Matched asymptotic expansions in financial engineering
نویسنده
چکیده
Modern financial practice depends heavily on mathematics and a correspondingly large theory has grown up to meet this demand. This paper focuses on the use of matched asymptotic expansions in option pricing; it presents illustrations of the approach in ‘plain vanilla’ option valuation, in valuation using a fast mean-reverting-stochastic volatility model, and in a model for illiquid markets. A tentative framework for matched asymptotic expansions applied directly to stochastic processes of diffusion type is also proposed.
منابع مشابه
Freezing in a Finite Slab Using Extensive Perturbation Expansions Method
In this paper Mathematica is used to solve the moving boundary problem of freezing in a finite slab for higher order perturbations. Mathematica is a new system which makes it possible to do algebra with computer. More specifically, it enables researchers to find the location of the ice at any time for as high order of perturbation as one whishes. Using of Mathematica and outer solution and an i...
متن کاملTransient Natural Convection Flow on an Isothermal Vertical Wall at High Prandtl Numbers: Second-Order Approximation
The method of matched asymptotic expansions, which has been used in previous studies of steady natural convection flow, is extended here to transient natural convection flow at high Prandtl number (Pr). Second-order expansion solutions, valid for large Prandtl numbers, are presented for the transient natural convection flow near a vertical surface which undergoes a step change in temperature. T...
متن کاملSecond Order Moment Asymptotic Expansions for a Randomly Stopped and Standardized Sum
This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright} where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of ran...
متن کاملComparison of the Matched Asymptotic Expansions Method
Either the matched asymptotic expansions method or the two-variable technique are available for treating boundary layer problems. A comparison of the two methods is achieved on dealing with elliptic boundary value problems. The two-variable technique is proved to be slightly more powerful than the matched expansions method. Nevertheless it fails to determine a closed class of approximate soluti...
متن کاملStokes Phenomenon and Matched Asymptotic Expansions
This paper describes the use of matched asymptotic expansions to illuminate the description of functions exhibiting Stokes phenomenon. In particular the approach highlights the way in which the local structure and the possibility of finding Stokes multipliers explicitly depend on the behaviour of the coefficients of the relevant asymptotic expansions.
متن کامل