected synergy and overpayment due to behavioural biases like hubris. In this paper we use an option pricing approach to decompose the observed takeover premia. We also test the implications of recent real options-based models of takeover premia and risk changes surrounding takeovers. We model the observed target stock price as a portfolio of unobserved stock price and a put option whose value depends on a number of target and deal characteristics that impinge on the probability of bid success. For a sample of over 200 UK cash takeover bids during 1990-2004, we estimate the put value using the Black-Scholes option pricing model and find that target firm revaluation accounts for a substantial part of the observed takeover premium and the put value accounts for a smaller, but still significant, proportion. The latter is higher in hostile, failed and longer bids. The put option value is also significantly correlated with the relative riskiness of bidders and targets, and synergy as predicted by Lambrecht (2004) . Movements in betas in the run up to takeover announcements and in the post-announcement period are consistent with the real options-based predictions of Hackbarth and Morellec (2008) . This study contributes to a better understanding of the true determinants of takeover premium and demonstrates the usefulness of option pricing models and provides a preliminary test of real options models in understanding and measuring the impact of UK takeovers on firm risk and shareholder gains. Copyright (c) 2010 Blackwell Publishing Ltd.

Estimating single factor jump diffusion interest rate models

Empirical studies have demonstrated that behaviour of interest rate processes can be better explained if standard diffusion processes are augmented with jumps in the interest rate process. In this article we examine the performance of both linear and nonlinear one-factor Chan–Karolyi–Longstaff–Sanders (CKLS) model in the presence of jumps. We conclude that empirical features of interest rate not captured by standard diffusion processes are captured by models with jumps and that the linear CKLS model provides sufficient explanation of the data.

Valuation of Two-Factor Interest Rate Contingent Claims Using Green's Theorem

Abstract Over the years a number of two-factor interest rate models have been proposed that have formed the basis for the valuation of interest rate contingent claims. This valuation equation often takes the form of a partial differential equation that is solved using the finite difference approach. In the case of two-factor models this has resulted in solving two second-order partial derivatives leading to boundary errors, as well as numerous first-order derivatives. In this article we demonstrate that using Greens theorem, second-order derivatives can be reduced to first-order derivatives that can be easily discretized; consequently, two-factor partial differential equations are easier to discretize than one-factor partial differential equations. We illustrate our approach by applying it to value contingent claims based on the two-factor CIR model. We provide numerical examples that illustrate that our approach shows excellent agreement with analytical prices and the popular Crank–Nicolson method.

Implied derivative security prices based two-factor interest model: a UK application

In this paper the extended Box Method recently introduced to finance is used to value bond and option prices based on the two-factor CKLS interest rate model. The two-factor CKLS model is estimated using the one-year Eurodollar rate for the UK as the long rate and either the one-week, or one-month Euro dollar rate for the UK as the short rate. Overall, it is found that both and option prices are sensitive to the model used.