A Closed-Form Expansion for the Conditional Expectations of the Extended CIR Process

2021 ◽  
Author(s):  
Nopporn Thamrongrat ◽  
Sanae Rujivan
Keyword(s):  
Closed Form ◽  
Conditional Expectations ◽  
Cir Process

APPROXIMATING LOCAL VOLATILITY FUNCTIONS OF STOCHASTIC VOLATILITY MODELS: A CLOSED-FORM EXPANSION APPROACH

2015 ◽  
Vol 29 (4) ◽  
pp. 547-563 ◽  
Author(s):  
Yu An ◽  
Chenxu Li
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Numerical Test ◽  
Stochastic Volatility Models ◽  
Marginal Distributions ◽  
Local Volatility ◽  
Volatility Models ◽  
Conditional Expectations

We propose a method for approximating equivalent local volatility functions of stochastic volatility models. Enlightened by the theory of generalized Wiener functionals proposed by Watanabe and Yoshida (1987, 1992), our key technique is to propose a closed-form expansion of conditional expectations involving marginal distributions generated by stochastic differential equations. A numerical test and an illustration of application are provided to demonstrate the efficiency of our approach.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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