The deterministic numerical valuation of American options under Heston’s stochastic volatility model is considered. The prices are given by a linear complementarity problem with a two-dimensional parabolic partial differential operator. A new truncation of the domain is described for small asset values while for large asset values and variance a standard truncation is used. The finite differenc...

This paper develops a Monte Carlo simulation method for solving option valuation problems. The method simulates the process generating the returns on the underlying asset and invokes the risk neutrality assumption to derive the value of the option. Techniques for improving the efficiency of the method are introduced. Some numerical examples are given to illustrate the procedure and additional a...

We propose a new methodology for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Itô processes. Our method can be applicable to a wide range of valuation problems including contingent claims associated with stocks, foreign exchange rates, the term structure of interest rates, and even their combinations. We illustrate ou...

Derivative assets analysis usually takes a model of the underlying price process as given and attempts to value derivative securities relative to that model. This paper studies the following “inverse” problem: given a valuation formula for a derivative asset, what can be inferred about the underlying asset price process? Assuming continuous sample paths, we show that a sufficiently regular pric...

Recent advances in information technology management reflect the growing understanding that the most significant asset at risk is not hardware or facilities but, rather, the information that those assets service. An ongoing debate exists as to how—or whether—information can be valued. This chapter provides an overview and detailed guidance for one proven method of information valuation, the Del...

A profession serves a public purpose. Consequently, an outline of the history of the actuarial profession must follow the public purposes served by actuaries in applying their basic science. The formation in London in 1762 of the Society for Equitable Assurances on Lives and Survivorships as a mutual company, initiated a process that created a public purpose for actuaries. A mutual insurance co...

To understand the pricing and performance of private equity (PE), we analyze the incomplete-markets portfolio choice problem facing a risk-averse limited partner (LP) investing in liquid stocks and bonds along with an illiquid PE investment. A general partner (GP) manages the PE asset and generates alpha on it and charges management and performance fees via carried interest in return. Our compl...

We investigate the relation between the fair price for European-style vanilla options and the probability of short-term returns on the underlying asset in the absence of transaction costs. If the asset’s future price has finite expectation, the option’s fair value satisfies a parabolic partial differential equation of the Black-Scholes type in the absence of arbitrage opportunities. However, th...

We analyse the valuation and hedging of a claim on a non-traded asset using a correlated traded asset under a partial information scenario, when the asset drifts are unknown constants. Using a Kalman filter and a Gaussian prior distribution for the unknown parameters, a full information model with random drifts is obtained. This is subjected to exponential indifference valuation. An expression ...

The term ‘no-good-deal pricing’ in this paper encompasses pricing techniques based on the absence of attractive investment opportunities – good deals – in equilibrium. We borrowed the term from [8] who pioneered the calculation of price bands conditional on the absence of high Sharpe Ratios. Alternative methodologies for calculating tighter-than-no-arbitrage price bounds have been suggested by ...