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Pricing Vulnerable Options Under Stochastic Assets And Liabilities
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Book Synopsis Pricing Vulnerable Options Under Stochastic Assets and Liabilities by : Yu-Chung Liu
Download or read book Pricing Vulnerable Options Under Stochastic Assets and Liabilities written by Yu-Chung Liu and published by . This book was released on 2009 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents both closed-form formulas and binomial tree algorithms to evaluate vulnerable derivatives. The payoff function extends mainly from the Klein (1996) and the Ammann (2001) credit risk frameworks. Three stochastic processes, the underlying stock price, the assets value of the option writer, and the liabilities value of the option writer, are suitably modeled. Closed-form solutions are derived for vulnerable European options under the suggested payoff function. A conditional binomial tree algorithm for two correlated stochastic processes, the underlying stock price and the asset-to-debt ratio process, are properly established. Moreover, adapting Rubinstein (1994) approach, a general binomial pyramid algorithm is set up. It is numerically illustrated that the proposed conditional binomial tree model contains the closed-form formula as a limiting case, for vulnerable European options.
Book Synopsis Pricing Derivative Credit Risk by : Manuel Ammann
Download or read book Pricing Derivative Credit Risk written by Manuel Ammann and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Credit risk is an important consideration in most financial transactions. As for any other risk, the risk taker requires compensation for the undiversifiable part of the risk taken. In bond markets, for example, riskier issues generally promise investors a higher yield. The same principle also applies to financial derivatives. Otherwise identical derivative securities will likely have differ ent prices if the counterparties are not of the same credit quality. Although this argument seems intuitively convincing, widely used pricing models for financial derivatives do not incorporate credit risk effects. This research monograph analyzes the effect of credit risk on financial derivatives prices. Credit risk can affect derivatives prices in a variety of ways. First, financial derivatives can be subject to counterparty default risk. Second, a derivative can be written on a security which is subject to credit risk, such as a corporate bond. Third, the credit risk itself can be the un derlying of a derivative instrument. The text focuses on valuation models which take into account counterparty risk but also addresses the other two valuation problems.
Book Synopsis Credit Risk Valuation by : Manuel Ammann
Download or read book Credit Risk Valuation written by Manuel Ammann and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an advanced introduction to models of credit risk valuation, concentrating on firm-value and reduced-form approaches and their application. Also included are new models for valuing derivative securities with credit risk. The book provides detailed descriptions of the state-of-the-art martingale methods and advanced numerical implementations based on multivariate trees used to price derivative credit risk. Numerical examples illustrate the effects of credit risk on the prices of financial derivatives.
Book Synopsis Valuation of Vulnerable European Call Options by : Michael P. Inglis
Download or read book Valuation of Vulnerable European Call Options written by Michael P. Inglis and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a simple model for valuing vulnerable options subject to default risk on the part of the option writer, which we refer to as the "variable default boundary" model. This pricing model allows for the presence of other liabilities in the capital structure of the option writer while recognizing that the growth in the value of the option itself may be a major source of financial distress. This model, retains the attractive features of Johnson and Stulz (1987) and Klein (1996) by linking the payout ratio, in the event of default, to the value of the option writer's assets and by explicitly allowing for correlation between the options writer's assets and the asset underlying the option. It also corrects a defect that occurs in most fixed default boundary models where the pricing equations do not assure that the payment to claimants upon default is no greater than the assets of the option writer. Our model also incorporates stochastic interest rates, using a Vasicek (1979) term structure model. An exact analytical solution to the variable default boundary model is not possible. However, we derive a simple approximate analytical solution, which depends on two parameters. We also develop an algorithm to estimate the optimal values of these parameters. Since Johnson and Stulz (1987) is a special case of our model the approximate analytical solution also provides an analytical solution to their model. Numerical examples compare the results of the approximate analytical solution to results derived from a Monte Carlo simulation. Comparisons to the results from the Black-Scholes-Merton model and the fixed default boundary model of Klein and Inglis (1999) are also given. Along with Klein and Inglis (1999), this thesis provides the only evidence of the importance of stochastic interest rates on the pricing and hedging of vulnerable European calls.
Book Synopsis Pricing Vulnerable Black-Scholes Options With Dynamic Default Barriers by : Cho-Hoi Hui
Download or read book Pricing Vulnerable Black-Scholes Options With Dynamic Default Barriers written by Cho-Hoi Hui and published by . This book was released on 2007 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quot;structural approachquot; to modeling credit risk specifies a stochastic process that the net asset value of the issuing firm is assumed to follow. If firm value falls below a certain quot;default barrier,quot; bankruptcy is triggered and the firm is assumed to default on its vulnerable obligations. In this article, Hui, Lo, and Lee apply the methodology to price vulnerable options written by a default risky firm. They show how a variety of default scenarios may be accommodated by use of a dynamic default barrier, while maintaining a closed-form valuation equation.
Book Synopsis Pricing Vulnerable European Options With Stochastic Default Barriers by : Cho-Hoi Hui
Download or read book Pricing Vulnerable European Options With Stochastic Default Barriers written by Cho-Hoi Hui and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a valuation model of European options incorporating a stochastic default barrier, which extends a constant default barrier proposed in the Hull-White model. The default barrier is considered as an option writer's liability. Closed-form solutions of vulnerable European option values based on the model are derived to study the impact of the stochastic default barriers on option values. The numerical results show that negative correlation between the firm values and the stochastic default barriers of option writers gives material reductions in option values where the options are written by firms with leverage ratios corresponding to BBB or BB ratings.
Book Synopsis Financial Derivatives Pricing by : Robert A. Jarrow
Download or read book Financial Derivatives Pricing written by Robert A. Jarrow and published by World Scientific. This book was released on 2008 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of original papers by Robert Jarrow that contributed to significant advances in financial economics. Divided into three parts, Part I concerns option pricing theory and its foundations. The papers here deal with the famous Black-Scholes-Merton model, characterizations of the American put option, and the first applications of arbitrage pricing theory to market manipulation and liquidity risk.Part II relates to pricing derivatives under stochastic interest rates. Included is the paper introducing the famous HeathOCoJarrowOCoMorton (HJM) model, together with papers on topics like the characterization of the difference between forward and futures prices, the forward price martingale measure, and applications of the HJM model to foreign currencies and commodities.Part III deals with the pricing of financial derivatives considering both stochastic interest rates and the likelihood of default. Papers cover the reduced form credit risk model, in particular the original Jarrow and Turnbull model, the Markov model for credit rating transitions, counterparty risk, and diversifiable default risk.
Book Synopsis Vulnerable Options and Good Deal Bounds - A Structural Model by : Agatha Murgoci
Download or read book Vulnerable Options and Good Deal Bounds - A Structural Model written by Agatha Murgoci and published by . This book was released on 2008 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We price vulnerable options - i.e. options where the counterparty may default. These are basically options traded on the OTC markets. Default is modeled in a structural framework. The technique employed for pricing is Good Deal Bounds. The method imposes a new restriction in the arbitrage free model by setting upper bounds on the Sharpe ratios of the assets. The potential prices which are eliminated represent unreasonably good deal. The constraint on the Sharpe ratio translates into a constraint on the stochastic discount factor. Thus, one can obtain tight pricing bounds. We provide a link between the objective probability measure and the range of potential risk neutral measures which has an intuitive economic meaning. We also provide tight pricing bounds for European calls and show how to extend the call formula to pricing other financial products in a consistent way. Finally, we analyze numerically the behaviour of the good deal pricing bounds.
Book Synopsis Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets by : Holger Kraft
Download or read book Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets written by Holger Kraft and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis summarizes most of my recent research in the field of portfolio optimization. The main topics which I have addressed are portfolio problems with stochastic interest rates and portfolio problems with defaultable assets. The starting point for my research was the paper "A stochastic control ap proach to portfolio problems with stochastic interest rates" (jointly with Ralf Korn), in which we solved portfolio problems given a Vasicek term structure of the short rate. Having considered the Vasicek model, it was obvious that I should analyze portfolio problems where the interest rate dynamics are gov erned by other common short rate models. The relevant results are presented in Chapter 2. The second main issue concerns portfolio problems with default able assets modeled in a firm value framework. Since the assets of a firm then correspond to contingent claims on firm value, I searched for a way to easily deal with such claims in portfolio problems. For this reason, I developed the elasticity approach to portfolio optimization which is presented in Chapter 3. However, this way of tackling portfolio problems is not restricted to portfolio problems with default able assets only, but it provides a general framework allowing for a compact formulation of portfolio problems even if interest rates are stochastic.
Book Synopsis Numerical Analysis Of Stochastic Volatility Jump Diffusion Models by : Abdelilah Jraifi
Download or read book Numerical Analysis Of Stochastic Volatility Jump Diffusion Models written by Abdelilah Jraifi and published by LAP Lambert Academic Publishing. This book was released on 2014-06-30 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the modern economic world, the options contracts are used because they allow to hedge against the vagaries and risks refers to fluctuations in the prices of the underlying assets. The determination of the price of these contracts is of great importance for investors.We are interested in problems of options pricing, actually the European and Quanto options on a financial asset. The price of that asset is modeled by a multi-dimentional jump diffusion with stochastic volatility. Otherwise, the first model considers the volatility as a continuous process and the second model considers it as a jump process. Finally in the 3rd model, the underlying asset is without jump and volatility follows a model CEV without jump. This model allow better to take into account some phenomena observed in the markets. We develop numerical methods that determine the values of prices for these options. We first write the model as an integro-differential stochastic equations system "EIDS," of which we study existence and unicity of solutions. Then we relate the resolution of PIDE to the computation of the option value.
Book Synopsis Pricing American Options on Risky Assets in a Stochastic Interest Rate Economy by : Kaushik I. Amin
Download or read book Pricing American Options on Risky Assets in a Stochastic Interest Rate Economy written by Kaushik I. Amin and published by . This book was released on 1991 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Valuation Under Stochastic Volatility by : Alan L. Lewis
Download or read book Option Valuation Under Stochastic Volatility written by Alan L. Lewis and published by . This book was released on 2000 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Pricing of Options on Assets with Stochastic Volatilities by : John Hull
Download or read book The Pricing of Options on Assets with Stochastic Volatilities written by John Hull and published by . This book was released on 1986 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pricing American Options in a Mild Stochastic Environment by : Moisa Altar
Download or read book Pricing American Options in a Mild Stochastic Environment written by Moisa Altar and published by . This book was released on 2008 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of pricing derivative financial products is central to the theory of capital markets. An option is a financial contract conveying its owner the right of buying or selling a financial asset (underlying asset) at a preset strike price K, at a fixed expiration date T (maturity). Unlike European options, which can be exercised only at maturity date, an American option can be exercised at any time t prior to the maturity date. Most of the option pricing methods, starting with the well-known Black-Scholes model (1973), are based on the assumption that the market uncertainty can be modeled by a Wiener process. In this context, while it is possible to obtain convenient analytical option pricing formulae for European options, it is very difficult to obtain exact results for American options. In the present paper, we assume that the market uncertainty is modeled by a more regular stochastic process, which was called, by A. Halanay, a mild stochastic environment. In this context, we are able to obtain precise stopping rules, determining the exact exercise time and the exact price of an American option.
Book Synopsis Credit Risk: Modeling, Valuation and Hedging by : Tomasz R. Bielecki
Download or read book Credit Risk: Modeling, Valuation and Hedging written by Tomasz R. Bielecki and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The motivation for the mathematical modeling studied in this text on developments in credit risk research is the bridging of the gap between mathematical theory of credit risk and the financial practice. Mathematical developments are covered thoroughly and give the structural and reduced-form approaches to credit risk modeling. Included is a detailed study of various arbitrage-free models of default term structures with several rating grades.
Book Synopsis Relative Pricing of Options with Stochastic Volatility by : Olivier Ledoit
Download or read book Relative Pricing of Options with Stochastic Volatility written by Olivier Ledoit and published by . This book was released on 1998 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper offers a new approach for pricing options on assets with stochastic volatility. We start by constructing the quot;surfacequot; of Black-Scholes implied volatilities for (readily observable) liquid, European call options with varying strike prices and maturities. Then, we show that the implied volatility of an at-the-money call option with time-to-maturity going tozero is equal to the underlying asset's instantaneous (stochastic) volatility. We then model the stochastic processes followed by the implied volatilities of options of all maturities and strike prices jointly with the stock price, and find a no-arbitrage condition that their drift must satisfy. Finally, we use the resulting arbitrage-free joint process for the stock price and its volatility to price other derivatives, such as standard but illiquid options as well as exotic options using numerical methods. The great advantage of our approach is that, when pricing these other derivatives, we are secure in the knowledge that the model values the hedging instruments - namely the stock and the simple, liquid options - consistently with the market. Our approach can easily be extended to allow for stochastic interest rates and a stochastic dividend yield, which may be particularly relevant to the pricing of currency and commodity options. We can also extend our model to price bond options when the term structure of interest rates has stochastic volatility.
Book Synopsis On Stochastic Dominance Optionbounds in Discrete and Continuous Space and Time with Stochastic and Deterministic Volatility and Pricing with Constant Relative Risk Aversion by : Eli Rose
Download or read book On Stochastic Dominance Optionbounds in Discrete and Continuous Space and Time with Stochastic and Deterministic Volatility and Pricing with Constant Relative Risk Aversion written by Eli Rose and published by . This book was released on 2020 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis makes original contributions to the field of asset pricing, which is a field dedicated to describing the prices of financial instruments and their characteristics. The prices of these financial instruments are determined by the behavior of investors who buy and sell them, and so asset pricing is ultimately done by modeling the behavior of investors. One method for achieving this is through the framework of stochastic dominance. This thesis specifically deals with a specific class of financial instruments called European options and reviews the literature on stochastic dominance option pricing and discusses new methods for finding stochastic dominance bounds on options in both discrete and continuous time under both deterministic and stochastic volatility. The results presented here extends the works of Ritchken and Kuo (1988) and Perrakis and Ryan (1984). Furthermore, stochastic dominance bounds for Heston's (1993) stochastic volatility model are obtained under certain assumptions. Finally, this thesis extends the work of Carr and Madan (1999) and solves for the characteristic function of the call price given the physical characteristic function under the CRRA utility model.
