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Option Pricing With Unobserved And Regime Switching Volatility
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Book Synopsis Option Pricing with Unobserved and Regime-Switching Volatility by : Sean D. Campbell
Download or read book Option Pricing with Unobserved and Regime-Switching Volatility written by Sean D. Campbell and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we use a regime-switching process to model the unobserved volatility of the underlying asset and derive a closed-form, risk-neutral option pricing formula. Specifically, our model implies the state price density (SPD) is a time-varying mixture of normals which can provide for time-varying excess kurtosis and skewness as agents learn about the state of volatility from realized returns. Furthermore, we show that our model generates the kinds of volatility quot;smilesquot; commonly found in option markets. We apply our two and three regime models to weekly Samp;P 500 option data and find our model fits the data better than other popular pricing models. Additionally, we find evidence that stock returns can be well-described by a markov switching framework with a very persistent low volatility regime followed by a less persistent moderate volatility regime and a highly non-persistent crash regime. Our estimation results don't suffer the so called quot;Peso Problemquot; as they come from option prices instead of the observed stock returns.
Book Synopsis Options Pricing and Hedging in a Regime-Switching Volatility Model by : Melissa Anne Mielkie
Download or read book Options Pricing and Hedging in a Regime-Switching Volatility Model written by Melissa Anne Mielkie and published by . This book was released on 2014 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both deterministic and stochastic volatility models have been used to price and hedge options. Observation of real market data suggests that volatility, while stochastic, is well modelled as alternating between two states. Under this two-state regime-switching framework, we derive coupled pricing partial differential equations (PDEs) with the inclusion of a state-dependent market price of volatility risk (MPVR) term. Since there is no closed-form solution for this pricing problem, we apply and compare two approaches to solving the coupled PDEs, assuming constant Poisson intensities. First we solve the problem using numerical solution techniques, through the application of the Crank- Nicolson numerical scheme. We also obtain approximate solutions in terms of known Black- Scholes formulae by reformulating our problem and applying the Cauchy-Kowalevski PDE theorem. Both our pricing equations and our approximate solutions give way to the analysis of the impact of our state-dependent MPVR on theoretical option prices. Using financially intuitive constraints on our option prices and Deltas, we prove the necessity of a negative MPVR. An exploration of the regime-switching option prices and their implied volatilities is given, as well as numerical results and intuition supporting our mathematical proofs. Given our regime-switching framework, there are several different hedging strategies to investigate. We consider using an option to hedge against a potential regime shift. Some practical problems arise with this approach, which lead us to set up portfolios containing a basket of two hedging options. To be more precise, we consider the effects of an option going too far in- and out-of-the-money on our hedging strategy, and introduce limits on the magnitude of such hedging option positions. A complementary approach, where constant volatility is assumed and investor's risk preferences are taken into account, is also analysed. Analysis of empirical data supports the hypothesis that volatility levels are a effected by upcoming financial events. Finally, we present an extension of our regime-switching framework with deterministic Poisson intensities. In particular, we investigate the impact of time and stock varying Poisson intensities on option prices and their corresponding implied volatilities, using numerical solution techniques. A discussion of some event-driven hedging strategies is given.
Book Synopsis An Option Pricing Model with Regime-Switching Economic Indicators by : Zongming Jr Ma
Download or read book An Option Pricing Model with Regime-Switching Economic Indicators written by Zongming Jr Ma and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing Under Regime Switching (analytical, PDE, and FFT Methods) by : Mohammad Yousef Akhavein Sohrabi
Download or read book Option Pricing Under Regime Switching (analytical, PDE, and FFT Methods) written by Mohammad Yousef Akhavein Sohrabi and published by . This book was released on 2011 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although globally used in option pricing, the Black-Scholes model has not been able to reflect the evolution of stocks in the real world. A regime-switching model which allows jumps in the underlying asset prices and the parameters of the corresponding stochastic process is more accurate. We evaluate the analytical solution for pricing of European options under a two-state regime switching model. Both the convergence of the analytical solution and the feature of implied volatility are investigated through numerical examples.
Book Synopsis Investigating the Market Price of Volatility Risk for Options in a Regime-Switching Market by : Melissa Mielkie
Download or read book Investigating the Market Price of Volatility Risk for Options in a Regime-Switching Market written by Melissa Mielkie and published by . This book was released on 2013 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: To bridge the gap between the output of theoretical option pricing models and observed option prices on exchanges, it is necessary to price the volatility risk inherent in financial markets. Non zero market risk premia have been found in previous financial literature through an exploration of market data, quantifying the relationship between implied and realized volatility. Building upon previous work by Mielkie and Davison (2013) where an approximate solution was derived for options written on underlying assets with regime-switching volatility, we analyze the impact of the market price of volatility risk on theoretical option prices. Using financially intuitive constraints, we prove the necessity of placing restrictions on the market prices of volatility risk in order to get reasonable option prices. In particular, we show that negative state-dependent market prices of volatility risk are necessary in order for the option prices and corresponding hedge ratios to be financially rational. An exploration of the regime-switching option prices and their implied volatilities is given, as well as numerical results and intuition supporting our mathematical proofs.
Book Synopsis Option Pricing when the Regime-switching Risk is Priced by : Tak Kuen Siu
Download or read book Option Pricing when the Regime-switching Risk is Priced written by Tak Kuen Siu and published by . This book was released on 2007 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing with Continuous-time Markov Chain Regime Switching by : Craig Steven Edwards
Download or read book Option Pricing with Continuous-time Markov Chain Regime Switching written by Craig Steven Edwards and published by . This book was released on 2004 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing and Hedging Analysis Under Regime-switching Models by : Chao Qiu
Download or read book Option Pricing and Hedging Analysis Under Regime-switching Models written by Chao Qiu and published by . This book was released on 2013 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis explores option pricing and hedging in a discrete time regime-switching environment. If the regime risk cannot be hedged away, then we cannot ignore this risk and use the Black-Scholes pricing and hedging framework to generate a unique pricing and hedging measure. We develop a risk neutral pricing measure by applying an Esscher Transform to the real world asset price process, with the focus on the issue of incompleteness of the market. The Esscher transform turns out to be a convenient and effective tool for option pricing under the discrete time regime switching models. We apply the pricing measure to both single variate European options and multivariate options. To better understand the effect of the pricing method, we also compared the results with those generated from two other risk neutral methods: the Black-Scholes model, and the natural equivalent martingale method. We further investigate the difference in hedging associated with different pricing measures. This is of interest when the choice of pricing method is uncertain under regime switching models. We compare four hedging strategies: delta hedging for the three risk neutral pricing methods under study, and mean variance hedging. We also develop a more general tool of tail ordering for hedging analysis in a general incomplete market with the uncertainty of the risk neutral measures. As a result of the analysis, we propose that pricing and hedging using the Esscher transform may be an effective strategy for a market where the regime switching process brings uncertainty.
Book Synopsis Option Pricing and Regime-switching by : John Driffill
Download or read book Option Pricing and Regime-switching written by John Driffill and published by . This book was released on 2000 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Regime-switching Option Pricing Models by : Amalia Christoforidou
Download or read book Regime-switching Option Pricing Models written by Amalia Christoforidou and published by . This book was released on 2015 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing Under Regime-Switching Models by : Frédéric Godin
Download or read book Option Pricing Under Regime-Switching Models written by Frédéric Godin and published by . This book was released on 2018 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although option pricing schemes in regime-switching frameworks were extensively explored in the literature, many models developed disregard the unobservability of regimes. In such a context, the traditional pricing approach pioneered by Hardy (2001) applied to vanilla options exhibits path-dependence even if the underlying asset price process can be embedded in a Markov process. This property is deemed counterintuitive and puzzling, warranting explanations and alternatives. The current work develops novel risk-neutral measures which remove the path-dependence issue. Pricing approaches based on dynamic programming and Monte-Carlo simulations which rely on the latter measures are illustrated.
Book Synopsis Option Pricing and Estimation of Financial Models with R by : Stefano M. Iacus
Download or read book Option Pricing and Estimation of Financial Models with R written by Stefano M. Iacus and published by John Wiley & Sons. This book was released on 2011-02-23 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
Book Synopsis Option Pricing and Hedging for Discrete Time Regime-Switching Models by : Bruno Remillard
Download or read book Option Pricing and Hedging for Discrete Time Regime-Switching Models written by Bruno Remillard and published by . This book was released on 2014 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose optimal mean-variance dynamic hedging strategies in discrete time under a multivariate Gaussian regime-switching model. The methodology, which also performs pricing, is robust to time-varying and clustering risk observed in financial time series. As such, it overcomes the main theoretical drawbacks of the Black-Scholes model. To support our approach, we provide univariate pricing results for monthly S&P 500 vanilla options. Then, we present the associated out-of-sample hedging results in the context of harvesting the implied versus realized volatility premium. Using the proposed methodology, the Sharpe ratio derived from the strategy doubles over the classical Black-Scholes delta-hedging methodology.
Book Synopsis Option Pricing with Anomalous Scaling and Infinite-State Switching Volatility by : Fulvio Baldovin
Download or read book Option Pricing with Anomalous Scaling and Infinite-State Switching Volatility written by Fulvio Baldovin and published by . This book was released on 2013 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volatility clustering, long-range dependence, non-Gaussianity and anomalous scaling are all well-known stylized facts of financial assets return dynamics. These elements have a relevant impact on the aptness of models for the pricing of options written on financial assets. We make us of a model developed in physics that captures the previously cited returns features. The model allows deriving closed form equations for option pricing. We present the model providing a financial interpretation of its components and discuss the parameters estimation. We then derive pricing equations and use them in an empirical application based on a major equity index option dataset.
Book Synopsis Perpetual American Vanilla Option Pricing Under Single Regime Change Risk - An Exhaustive Study by : Miquel Montero
Download or read book Perpetual American Vanilla Option Pricing Under Single Regime Change Risk - An Exhaustive Study written by Miquel Montero and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in which some of the properties volatility and dividend policy of the underlying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because most relevant facts usually entail sharp predictable consequences. The effect of this potential risk on perpetual American vanilla options is remarkable: the very equation that will determine the fair price depends on the solution to be found. Sound results are found under the optics both of finance and physics. In particular, a parallelism among the overall outcome of this problem and a phase transition is established.
Book Synopsis Pricing American Options in Regime-Switching Models by : Svetlana Boyarchenko
Download or read book Pricing American Options in Regime-Switching Models written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pricing problem for American options in Markov-modulated Lévy models is solved. The early exercise boundaries and prices are calculated using a generalization of Carr's randomization procedure for regime-switching models. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. In contrast with the earlier version of the method, an explicit algorithm is formulated for wide classes of Lévy processes, and FFT and iFFT are used.
Book Synopsis Option Pricing Under Alternative Regime Switching Specifications by : Kyriakos Chourdakis
Download or read book Option Pricing Under Alternative Regime Switching Specifications written by Kyriakos Chourdakis and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
