A Note on Forward Price and Forward Measure

The forward measure is convenient in calculating various contingent claim prices under stochastic interest rates. We demonstrate that caution needs to be drawn when the forward measure is used to price contingent claims that involve multiple cash flows. We also derive partial different equations for the forward price to demonstrate how forward contracts can be used for dynamic hedging and how hedges can be conducted if the payoff of a contingent claim depends on the forward price.     

Pricing catastrophe options with stochastic claim arrival intensity in claim time

We model claim arrival and loss uncertainties jointly in a doubly-binomial framework to price an Asian-style catastrophe (CAT) option with a non-traded underlying loss index using the no-arbitrage martingale pricing methodology. We span these uncertainties by benchmarking to the shadow price of a one-claim bond and the premium of a reinsurance contract. We implement a stochastic time change from calendar time to claim time to more efficiently price the CAT option as a random sum – a binomial sum of claim time binomial Asian option prices. This choice of the operational time dimension allows us to incorporate different patterns of catastrophe arrivals by adjusting the claim arrival probability. We demonstrate this versatility by incorporating a mean-reverting Ornstein-Uhlenbeck intensity arrival process. Simulation results verify our model predictions and demonstrate how the claim arrival probability varies with the expected claim arrival intensity.     

Capital Budgeting for Advertising Expenditures: A Contingent Claims Approach

Advertising expenditures constitute a big part of the budgets of firms. Through their impact on demand and costs, advertising activities affect the firm's pricing and output decisions as well as the firm's market value. Yet, there is no analytical framework by which these effects can be measured. This paper develops a cash flow model for a product where the advertising budget is divided between a strategic component designed to increase expected demand and a contingent component allocated to be used only if sales fall short of capacity. Contingent claims techniques are employed to evaluate the present value of the cash flows and to provide a framework for determining the size of the advertising budget, and the pricing and production strategies that maximize the firm's value. The impact of the price sensitivity, volatility, and growth rate of demand on the size of the advertising budget is also analyzed.     

A sequential pricing framework for corporate securities: The case of rating-trigger step-up/-down bonds

We develop a sequential pricing framework in a continuous time cash flow model allowing for repeated valuation of different cash flow claims. One claim is valued until a prespecified boundary is hit, which is subsequently used as the new valuation starting point for the next claim. This highly flexible pricing framework is applied to the pricing of rating-trigger step-up/-down corporate bonds, the coupon payments of which depend on the issuing company’s credit rating. We present a simple closed-form pricing solution for this type of bonds including both a step-up and step-down threshold, as well as a lower default boundary.     

Sensitivity analysis of long-term cash flows

This paper conducts a sensitivity analysis of long-term cash flows. The price of the cash flow at time zero is given by the pricing operator of a Markov diffusion acting on the cash flow function. We study the extent to which the price of the cash flow is affected by small perturbations of the underlying Markov diffusion. The main tool is the Hansen–Scheinkman decomposition, which is a method to express the cash flow in terms of eigenvalues and eigenfunctions of the pricing operator. By incorporating techniques developed by Fournié et al. (Finance Stoch. 3:391–412, 1999), the sensitivities of long-term cash flows can be represented via simple expressions in terms of eigenvalues and eigenfunctions.     

Convenience yields

This paper revisits the notion of a convenience yield in the context of modern option pricing theory. We show that, with a proper specification of the cash flows to holding a commodity, a convenience yield as a separate concept does not exist. Rather, a convenience yield is best viewed as a label given to certain cash flows generated from storing a commodity. In particular, it represents the payoffs from two embedded options which we call the scarcity and usage options. This characterization of a convenience yield is new to the literature, although consistent with its existing interpretations and uses.     

A counter-example to an option pricing formula under transaction costs

In the paper by Melnikov and Petrachenko (Finance Stoch. 9: 141–149, 2005), a procedure is put forward for pricing and replicating an arbitrary European contingent claim in the binomial model with bid-ask spreads. We present a counter-example to show that the option pricing formula stated in that paper can in fact lead to arbitrage. This is related to the fact that under transaction costs a superreplicating strategy may be less expensive to set up than a strictly replicating one.     

Quantifying time value errors

Time valuation of cash flows is an essential part of personal financial planning and management. Many financial arrangements are priced according to a cash-flow valuation model. Expected cash flows associated with a stock or bond are discounted at an appropriate risk-adjusted rate in order to determine the fair value of the financial asset. Home mortgage loans are priced according to the discounted value of the future principal and interest cash flows. Yet, despite the importance of the discounted cash flow methodology in pricing assets, computational errors are often made when discount factors are not calculated precisely. This article attempts to quantify the magnitude of the error when the mathematical function for present value is ignored and interpolation is used instead to determine the discount factor.     

Conditional performance evaluation and the relevance of money flows for Australian international equity funds

This paper assesses the importance of fund flows in the performance evaluation of Australian international equity funds. Two concepts of fund flows are considered in the context of a conditional asset pricing model. The first measure is net fund flow relative to fund size and the second is net fund flow relative to sector flows. We find that incorporating a fund flow measure relative to the sector flow results in a reduction of measured perverse market timing. The results indicate that, at the individual fund level, cash flows are relevant in assessing management outcomes.     

Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model

Discounting cash flows requires an equilibrium model to determine the cost of capital. The CAPM of Sharpe and the intertemporal asset pricing model of Merton (1973) offer a theoretical justification for discounting at a constant risk adjusted rate. Two problems arise with this application. First, for mean reverting cash flows the risk adjustment is unknown, and second, if the present value is compounded forward then the distribution of future wealth is likely right skewed. I develop equilibrium discount rates for cash flows whose level or growth rate is mean reverting. Serial correlation also largely eliminates the skewness problem.     

Interest Rate Derivatives in a Duffie and Kan Model with Stochastic Volatility: An Arrow-Debreu Pricing Approach

Simple analytical pricing formulae have been derived, by different authors and for several derivatives, under the Gaussian Langetieg (1980) model. The purpose of this paper is to use such exact Gaussian solutions in order to obtain approximate analytical pricing formulas under the most general stochastic volatility specification of the Duffie and Kan (1996) model. Using Gaussian Arrow-Debreu state prices, first order stochastic volatility approximate pricing solutions will be derived only involving one integral with respect to the time-to-maturity of the contingent claim under valuation. Such approximations will be shown to be much faster than the existing exact numerical solutions, as well as accurate.     

Window Double Barrier Options

This paper examines a path-dependent contingent claim called the window double barrier option, including standard but also more exotic features such as combinations of single and double barriers. Price properties and hedging issues are discussed, as well as financial applications.Explicit formulae are provided, along with simple techniques for theirimplementation. Numerical results show that they compare very favourablywith alternative pricing approaches in terms of accuracy and efficiency.     

Spanning and efficiency in an economy with collective and individual risks

Much of the literature on incomplete markets emphasizes the study of conditions under which security market returns, either with or without derivative securities, span some exogenous set of cash flows. It is argued here that the only set of exogenous cash flows to which this literature is applicable are those that are contingent on existing assets' returns. The reason for this is that cash flows created by firms' production decisions are likely to be influenced by individual (unique) risk that is not incorporated into the market's existing information structure. The results of this article show that, if individual risk is pervasive, efficient allocation is likely to be achieved only in a large asset market which allows for the diversification of individual risk. The conditions for such diversification are derived and their implications discussed.     

FINANCING INNOVATIONS AND CAPITAL STRUCTURE CHOICES

The last two decades have seen a stream of innovation in financial markets, especially in corporate bonds. Some of these innovations—notably, hybrid debt—have provided firms with more flexibility in designing cash flows on borrowings, allowing them to match cash flows on financing more closely to cash flows on assets. In so doing, the use of such innovative securities has increased corporate debt capacity and hence firm value.
But if such changes have been mostly good news for corporate treasurers, the relentless torrent of innovation has sometimes resulted in firms issuing these new securities for the wrong reasons. Some have done so to take advantage of loopholes in the way ratings agencies and regulatory agencies define debt and equity—and others to exploit perceived pricing anomalies—without considering the effect of such securities on the firm's overall risk profile. In this context, it is worth noting that as corporate bonds have become more complex, investment bankers have made themselves indispensable to the process by providing pricing as well as selling support. This article aims to help managers distinguish when financing with complex securities serves their company's interests, and when it can end up hurting them.     

Contingent capital with a dual price trigger

This paper evaluates a form of contingent capital for financial institutions that converts from debt to equity if two conditions are met: the firm's stock price is at or below a trigger value and the value of a financial institutions index is also at or below a trigger value. This structure potentially protects financial firms during a crisis, when all are performing badly, but during normal times permits a bank performing badly to go bankrupt. I discuss a number of issues associated with the design of a contingent capital claim, including susceptibility to manipulation, whether conversion should be for a fixed dollar amount of shares or a fixed number of shares; uniqueness of the share price when contingent capital is outstanding; the susceptibility of different contingent capital schemes to different kinds of errors (under and over-capitalization); and the losses likely to be incurred by shareholders upon the imposition of a requirement for contingent capital. I also present an illustrative pricing example.     

Corporate Sales, Equity Trading, and Risk

This paper proposes and investigates an explanation for a positive association between the signed value of common share returns and trading activity. The mixture of distributions model for stock returns and trading is applied with the added assumption that product sales for a firm is the directing process which generates the flow of information to equity markets. Because trading depends upon information arrival, sales and trading are positively related. Also, because contribution margin is positive, cash flows increase with sales. Dependence of both cash flows and trading on sales implies that returns and trading are also positively related. This explanation is tested in this paper.     

The Pricing Effects of Interfirm Cash Tender Offers

The tools provided by option-pricing theory are used to examine the wealth effects of interfirm cash tender offers. The analysis provides evidence consistent with the “synergy” theory of corporate takeovers and has implications concerning the economic effects of regulations of cash tender offers. The analysis further suggests that the market prices information uncertainty in a manner not captured by the standard Capital Asset Pricing Model. The study introduces a technique for unbundling the prices of a primary asset and a contingent claim when only the prices of the combination are observed.     

Effects of cash flow statement reclassifications pursuant to the SEC’s one-time allowance

In February 2006, the Securities and Exchange Commission (SEC) announced a one-time opportunity for firms with misclassified cash flow items to correct these errors without issuing an official restatement. To assess the impact of these reclassifications, we determine the types of firms affected by this allowance and the types of reclassifications in the operating, investing, and financing categories of the cash flow statement. We find that, consistent with the SEC’s concerns, firms overstated net operating cash flows and understated net investing cash flows, thereby misrepresenting cash flows. In addition, the most frequent line-item reclassifications echo the SEC’s concerns about the presentation of discontinued operations and dealer floor plan financing arrangements. Insurance claim proceeds and beneficial interests in securitized loans, however, appear less problematic than the SEC expected. Overall, our findings indicate that the SEC’s plan was relatively successful and, for firms that took advantage of the allowance period, these cash flow restatements only exerted a marginally negative effect in the capital market.     

A risk-based approach for pricing American options under a generalized Markov regime-switching model

This paper considers a risk-based approach for pricing an American contingent claim in an incomplete market described by a continuous-time, Markov, regime-switching jump-diffusion model. We formulate the valuation problem as a stochastic differential game and use dynamic programming. Verification theorems for the Hamilton–Jacobi–Bellman–Issacs (HJBI) variational inequalities of the games are used to determine the seller's and buyer's prices and optimal exercise strategies.