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Pricing Vulnerable European Options With Stochastic Default Barriers
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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 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 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 Incorporating Default Risk Into the Black-Scholes Model Using Stochastic Barrier Option Pricing Theory by : Don R. Rich
Download or read book Incorporating Default Risk Into the Black-Scholes Model Using Stochastic Barrier Option Pricing Theory written by Don R. Rich and published by . This book was released on 1993 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pricing the Vulnerable American Options by : Jun (James) Yang
Download or read book Pricing the Vulnerable American Options written by Jun (James) Yang and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis extends the models of Johnson and Stulz (1997), Klein (1996) and Klein and Inglis (2001) to price vulnerable American options. Most existing models mainly focus on the pricing of vulnerable European options, especially call options. This thesis focuses on vulnerable American options and especially put options. The model incorporates the default boundary at the time of maturity as in Klein and Inglis (2001), and allows the default barrier before maturity changes with the underlying asset price. The thesis compares the vulnerable American options with vanilla American options and studies some interesting properties of vulnerable American options under the assumption, which are quite different from those of vanilla American options.
Book Synopsis Efficient Pricing Barrier Options and CDS in Lévy Models with Stochastic Interest Rate by : Svetlana Boyarchenko
Download or read book Efficient Pricing Barrier Options and CDS in Lévy Models with Stochastic Interest Rate written by Svetlana Boyarchenko and published by . This book was released on 2015 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, advantages of conformal deformations of the contours of integration in pricing formulas for European options have been demonstrated in the context of wide classes of L'evy models, the Heston model and other affine models. Similar deformations were used in one-factor L'evy models to price options with barrier and lookback features and CDSs. In the present paper, we generalize this approach to models of structural default, where the dynamics of assets follows an exponential L'evy process $X_t$, and the interest rate $r_t$ is stochastic. Assuming that $X_t$ and $r_t$ are independent, and the infinitesimal generator of the pricing semigroup in the model for the short rate, is (block)-diagonalizable, we develop a variation of the pricing procedure for L'evy models which is almost as fast as in the case of the constant interest rate. Numerical examples show that about 0.15 sec suffice to calculate prices of 8 options of same maturity in a two-factor model with the error tolerance $5 cdot 10^{-5}$ sec. and less; in a three-factor model, accuracy of order 0.001-0.005 is achieved in about 0.2 sec. Similar results are obtained for quanto CDS, where an additional stochastic factor is the exchange rate. We suggest a class of L'evy models with the stochastic interest rate driven by 1-2 (possibly, 3) factors, which allows for fast calculations. This class can satisfy the current requirements by regulators for banks to have sufficiently sophisticated credit risk models.
Book Synopsis Pricing Some European-style Options with Stochastic Volatility by : Siti Nur Iqmal Ibrahim
Download or read book Pricing Some European-style Options with Stochastic Volatility written by Siti Nur Iqmal Ibrahim and published by . This book was released on 2013 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Barrier Options Pricing in the Heston Stochastic Volatility Model by : Vitalija Alisauskaite
Download or read book Barrier Options Pricing in the Heston Stochastic Volatility Model written by Vitalija Alisauskaite and published by . This book was released on 2010 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of Banking & Finance written by and published by . This book was released on 2001 with total page 1332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pricing Derivatives With Barriers in a Stochastic Interest Rate Environment by : Carole Bernard
Download or read book Pricing Derivatives With Barriers in a Stochastic Interest Rate Environment written by Carole Bernard and published by . This book was released on 2010 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a general valuation approach to price barrier options when the term structure of interest rates is stochastic. These products' barriers may be constant or stochastic, in particular we examine the case of discounted barriers (at the instantaneous interest rate). So, in practice, we extend Rubinstein and Reiner (1991), who give closed-form formulas for pricing barrier options in a Black and Scholes context, to the case of a Vasicek modeling of interest rates. We are therefore in the situation of pricing barrier options semi-explicitly or explicitly (depending on the shape of the barrier) with stochastic Vasicek interest rates. The model is illustrated with a specific contract, an up and out call with rebate, hence a typical barrier option. This example is merely here to show how any standard barrier option can be priced and its Greeks be obtained in such a context. The validity of the approximation is analyzed and the sensitivity to the barrier level and to discretization schemes are also derived.
Book Synopsis Pricing Window Barrier Options with a Hybrid Stochastic-Local Volatility Model by : Yu Tian
Download or read book Pricing Window Barrier Options with a Hybrid Stochastic-Local Volatility Model written by Yu Tian and published by . This book was released on 2014 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present our research on pricing window barrier options under a hybrid stochastic-local volatility (SLV) model in the foreign exchange (FX) market. Due to the hybrid effect of the local volatility and stochastic volatility components of the model, the SLV model can reproduce the market implied volatility surface, and can improve the pricing accuracy for exotic options at the same time. In this paper, numerical techniques such as Monte Carlo and finite difference methods for standard exotic barrier options under the SLV model are extended to pricing window barrier options and numerical results produced by the SLV model are used to examine the performance and accuracy of the model for pricing window barrier options.
Book Synopsis How Important is a Variable Default Boundary when Pricing Vulnerable European Options? by : Michael C. H. Au
Download or read book How Important is a Variable Default Boundary when Pricing Vulnerable European Options? written by Michael C. H. Au and published by . This book was released on 1997 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analytic Methods for Pricing Double Barrier Options in the Presence of Stochastic Volatility by : Oliver Faulhaber
Download or read book Analytic Methods for Pricing Double Barrier Options in the Presence of Stochastic Volatility written by Oliver Faulhaber and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Exact Pricing with Stochastic Volatility and Jumps by : Fernanda D'Ippoliti
Download or read book Exact Pricing with Stochastic Volatility and Jumps written by Fernanda D'Ippoliti and published by . This book was released on 2014 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stochastic volatility jump-diffusion model for pricing derivatives with jumps in both spot returns and volatility dynamics is presented. This model admits, in the spirit of Heston, a closed-form solution for European-style options. The structure of the model is also suitable to obtain the fair delivery price of variance swaps. To evaluate derivatives whose value does not admit a closed-form expression, a methodology based on an "exact algorithm'', in the sense that no discretization of equations is required, is developed and applied to barrier options. Goodness of pricing algorithm is tested using DJ Euro Stoxx 50 market data for European options. Finally, the algorithm is applied to compute prices and Greeks of barrier options.
Download or read book The Journal of Derivatives written by and published by . This book was released on 2002 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis European Option Pricing with Stochastic Bond Prices by : Bruno H. Solnik
Download or read book European Option Pricing with Stochastic Bond Prices written by Bruno H. Solnik and published by . This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Perturbation Methods in Applied Mathematics by : J. Kevorkian
Download or read book Perturbation Methods in Applied Mathematics written by J. Kevorkian and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised and updated version, including a substantial portion of new material, of J. D. Cole's text Perturbation Methods in Applied Mathe matics, Ginn-Blaisdell, 1968. We present the material at a level which assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate level course on the subject. The applied mathematician, attempting to understand or solve a physical problem, very often uses a perturbation procedure. In doing this, he usually draws on a backlog of experience gained from the solution of similar examples rather than on some general theory of perturbations. The aim of this book is to survey these perturbation methods, especially in connection with differ ential equations, in order to illustrate certain general features common to many examples. The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations. In essence, a perturbation procedure consists of constructing the solution for a problem involving a small parameter B, either in the differential equation or the boundary conditions or both, when the solution for the limiting case B = 0 is known. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of B.
