Equity warrants pricing model under Fractional Brownian motion and an empirical study
TL;DR: This paper construct equity warrants pricing model under Fractional Brownian motion, deduce the European options pricing formula with a simple method, then propose the warrants pricing formula, and extend it to cover equity warrants on a stock providing dividends.
Abstract: In this paper, we construct equity warrants pricing model under Fractional Brownian motion, deduce the European options pricing formula with a simple method, then propose the warrants pricing formula, and extend it to cover equity warrants on a stock providing dividends. Finally, taking Changdian warrant in Chinese stock market as an example, we illustrate that the results based on the new warrants pricing formula is more accuracy than the classical results based on traditional pricing model.
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TL;DR: In this paper, the problem of pricing European currency options in the mixed fractional Brownian environment is dealt with and both the pricing formula and the mixed-fractional partial differential equation for European call currency options are obtained.
Abstract: This paper deals with the problem of pricing European currency options in the mixed fractional Brownian environment. Both the pricing formula and the mixed fractional partial differential equation for European call currency options are obtained. Some Greeks and the estimator of volatility are also provided. Empirical studies and simulation results confirm the theoretical findings and show that the mixed fractional Brownian pricing model is a reasonable one.
53 citations
TL;DR: In this article, the authors proposed a general foreign equity option pricing framework that unifies the vast foreign-equity option pricing literature and incorporates the stochastic volatility into FEE pricing, where the time-changed Levy processes are used to model the underlying assets price of foreign equity options and the closed form pricing formula is obtained through the use of characteristic function methodology.
Abstract: In this paper we propose a general foreign equity option pricing framework that unifies the vast foreign equity option pricing literature and incorporates the stochastic volatility into foreign equity option pricing. Under our framework, the time-changed Levy processes are used to model the underlying assets price of foreign equity option and the closed form pricing formula is obtained through the use of characteristic function methodology. Numerical tests indicate that stochastic volatility has a dramatic effect on the foreign equity option prices.
15 citations
TL;DR: A pricing formula is derived for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion and it is applied to price Asian power options on the stocks that pay constant dividends when the payoff is a power function.
14 citations
Cites background from "Equity warrants pricing model under..."
...Fractional Brownian motion has been suggested to display the long-range dependence and fluctuation observed in the empirical data [2, 3, 4]....
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TL;DR: In this paper, a combination of maximum likelihood approach and Powell's method was used to estimate the parameters of mixed Brownian-fractional Brownian motions. But the performance of this method was not compared with the approach proposed by Filatova (2008).
10 citations
10 citations
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TL;DR: In this paper, a theoretical valuation formula for options is derived, based on the assumption that options are correctly priced in the market and it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks.
Abstract: If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.
28,434 citations
Book•
01 Jan 1982
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
24,199 citations
8,252 citations
01 Jul 1984
TL;DR: A blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) is presented in this article.
Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
7,560 citations
TL;DR: In this article, an intertemporal model for the capital market is deduced from portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time.
Abstract: An intertemporal model for the capital market is deduced from the portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time. Explicit demand functions for assets are derived, and it is shown that, unlike the one-period model, current demands are affected by the possibility of uncertain changes in future investment opportunities. After aggregating demands and requiring market clearing, the equilibrium relationships among expected returns are derived, and contrary to the classical capital asset pricing model, expected returns on risky assets may differ from the riskless rate even when they have no systematic or market risk. ONE OF THE MORE important developments in modern capital market theory is the Sharpe-Lintner-Mossin mean-variance equilibrium model of exchange, commonly called the capital asset pricing model.2 Although the model has been the basis for more than one hundred academic papers and has had significant impact on the non-academic financial community,' it is still subject to theoretical and empirical criticism. Because the model assumes that investors choose their portfolios according to the Markowitz [21] mean-variance criterion, it is subject to all the theoretical objections to this criterion, of which there are many.4 It has also been criticized for the additional assumptions required,5 especially homogeneous expectations and the single-period nature of the model. The proponents of the model who agree with the theoretical objections, but who argue that the capital market operates "as if" these assumptions were satisfied, are themselves not beyond criticism. While the model predicts that the expected excess return from holding an asset is proportional to the covariance of its return with the market
6,294 citations