We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method re- cently developed in [ 7, 8, 10 ] for short time asymptotic expansions of heat kernels, and obtain a family of general explicit closed form approx- imate solutions for both the pricing kernel and derivative price  . We also perform analytic as well as a numerical error analysis, and compare our results to other known methods.
We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [ 5, 6, 8 ] for short-time asymptotic expansions of heat kernels, and obtain a family of general closed-form approximate solutions for both the pricing kernel and derivative price . A bootstrap scheme allows us to extend our method to large time . We also perform analytic as well as a numerical error analysis, and compare our results to other known methods.
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re- cently
that we have recently
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7, 8, 10
5, 6, 8
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short time
short-time
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explicit closed form approx- imate
closed-form approximate
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. A bootstrap scheme allows us to extend our method to large time