Valuation Of Path Dependent Options
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Author | : Chunsheng Zhou |
Publisher | : |
Total Pages | : 21 |
Release | : 1997 |
Genre | : |
ISBN | : |
The payoffs of path-dependent options depend not only on the nal values, but also on the sample paths of the prices of the underlying assets. A rigorous modeling of the under-lying asset price processes which can appropriately describe the sample paths is therefore critical for pricing path-dependent options. This paper allows for discontinuities in the sample paths of the underlying asset prices by assuming that these prices follow jump di usion processes. A general yet tractable approach is presented to value a variety of path-dependent options with discontinuous processes. The numerical examples show that ignoring the jump risk may lead to serious biases in path- dependent option pricing.
Author | : Eric S. Reiner |
Publisher | : |
Total Pages | : |
Release | : 1991 |
Genre | : |
ISBN | : |
Author | : Marek Capiński |
Publisher | : Cambridge University Press |
Total Pages | : 179 |
Release | : 2012-09-13 |
Genre | : Business & Economics |
ISBN | : 1107001692 |
Master the essential mathematical tools required for option pricing within the context of a specific, yet fundamental, pricing model.
Author | : Stefan Scholz |
Publisher | : |
Total Pages | : 187 |
Release | : 2002 |
Genre | : |
ISBN | : |
Author | : Bin Gao |
Publisher | : |
Total Pages | : 47 |
Release | : 2009 |
Genre | : |
ISBN | : |
In this paper, we propose a general method for pricing and hedging non-standard American options. The proposed method applies to any kind of American-style contract for which the payoff function has a Markovian representation in the state space. Specifically, we obtain an analytic solution for the value and hedge parameters of path-dependent American options such as barrier options. The solution includes standard American options as a special case. The analytic formula also allows us to identify and exploit two key properties of the optimal exercise boundary-homogeneity in price parameters and time-invariance acirc;not; for American options. In addition, some new put-call acirc;not;Ssymmetryacirc;not;? relations are also derived. These properties suggest a new, efficient and integrated approach to pricing and hedging a variety of standard and non-standard American options. From an implementation perspective, this approach avoids the current practice of repetitive computation of options prices and hedge ratios. Our implementation of the analytic formula for barrier options indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. In some cases, our method is faster by about four orders of magnitude than existing numerical methods with equal accuracy. In particular, the method overcomes the difficulty that existing numerical methods have in dealing with prices close to the barrier, the case where the barrier matters most.
Author | : Andrew Matacz |
Publisher | : |
Total Pages | : 22 |
Release | : 2001 |
Genre | : |
ISBN | : |
In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computational burden placed on the subsequent numerical evaluation. For short-medium term options it leads to a general approximation formula that only requires the evaluation of a one dimensional integral. I illustrate the application of the method to Asian options and occupation time derivatives.
Author | : Chunsheng Zhou |
Publisher | : |
Total Pages | : 44 |
Release | : 1997 |
Genre | : Derivative securities |
ISBN | : |
Author | : Bin Gao |
Publisher | : |
Total Pages | : 59 |
Release | : 1996 |
Genre | : Options (Finance) |
ISBN | : |
Author | : Peter Guangping Zhang |
Publisher | : World Scientific |
Total Pages | : 696 |
Release | : 1998-06-17 |
Genre | : Business & Economics |
ISBN | : 9814496146 |
This is the first systematic and extensive book on exotic options. The book covers essentially all popular exotic options currently trading in the Over-the-Counter (OTC) market, from digitals, quantos, spread options, lookback options, Asian options, vanilla barrier options, to various types of exotic barrier options and other options. Each type of exotic options is largely written in a separate chapter, beginning with the basic concepts of the products and then moving on to how to price them in closed-form solutions. Many pricing formulae and analyses which have not previously appeared in the literature are included and illustrated with detailed examples. It will be of great interest to traders, marketers, analysts, risk managers, professors, graduate students, and anyone who is interested in what is going on in the rapidly changing financial market.
Author | : Gudbjort Gylfadottir |
Publisher | : |
Total Pages | : |
Release | : 2010 |
Genre | : |
ISBN | : |
ABSTRACT: This dissertation is concerned with the pricing of path-dependent options where the underlying asset is modeled as a continuous-time exponential Lévy process and is monitored at discrete dates. These options enable their users to tailor random payoff outcomes to their particular risk profiles and are widely used by hedgers such as large multinational corporations and speculators alike. The use of continuous-time models since the breakthrough paper of Black and Scholes has been greatly facilitated by advances in stochastic calculus and the mathematical elegance it provides. The recent financial crisis started in 2008 has highlighted the importance of models that incorporate the possibility of sudden, large jumps as well as the higher likelihood of adverse outcomes as compared with the classical Black-Scholes model. Increasingly, exponential Lévy processes have become preferred alternatives, thanks in particular to the explicit Lévy-Khinchin representation of their characteristic functions. On the other hand, the restriction of monitoring dates to a discrete set increases the mathematical and computational complexity for the pricing of path-dependent options even in the classical Black-Scholes model. This dissertation develops new techniques based on recent advances in the fast evaluation and inversion of Fourier and Hilbert transforms as well as classical results in fluctuation theory, particularly those involving random walk duality and ladder epochs.