Inventory Decision under Demand Uncertainty: A Contingent Claims Approach

This study uses the discrete-time option pricing model for the evaluation of the firm's inventory decision under demand uncertainty. The paper establishes the following optimal inventory decision implications: the optimal order quantity is positively related to the product selling price, product salvage value, interest rate, and the size of the outstanding orders; and negatively related to the product cost. The effect of demand uncertainty on the optimal order quantity is shown to be ambiguous. This study also shows that the maximum present value of profit from the contingent claims approach can be substantially different from that of the modified standard newsboy problem.     

The valuation at origination of fixed-rate mortgages with default and prepayment

This paper develops a model to rationally price fixed-rate mortgages, using the arbitrage principles of option pricing theory. The paper incorporates amortization, prepayment and default in valuing the mortgage. Having completely specified the model, numerical procedures value the different features of the mortgage contract under a variety of economic conditions. The necessity of having both the interest rate and the house price as explanatory variables, due to the interaction of default and prepayment, is demonstrated. The numerical solutions presented center around mortgage pricing at origination. Thus, variations in the equilibrium contract rate are examined for differing economic conditions and changes in the contract. Finally, by presenting a complete model, the paper yields insights for the existence of common institutional practices.     

Fair Value and Risk Profile for Presale Contracts of Condominiums

Developers usually presell new condominiums, requiring purchasers to make down payments on a contract that allows them to purchase, at a fixed price, the finished condominiums on a later date. This presale contract is akin to a financial call option sold by the builder to the purchaser of the condo. In this paper, we value the presale contract from both the purchaser’s and the developer’s points of view. We examine the influence of various opt-out clauses, different interest rates and other factors on the value of presale contracts. We discuss the extent of risk sharing between the purchasers and the developers according to varying levels of down payments. We conclude that developers enjoy a reduction in risk without a corresponding reduction in expected profits by holding a presale.     

American step-up and step-down default swaps under Lévy models

This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection buyer or seller the right to step-up, step-down, or cancel the swap position. The pricing problem is formulated under a structural credit risk model based on Lévy processes. This leads to the analytic and numerical studies of several optimal stopping problems subject to early termination due to default. In a general spectrally negative Lévy model, we rigorously derive the optimal exercise strategy. This allows for instant computation of the credit spread under various specifications. Numerical examples are provided to examine the impacts of default risk and contractual features on the credit spread and exercise strategy.     

Land Development: Risk, Return and Risk Management

We model and examine the financial aspects of the land development process incorporating the industry practice of preselling lots to builders through the use of option contracts as a risk management technique. Using contingent claims valuation, we are able to determine endogenously the land value, presale option value, credits spreads and the effects of presales on debt pricing and equity expected returns. We show that using presales options effectively shift market risk from the land developer to the builder. Results from the model are consistent with the high rates of return on equity observed in empirical surveys; they also suggest that developers may be justified in pursuing projects with substantially lower expected returns to equity when a large number of lots can be presold. Additionally, we show that presales reduce default risk dramatically for leveraged projects and can support a considerable reduction in the cost of construction financing. Large debt risk premiums are justified for highly levered projects, which helps explain the use of mezzanine financing in the land development industry to reduce expected default costs.

金融双语信用违约互换

Credit default swaps can be thought of as an insurance against the default of some underlying instrument1, or as a put option on the underlying instrument. In a typical credit default swap, as shown in figure, the party selling the credit risk (or the "protection buyer") makes periodic payments to the "protection seller" of a negotiated number of basis points , times the notional amount of the underlying bond or loan.     

Parameter estimation risk in asset pricing and risk management: A Bayesian approach

Parameter estimation risk is non-trivial in both asset pricing and risk management. We adopt a Bayesian estimation paradigm supported by the Markov Chain Monte Carlo inferential techniques to incorporate parameter estimation risk in financial modelling. In option pricing activities, we find that the Merton's Jump-Diffusion (MJD) model outperforms the Black-Scholes (BS) model both in-sample and out-of-sample. In addition, the construction of Bayesian posterior option price distributions under the two well-known models offers a robust view to the influence of parameter estimation risk on option prices as well as other quantities of interest in finance such as probabilities of default. We derive a VaR-type parameter estimation risk measure for option pricing and we show that parameter estimation risk can bring significant impact to Greeks' hedging activities. Regarding the computation of default probabilities, we find that the impact of parameter estimation risk increases with gearing level, and could alter important risk management decisions.     

Pricing of Loan Commitments for Facilitating Stochastic Liquidity Needs

A bank loan commitment is often priced as a European-style put option that is used by a company with a known borrowing need on a known future date to lock in an interest rate. The literature has abstracted some of the important institutional features of a loan commitment contract. First, the timing, number, and size of the loan takedowns under such a contract are often random, rather than fixed. Second, companies often use loan commitment contracts to reduce the transaction costs of frequent borrowing and to serve as a guarantee for large and immediate random liquidity needs. Third, commercial banks maintain liquidity reserves for making random spot loans or random committed loans. Partial loan takedowns raise, rather than lower, the opportunity cost of a committed bank??s holding of excess capacity. This paper introduces a ??stochastic needs-based?? pricing model that incorporates these features. Simulations are conducted to illustrate the effects of various parameters on the fair price of a loan commitment.     

One size does not fit all: Selling firms to private equity versus strategic acquirers

This paper investigates the selling process of firms acquired by private equity versus strategic buyers. In a single regression setup we show that selling firms choose between formal auctions, controlled sales and private negotiations to fit their firm and deal characteristics including profitability, R&D, deal initiation and type of the eventual acquirer (private equity or strategic buyer). At the same time, a regression model determining the buyer type shows that private equity buyers pursue targets that have more tangible assets, lower market-to-book ratios and lower research and development expenses relative to targets bought by strategic buyers. To reflect possible interdependencies between these two choices and their impact on takeover premium, as a last step, we estimate a simultaneous model that includes the selling mechanism choice, buyer type and premium equations. Our results show that the primary decision within the whole selling process is the target firm's decision concerning whether to sell the firm in an auction, controlled sale or negotiation which then affects the buyer type. These two decisions seem to be optimal as then they do not impact premium.     

Guarantees in With-Profit and Unitized With-Profit Life Insurance Contracts: Fair Valuation Problem in Presence of the Default Option

The purpose of the article is to apply contingent claim theory to the valuation of the type of participating life insurance policies commonly sold in the UK. The article extends the techniques developed by Haberman, Ballotta, and Wang (2003) to allow for the default option. The default option is a feature of the design of these policies, which recognizes that the insurance company's liability is limited by the market value of the reference portfolio of assets underlying the policies that have been sold. The valuation approach is based on the classical contingent claim pricing “machinery,” underpinned by Monte Carlo techniques for the computation of fair values. The article addresses in particular the issue of a fair contract design for a complex type of participating policy and analyzes in detail the feasible set of policy design parameters that would lead to a fair contract and the trade‐offs between these parameters.     

Capital budgeting, information timing, and the value of abandonment options

This paper investigates how an abandonment option influences the optimal timing of information in a sequential adverse selection capital budgeting model. While the divisional manager has imperfect private pre-contract information, headquarters can time whether the manager obtains perfect project information before (timely information) or after (delayed information) the contract is signed. In the absence of the abandonment option, headquarters favors timely (delayed) information if the investment costs are high (low). The presence of the abandonment option favors delayed information because under the timely information regime the value of the abandonment option is zero, whereas under the delayed information regime the value of the option is positive.     

“Analysis of Incremental Returns of Canadian Mutual Funds”, J. F. Carrière; C. F. Hill,April 2001

Abstract

The determination and allocation of economic capital is important for pricing, risk management, and related insurer financial decision making. This paper considers the allocation of economic capital to lines of business in insurance. We show how to derive closed-form results for the complete markets, arbitrage-free allocation of the insurer default option value, or insolvency exchange option, to lines of business for an insurer balance sheet. We assume that individual lines of business and the surplus ratio are joint log-normal although the method we adopt allows other assumptions. The allocation of the default option value is required for fair pricing in the multiline insurer. We discuss and illustrate other methods of capital allocation, including Myers-Read, and give numerical examples for the capital allocation of the default option value based on explicit payoffs by line.     

American options and callable bonds under stochastic interest rates and endogenous bankruptcy

A new characterization of the American-style option is proposed under a very general multifactor Markovian and diffusion framework. The efficiency of the proposed pricing solutions is shown to depend only on the use of a viable valuation method for the corresponding European-style option and for the transition density of the model’s state variables. Under a Gauss-Markov stochastic interest rates setup, these new American option pricing solutions are shown to offer a much better accuracy-efficiency trade-off than the approximations already available in the literature. This result is also used to price callable corporate bonds under an endogenous bankruptcy structural approach, by decomposing the option to call or default into a European put on the firm value plus two early exercise premium components.     

A jump-diffusion approach to modelling vulnerable option pricing

Following the framework of Klein [1996. Journal of Banking and Finance 20, 1211–1229], this paper presents an improved method of pricing vulnerable options under jump diffusion assumptions about the underlying stock prices and firm values which are appropriate in many business situations. In contrast to Klein [1996. Journal of Banking and Finance 20, 1211–1229] model, jumps can be used to model sudden changes in stock prices and firm values. Further, with the jump risk, a firm can default instantaneously because of an unexpected drop in its value. Therefore, our model is able to provide sufficient conceptual insights about the economic mechanism of vulnerable option pricing. The numerical results show that a jump occurrence in firm values can increase the likelihood of default and reduce the vulnerable option prices.     

Pricing Black-Scholes options with correlated credit risk

This paper presents an improved method of pricing vulnerable Black-Scholes options under assumptions which are appropriate in many business situations. An analytic pricing formula is derived which allows not only for correlation between the option's underlying asset and the credit risk of the counterparty, but also for the option writer to have other liabilities. Further, the proportion of nominal claims paid out in default is endogenous to the model and is based on the terminal value of the assets of the counterparty and the amount of other equally ranking claims. Numerical examples compare the results of this model with those of other pricing formulas based on alternative assumptions, and illustrate how the model can be calibrated using market data.     

Pricing Double-Trigger Reinsurance Contracts: Financial Versus Actuarial Approach

This article discusses various approaches to pricing double‐trigger reinsurance contracts—a new type of contract that has emerged in the area of ‘‘alternative risk transfer.’’ The potential coverage from this type of contract depends on both underwriting and financial risk. We determine the reinsurer's reservation price if it wants to retain the firm's same safety level after signing the contract, in which case the contract typically must be backed by large amounts of equity capital (if equity capital is the risk management measure to be taken). We contrast the financial insurance pricing models with an actuarial pricing model that has as its objective no lessening of the reinsurance company's expected profits and no worsening of its safety level. We show that actuarial pricing can lead the reinsurer into a trap that results in the failure to close reinsurance contracts that would have a positive net present value because typical actuarial pricing dictates the type of risk management measure that must be taken, namely, the insertion of additional capital. Additionally, this type of pricing structure forces the reinsurance buyer to provide this safety capital as a debtholder. Finally, we discuss conditions leading to a market for double‐trigger reinsurance contracts.     

Futures Options and the Volatility of Futures Prices

Assuming nonstochastic interest rates, European futures options are shown to be European options written on a particular asset referred to as a futures bond. Consequently, standard option pricing results may be invoked and standard option pricing techniques may be employed in the case of European futures options. Additional arbitrage restrictions on American futures options are derived. The efficiency of a number of futures option markets is examined. Assuming that at-the-money American futures options are priced accurately by Black's European futures option pricing model, the relationship between market participants' ex ante assessment of futures price volatility and the term to maturity of the underlying futures contract is also investigated empirically.     

Dynamic monopoly pricing and herding

We study dynamic pricing by a monopolist selling to buyers who learn from each other's purchases. The price posted in each period serves to extract rent from the current buyer, as well as to control the amount of information transmitted to future buyers. As information increases future rent extraction, the monopolist has an incentive to subsidize learning by charging a price that results in information revelation. Nonetheless, in the long run, the monopolist generally induces herding by either selling to all buyers or exiting the market.     

An offer you can't refuse: early contracting with endogenous threat

A seller has private information on the future gains from trade with a buyer, but the buyer has the option to invest to produce the good internally. Both the buyer and the seller can efficiently trade ex post under complete information. Despite the lack of information, the buyer sometimes gains by making an early contract offer to the seller. The early contract divides the different types of sellers according to their information, which renders the threat of producing the good in‐house credible and enables the buyer to extract a larger share of the gains from trade. Several extensions are investigated.     

A comparative study of the probability of default for global financial firms

This article presents a modification of Merton’s (1976) ruin option pricing model to estimate the implied probability of default from stock and option market prices. To test the model, we analyze all global financial firms with traded options in the US and focus on the subprime mortgage crisis period. We compare the performance of the implied probability of default from our model to the expected default frequencies based on the Moody’s KMV model and agency credit ratings by constructing cumulative accuracy profiles (CAP) and the receiver operating characteristic (ROC). We find that the probability of default estimates from our model are equal or superior to other credit risk measures studied based on CAP and ROC. In particular, during the subprime crisis our model surpassed credit ratings and matched or exceeded KMV in anticipating the magnitude of the crisis. We have also found some initial evidence that adding off-balance-sheet derivatives exposure improves the performance of the KMV model.