We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasiński interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Loève expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them useful for nu…
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10 results for “Black-Karasinski”
Improves financial instrument pricing using neural networks.
problem Financial instrument pricing within Black-Karasinski model.
method Enhances path-integral approximation with neural networks.
result Demonstrates superior outcomes for multiple calibrations.
From the Black-Karasinski to the Verhulst model to accommodate the unconventional Fed's policyq-fin.CP
The paper modifies interest rate models to better fit current economic conditions.
problem Current interest rate models do not accurately reflect the Fed's policy and market conditions.
method Proposes a modified Black-Karasinski model (Stochastic Verhulst model) for better economic environment representation.
result The Verhulst model's dynamics are well-suited for current economic conditions and Fed actions.
A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricingq-fin.CP
Improved path integral method for financial derivatives pricing.
problem Analytical intractability of financial derivative pricing models.
method Generalized semi-classical path integral approach to time-dependent Hamiltonians.
result Accuracy and computational efficiency of the path integral approach for derivatives pricing.
Developing a semi-analytical approximation for general default intensity models
problem Accurate and efficient pricing of default intensity models
method Path-integral formalism
result Accurate results for the Black-Karasinski model
We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process x(t) in the terminal measure r(t) = a(t) exp(x(t)). These models include the Black, Derman, Toy and Black, Karasinski models in the terminal measure. We show that such intere…
Path Integral and Asset Pricingq-fin.MF
We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White model, we can apply the same techniques to "less-tractable" models such as the …
Developed unbiased estimators for Heston model with stochastic interest rates.
problem Estimating the Heston model with stochastic interest rates.
method Combined unbiased estimators with the Heston model and developed a semi-exact log-Euler scheme.
result Convergence rate of in the norm for a wide range of models.
Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densitiesq-fin.CP
We show how effective-potential path-integrals methods, stemming on a simple and nice idea originally due to Feynman and successfully employed in Physics for a variety of quantum thermodynamics applications, can be used to develop an accurate and easy-to-compute semi-analytical approximation of transition probabilities…
Develops ML method for solving financial equations.
problem Solving financial equations efficiently and accurately.
method Combines semi-analytical and numerical techniques.
result Significantly faster and more accurate solutions.