Diss. Stockholm : Handelshögsk.

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During the last two decades there has been an explosion in the number of complex financial instruments that are traded on the financial markets. Naturally, being able to value the increasing number of traded complex financial instruments has an academic interest. Such valuation methods are, however, certainly not only of interest to academics. For agents on the financial markets, it is of crucial importance to be able to assess the value of new exotic securities. This is equally true for financial services firms that construct and promote the instruments, borrowers that sell the products for the financing of their activities and investors that buy the products. Many new financial instruments have attributes that make Contingent Claims Analysis (CCA) superior to other currently known valuation methods. CCA is a technique for determining the price of an asset whose payoffs depend upon the evolution of one or more underlying state variables. One problem that often arises when this framework is used is that it is not possible to find a closed-form solution for the price. Numerical methods must therefore be relied on. Furthermore, in many cases and especially in cases where there is more than one underlying state variable, which many complex financial instruments require for accurate valuation, numerical methods become computationally laborious. Hence, research concerning and development of efficient numerical methods that can be used in the CCA context is important. This dissertation consists of four different papers (papers A to D). Paper A provides discussion of the process of financial innovation. A lengthy appendix is attached to paper A. In this appendix, more thn 100 more or less complex financial instruments are described briefly. Papers B to D have a common theme, which is valuation of complex financial instruments with the help of CCA and numerical methods. The research task of paper B is to answer a question that has unclear status in academic literature. The question is "How do errors (or different modelling choices) in boundary conditions affect solutions when the implicit finite difference method is used?". In papers C and D, numerical methods which can be used to price financial instruments with several underlying state variables are developed and tested. The methods in paper C are finite difference methods, and the method in paper D is a lattice (or tree) approach. / Diss. Stockholm : Handelshögsk.

This dissertation includes three essays, which investigate contingent claims pricing subject to credit risk based on the structural approach and analyze associated issues of corporate finance. The first essay develops and examines a partial equilibrium model to investigate the effects of macroeconomic condition and firm-level productivity shocks on the determination of optimal debt ratio. The model extends the contingent-claims models of the firm's capital structure by incorporating both the industry demand and firm-level supply factors into the firm's earnings and unlevered asset value. Our model predicts that the optimal debt ratio is negatively correlated to the macroeconomic conditions and the firm-level productivity. Furthermore, the theoretical implications are totally supported by the pooled feasible generalized least squares estimation with 311 Taiwanese listed manufacturing firms' quarterly data over the period from 1994 to 2003. The differences between the high-tech electronics and other manufacturing firms are also investigated, and particularly the high-tech firms are not tied up with the macroeconomic conditions while the others are. The second essay presents a contingent claim valuation of a callable convertible bond with the issuer's credit risk. The optimal call, voluntary conversion and bankruptcy strategies are jointly determined by shareholders and bondholders to maximize the equity value and the bond value, respectively. Our model not only incorporates tax benefits, bankruptcy costs, refunding costs and a call notice period, but also takes account of the issuer's debt size and structure. The numerical results show that the predicted optimal call policies are generally consistent with recent empirical findings; therefore calling convertible bonds too late or too early can be rational. The third essay provides a closed-form valuation formula for the Black-Scholes options subject to interest rate risk and credit risk. Not only does our model allow for the possible default of the option issuer prior to the option's maturity, but also considers the correlations among the option issuer's total asset, the underlying stock, and the default-free zero coupon bond. We further tailor-make a specific credit-linked option for hedging the default risk of the option issuer. The numerical results show that the default risk of the option issuer significantly reduces the option values, and the vulnerable option values may be remarkably overestimated in the case where the default can occur only at the maturity of the option.

Contingent claims models have recently been applied to the field of corporate insolvency prediction in an attempt to provide the art with a theoretical methodology that has been lacking in the past. Limited studies have been carried out in order to empirically compare the performance of these “market” models with that of their accounting number-based counterparts. This thesis contributes to the literature in several ways: The thesis traces the evolution of the art of corporate insolvency prediction from its inception through to the present day, combining key developments and methodologies into a single document of reference. I use receiver operating characteristic curves and tests of economic value to assess the efficacy of sixteen models, carefully selected to represent key moments in the evolution of the art, and tested upon, for the first time, post-IFRS UK data. The variability of model efficacy is also measured for the first time, using Monte Carlo simulation upon 10,000 randomly generated training and validation samples from a dataset consisting of over 12,000 firmyear observations. The results provide insights into the distribution of model accuracy as a result of sample selection, which is something which has not appeared in the literature prior to this study. I find overall that the efficacy of the models is generally less than that reported in the prior literature; but that the theoretically driven, market-based models outperform models which use accounting numbers; the latter showing a relatively larger efficacy distribution. Furthermore, I obtain the counter-intuitive finding that predictions based on a single ratio can be as efficient as those which are based on models which are far more complicated – in terms of variable variety and mathematical construction. Finally, I develop and test a naïve version of the down-and-out-call barrier option model for insolvency prediction and find that, despite its simple formulation, it performs favourably compared alongside other market-based models.

This dissertation consists of six separate papers dealing with the valuation of financial guarantees and risky debt contract. Each of these papers is independent and distinct. The main theme is the valuation of securities by contingent claims analysis (CCA). Paper 1: Valuation of Financial Guarantees – A Presentation and a Critique.One purpose of this paper is to derive a pricing formula for a deposit guarantee, when the assets of the bank exhibit downward jumps due to extraordinary loan defaults. In this respect, we use the framework of Merton (1976), where a stock option is priced under the assumption of a jump-diffusion process for the underlying stock. Paper 2: Valuation of Deposit Insurance – An Alternative Approach.This paper extends paper 1 in the respect that the guarantor, in this case a deposit insurance agency, will nullify the guarantee contract and liquidate the bank when it gets insolvent. The liquidation is assumed to involve some costs like legal and realization costs. In fact, since the guarantee contract will never get in-the-money, the guarantee will receive value only from these liquidation costs. Paper 3: Financial Guarantees and Asymmetric Information.In this paper, we make the assumption that the guarantor cannot observe the solvency process, unless it carries out audits. This is different from the normal perfect information assumption for this kind of analysis. Since audits are often costly, and this burdens the guarantee value, the guarantor will search for an audit strategy, which minimizes the guarantee value. Paper 4: Valuation of Barrier Contracts – A Simplified Approach.Many types of financial contracts can be classified as "barrier contracts". This description comes from their feature of allowing either contractual part to take some kind of action during the lifetime of the contract contingent on some pre-specified event. In this sense, the deposit insurance contract in analysed in paper 2 can be regarded as a barrier contract. The previous valuation models of barrier contracts are often considerably advanced and have tended to obscure the underlying economics. It is the path-dependence and stopping-time features that primarily make the derivation of these pricing formulas complicated. Our model simplifies this procedure by deriving the important "first passage time" distribution from a binomial model instead of using the reflection principle. Paper 5: Valuation of Risky Debt in the Presence of Jumps, Safety Barriers and Collaterals.This paper deals with different aspects of risky debt valuation with the CCA approach. The term. "risky", refers to the probability of default on the promised payment by the borrower. Paper 6: Portfolio Selection and the Pricing of Personal Loan Contracts.The CCA literature that follows Black and Scholes (1973), has mainly taken the underlying asset dynamics for given. Although it may be appropriate for stock options, we consider this assumption too simplifying with regards to personal loan contracts. It is obvious that the borrower’s consumption-investment decision affects his wealth process, on which the loan contract is contingent. Moreover, we believe that individuals actually have preferences to repay loans for different reasons such as the existence of reputational costs or legal penalties that affect the borrower in case of loan default. / Diss. av båda förf.  Stockholm : Handelshögskolan

The thesis builds a model for pricing the liabilities of a firm. The liabilities - stocks, loans, bonds - fundamentally all depend on the value of the firm's assets. By looking at balance sheet data, such as the nominal amount of debt outstanding, and market prices, such as time series of stock prices, the value and volatility of the assets can be estimated. Finally, e.g. bank loans to the same firm can be priced in terms of these values. Thus, the purpose of the whole exercise is to use the information content in stock prices to infer the value of loans. / Diss. Stockholm : Handelshögsk.

This volume consists of four papers, which in principle could be read in any order. The common denominator is that they deal with contingent claims models of a firm's securities or related derivatives. A Framework for Valuing Corporate Securities Early applications of contingent claims analysis to the pricing of corporate liabilities tend to restrict themselves to situations where debt is perpetual or where financial distress can only occur at debt maturity. This paper relaxes these restrictions and provides an exposition of how most corporate liabilities can be valued as packages of two fundamental barrier contingent claims: a down-and-out call and a binary option. Furthermore, it is shown how the comparative statics of the resulting pricing formulae can be derived.A New Compound Option Pricing ModelThis paper extends the Geske (1979) compound option pricing model to the case where the security on which the option is written is a down-and-out call as opposed to a standard Black and Scholes call. Furthermore, we develop a general and flexible framework for valuing options on more complex packages of contingent claims - any claim that can be valued using the ideas in chapter 1. This allows us to study the interaction between the detailed characteristics of a firm's capital structure and the prices of for example stock options.Implementing Firm Value Based ModelsThis paper evaluates an implementation procedure for contingent claims models suggested by Duan (1994). Duan's idea is to use time series data of traded securities such as shares of common stock in order to estimate the dynamics of the firm's asset value. Furthermore, we provide an argument which allows us to relax the (common) assumption that the firm's assets may be continuously traded. It is sufficient to assume that the firm's assets are traded at one particular point in time.Asset Substitution, Debt Pricing, Optimal Leverage and MaturityChapters 1-3 have focused on the problem of pricing corporate securities.They have thus abstracted strategic aspects of corporate finance theory. This paper is an attempt to combine the contingent claims literature with the non-dynamic corporate finance literature. I allow the management of the firm to alter its investment policy strategically. This yields a model which allows us to examine the relationship between bond prices, agency costs, optimal leverage and maturity. / Diss. Stockholm : Handelshögsk.

This dissertation explores the application of the techniques of mathematical finance to the achievement of investment targets and financial stability. It contains three self-contained but broadly related essays. Sharpe et al. proposed the idea of having an expected utility maximizer choose a probability distribution for future wealth as an input to her investment problem rather than a utility function. They developed the Distribution Builder as one way to elicit such a distribution. In a single-period model, they then showed how this desired distribution for terminal wealth can be used to infer the investor's risk preferences. In the first essay, we adapt their idea, namely that a desired distribution for future wealth is an alternative input attribute for investment decisions, to continuous time. In a variety of scenarios, we show how the investor's desired distribution, combined with her initial wealth and market-related input, can be used to determine the feasibility of her distribution, her implied risk preferences, and her optimal policies throughout her investment horizon. We then provide several examples. In the second essay, we consider an investor who must a priori liquidate a large position in a primary risky asset whose price is influenced by the investor's liquidation strategy. Liquidation must be complete by a terminal time T, and the investor can hedge the market risk involved with liquidation over time by investing in a liquid proxy asset that is correlated with the primary asset. We show that the optimal strategies for an investor with constant absolute risk aversion are deterministic and we find them explicitly using calculus of variations. We then analyze the strategies and determine the investor's indifference price. In the third essay, we use contingent claims analysis to study several aggregate distance-to-default measures of the S&P Financial Select Sector Index during the years leading up to and including the recent financial crisis of 2007-2009. We uncover mathematical errors in the literature concerning one of these measures, portfolio distance-to-default, and propose an alternative measure that we show has similar conceptual and in-sample econometric properties. We then compare the performance of the aggregate distance-to-default measures to other common risk indicators. / text