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Register a new userEquity warrant pricing under subdiffusive fractional Brownian motion of the short rate
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In this paper we propose an extension of the Merton model. We apply the subdiffusive mechanism to analyze equity warrant in a fractional Brownian motion environment, when the short rate follows the subdiffusive fractional Black-Scholes model. We obtain the pricing formula for zero-coupon bond in the introduced model and derive the partial differential equation with appropriate boundary conditions for the valuation of equity warrant. Finally, the pricing formula for equity warrant is provided under subdiffusive fractional Brownian motion model of the short rate.
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The purpose of this paper is to analyze the problem of option pricing when the short rate follows subdiffusive fractional Merton model. We incorporate the stochastic nature of the short rate in our option valuation model and derive explicit formula for call and put option and discuss the corresponding fractional Black-Scholes equation. We present some properties of this pricing model for the cases of $alpha$ and $H$. Moreover, the numerical simulations illustrate that our model is flexible and easy to implement.
A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign currency option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The minimal price of a currency option under transaction costs is obtained as time-step $Delta t=left(frac{t^{beta-1}}{Gamma(beta)}right)^{-1}left(frac{2}{pi}right)^{frac{1}{2H}}left(frac{alpha}{sigma}right)^{frac{1}{H}}$ , which can be used as the actual price of an option. In addition, we also show that time-step and long-range dependence have a significant impact on option pricing.
This study deals with the problem of pricing compound options when the underlying asset follows a mixed fractional Brownian motion with jumps. An analytic formula for compound options is derived under the risk neutral measure. Then, these results are applied to value extendible options. Moreover, some special cases of the formula are discussed and numerical results are provided.
The Wiener-Hopf factorization is obtained in closed form for a phase type approximation to the CGMY L{e}vy process. This allows, for the approximation, exact computation of first passage times to barrier levels via Laplace transform inversion. Calibration of the CGMY model to market option prices defines the risk neutral process for which we infer the first passage times of stock prices to 30% of the price level at contract initiation. These distributions are then used in pricing 50% recovery rate equity default swap (EDS) contracts and the resulting prices are compared with the prices of credit default swaps (CDS). An illustrative analysis is presented for these contracts on Ford and GM.
Replacing Black-Scholes driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented in the financial market. We present the development, testing, and implementation of a simplified alternative to using fractional Brownian motion for pricing derivatives. By relaxing the assumption of past independence of Brownian motion but retaining the Markovian property, we are developing a competing model that retains the mathematical simplicity of the standard Black-Scholes model but also has the improved accuracy of allowing for past dependence. This is achieved by replacing Black-Scholes underlying process, Brownian motion, with a particular Gaussian Markov process, proposed by Vladimir Dobri{c} and Francisco Ojeda.
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