Likelihood Ratio Method and Algorithmic Differentiation: Fast Second Order Greeks
نویسنده
چکیده
We show how Adjoint Algorithmic Differentiation can be combined with the so-called Pathwise Derivative and Likelihood Ratio Method to construct efficient Monte Carlo estimators of second order price sensitivities of derivative portfolios. We demonstrate with a numerical example how the proposed technique can be straightforwardly implemented to greatly reduce the computation time of second order risk.
منابع مشابه
Monte Carlo evaluation of sensitivities in computational finance
In computational finance, Monte Carlo simulation is used to compute the correct prices for financial options. More important, however, is the ability to compute the so-called “Greeks”, the first and second order derivatives of the prices with respect to input parameters such as the current asset price, interest rate and level of volatility. This paper discusses the three main approaches to comp...
متن کاملAAD and least-square Monte Carlo: Fast Bermudan-style options and XVA Greeks
We show how Adjoint Algorithmic Differentiation (AAD) can be used to calculate price sensitivities in regression-based Monte Carlo methods reliably and orders of magnitude faster than with standard finite-difference approaches. We present the AAD version of the celebrated least-square algorithms of Tsitsiklis and Van Roy (2001) and Longstaff and Schwartz (2001). By discussing in detail examples...
متن کاملFast Greeks by algorithmic differentiation
We show how algorithmic differentiation can be used to efficiently implement the pathwise derivative method for the calculation of option sensitivities using Monte Carlo simulations. The main practical difficulty of the pathwise derivative method is that it requires the differentiation of the payout function. For the type of structured options for which Monte Carlo simulations are usually emplo...
متن کاملCalibration in Finance: Very Fast Greeks Through Algorithmic Differentiation and Implicit Function
Adjoint Algorithmic Differentiation is an efficient way to obtain price derivatives with respect to the data inputs. We describe how the process efficiency can be further improved when a model calibration is performed. Using the implicit function theorem, differentiating the numerical process used in calibration is not required. The resulting implementation is more efficient than automatic diff...
متن کاملHigher Order Approximations for Derivatives using Hypercomplex-Steps
Complex-step differentiation is a recent popular method to compute a real valued function and its first derivative approximately with second order error using imaginary step size. We propose a generalization of complex-step method to compute a complex valued function and its derivatives up to order n – 1 with approximate error of order n, for any desired integer n. For this, we use a hypercompl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Algorithmic Finance
دوره 4 شماره
صفحات -
تاریخ انتشار 2015