On Dufresne’s translated perpetuity and some Black-Scholes annuities
نویسنده
چکیده
Let (Et, t ≥ 0) be a geometric Brownian motion. In this paper, we compute the law of a generalization of Dufresne’s translated perpetuity (following the terminology of Salminen-Yor) : ∫ +∞ 0 E s (E2 s + 2aEs + b)2 ds, and show that, in some cases, this perpetuity is identical in law with the first hitting time of a threedimensional Bessel process with drift. We also study the law of the following couple of annuities (∫ t
منابع مشابه
On Black-Scholes equation; method of Heir-equations, nonlinear self-adjointness and conservation laws
In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.
متن کاملRobustly Hedging Variable Annuities with Guarantees Under Jump and Volatility Risks
Accurately quantifying and robustly hedging options embedded in the guarantees of variable annuities is a crucial task for insurance companies in preventing excessive liabilities. Due to sensitivities of the benefits to tails of the account value distribution, a simple Black-Scholes model is inadequate. A model which realistically describes the real world price dynamics over a long time horizon...
متن کاملEuropean option pricing of fractional Black-Scholes model with new Lagrange multipliers
In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...
متن کاملNumerical algorithm for discrete barrier option pricing in a Black-Scholes model with stationary process
In this article, we propose a numerical algorithm for computing price of discrete single and double barrier option under the emph{Black-Scholes} model. In virtue of some general transformations, the partial differential equations of option pricing in different monitoring dates are converted into simple diffusion equations. The present method is fast compared to alterna...
متن کاملModifying the Black-Scholes model to valuate preemption right
In this paper, we try and valuate preemption rights by modifying the Black-Scholes model, which is widely used to valuate options and other derivatives. Here we first present the basics of the Black-Scholes model and then we discus modification of the model to be fit for preemption right valuation. At the end, we valuate four of the preemptive rights using the proposed model
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013