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

Alexander Levin ()
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Alexander Levin: The Dime Bancorp, Inc., Treasury Department, 589 5th Ave, New York, NY 10017, USA

International Journal of Theoretical and Applied Finance (IJTAF), 1998, vol. 01, issue 03, 349-376

Abstract: 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.

Keywords: Linear stochastic systems; statistical moments; state variables; closed-form analytics; Gaussian term structure models; arbitrage-free conditions; JEL classification codes: C490; E430; E490 (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1142/S0219024998000205

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