DERIVING CLOSED-FORM SOLUTIONS FOR GAUSSIAN PRICING MODELS: A SYSTEMATIC TIME-DOMAIN APPROACH

1999 ◽  
pp. 25-52
Author(s):  
ALEXANDER LEVIN
Keyword(s):  
Closed Form ◽  
Time Domain ◽  
Pricing Models ◽  
Closed Form Solutions

Deriving Closed-Form Solutions for Gaussian Pricing Models: A Systematic Time-Domain Approach

1998 ◽  
Vol 01 (03) ◽  
pp. 349-376 ◽  
Author(s):  
Alexander Levin
Keyword(s):  
Interest Rate ◽  
Differential Equations ◽  
Closed Form ◽  
Term Structure ◽  
Time Domain ◽  
State Variables ◽  
Algebraic Equations ◽  
Pricing Models ◽  
Closed Form Solutions ◽  
Number Of Factors

A systematic time-domain approach is presented to the derivation of closed-form solutions for interest-rate contingent assets. A financial system "asset — interest rate market" is assumed to follow an any-factor system of linear stochastic differential equations and some piece-wise defined algebraic equations for the payoffs. Closed-form solutions are expressed through the first two statistical moments of the state variables that are proven to satisfy a deterministic linear system of ordinary differential equations. A number of examples are given to illustrate the method's effectiveness. With no restrictions on the number of factors, solutions are derived for randomly amortizing loans and deposits; any European-style swaptions, caps, and floors; conversion options; Asian-style options, etc. A two-factor arbitrage-free Gaussian term structure is introduced and analyzed.

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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